Event-Related EEG Time-Frequency Analysis: An Overview of Measures and An Analysis of Early Gamma Band Phase Locking in Schizophrenia

Article (PDF Available)inSchizophrenia Bulletin 34(5):907-26 · October 2008with143 Reads
DOI: 10.1093/schbul/sbn093 · Source: PubMed
An increasing number of schizophrenia studies have been examining electroencephalography (EEG) data using time-frequency analysis, documenting illness-related abnormalities in neuronal oscillations and their synchronization, particularly in the gamma band. In this article, we review common methods of spectral decomposition of EEG, time-frequency analyses, types of measures that separately quantify magnitude and phase information from the EEG, and the influence of parameter choices on the analysis results. We then compare the degree of phase locking (ie, phase-locking factor) of the gamma band (36–50 Hz) response evoked about 50 milliseconds following the presentation of standard tones in 22 healthy controls and 21 medicated patients with schizophrenia. These tones were presented as part of an auditory oddball task performed by subjects while EEG was recorded from their scalps. The results showed prominent gamma band phase locking at frontal electrodes between 20 and 60 milliseconds following tone onset in healthy controls that was significantly reduced in patients with schizophrenia (P = .03). The finding suggests that the early-evoked gamma band response to auditory stimuli is deficiently synchronized in schizophrenia. We discuss the results in terms of pathophysiological mechanisms compromising event-related gamma phase synchrony in schizophrenia and further attempt to reconcile this finding with prior studies that failed to find this effect.
Event-Related EEG Time-Frequency Analysis: An Overview of Measures and An
Analysis of Early Gamma Band Phase Locking in Schizophrenia
Brian J. Roach
and Daniel H. Mathalon
Mental Health Service, Veterans Affairs Medical Center and
Northern California Institute for Research and Education, San
Francisco, CA;
University of California at San Francisco, San
Francisco, CA
An increasing number of schizophrenia studies have been
examining electroencephalography (EEG) data using
time-frequency analysis, documenting illness-related ab-
normalities in neuronal oscillations and their synchroniza-
tion, particularly in the gamma band. In this article, we
review common methods of spectral decomposition of
EEG, time-frequency analyses, types of measures that sep-
arately quantify magnitude and phase information from the
EEG, and the influence of parameter choices on the anal-
ysis results. We then compare the degree of phase locking
(ie, phase-locking factor) of the gamma band (36–50 Hz)
response evoked about 50 milliseconds following the pre-
sentation of standard tones in 22 healthy controls and
21 medicated patients with schizophrenia. These tones
were presented as part of an auditory oddball task per-
formed by subjects while EEG was recorded from their
scalps. The results showed prominent gamma band phase
locking at frontal electrodes between 20 and 60 millisec-
onds following tone onset in healthy controls that was sig-
nificantly reduced in patients with schizophrenia (P 5 .03).
The finding suggests that the early-evoked gamma band re-
sponse to auditory stimuli is deficiently synchronized in
schizophrenia. We discuss the results in terms of patho-
physiological mechanisms compromising event-related
gamma phase synchrony in schizophrenia and further at-
tempt to reconcile this finding with prior studies that failed
to find this effect.
Key words: time-frequency analysis/EEG/power/phase
Electroencephalography (EEG) recordings have long
been used to help identify sensory and cognitive deficits
in individuals with schizophrenia through analyses of
event-related potentials (ERPs). While the examination
of ERPs have provided useful insights into the nature
and timing of neuronal events that subserve sensory, per-
ceptual, and cognitive processes, the EEG data from
which ERPs are derived have received relatively little at-
tention until fairly recently. Aside from the increasing
availability of computer hardware and software for con-
ducting computationally intensive EEG time-frequency
analyses, recent interest in studying event-related EEG
stems from developments in basic and systems neurosci-
ence suggesting that neural oscillations and their
synchronization represent important mechanisms for in-
terneuronal communication and binding of information
that is processed in distributed brain regions. EEG data
comprise the volume-conducted summation of these neu-
ral oscillations and their synchronizations, providing an
opportunity to translate what is known from basic neu-
roscience about the modulation of these oscillations to in
vivo human EEG studies and to gain new insights into the
pathophysiological processes underlying cognitive defi-
cits and clinical symptoms in neuropsychiatric disorders
such as schizophrenia. The interest in studying abnormal
neural synchrony in schizophrenia, as reflected in EEG
data, is also motivated by empirical findings implicating
compromise of mechanisms that subserve neural oscilla-
tions and their synchronization.
The principal approach to studying event-related EEG
oscillations involves decomposition of the EEG signals
into magnitude and phase information for each fre-
quency present in the EEG (so-called ‘‘spectral decompo-
sition’’) and to characterize their changes over time (on
a millisecond time scale) with respect to task events.
Broadly speaking, this approach is referred to as
‘‘time-frequency analysis.’’ Time-frequency analysis
comprises many methods and measures that capture dif-
ferent aspects of EEG magnitude and phase relation-
ships. While some are conceptually and mathematically
related, others are conceptually distinct and complemen-
tary in terms of the information they provide about neu-
ral activity. As the EEG or magnetoencephalography
(MEG) data describing abnormal neurooscillatory activ-
ity in schizophrenia begins to proliferate,
it is important
to maintain an appreciation of the distinctions among the
measures used and their mathematical underpinnings.
To whom correspondence should be addressed; VAMC 116D,
4150 Clement Street, San Francisco, CA 94121; tel: 415-221-4810,
fax: 415-750-6622, e-mail: daniel.mathalon@ucsf.edu.
Schizophrenia Bulletin vol. 34 no. 5 pp. 907–926, 2008
Advance Access publication on August 6, 2008
Ó The Author 2008. Published by Oxford University Press on behalf of the Maryland Psychiatric Research Center. All rights reserved.
For permissions, please email: journals.permissions@oxfordjournals.org.
Accordingly, in the present article, we provide an over-
view of EEG time-frequency analysis, including a discus-
sion of the information it provides relative to traditional
ERP analysis, a review of some of the major analytic
approaches to spectral decomposition of EEG, and an
emphasis on the conceptual differences among the meas-
ures that are commonly associated with the concept of
‘‘neural synchrony.’’ In addition, we present a time-
frequency analysis of EEG data from a simple auditory
oddball task in healthy control subjects to illustrate the
impact of different parameter choices on the resulting
time-frequency decomposition, focusing on the 50-
millisecond poststimulus gamma band response elicited
by standard tones. This is followed by an analysis that
directly compares healthy controls and patients with
schizophrenia on this gamma band response.
Contrasting Traditional ERP Analysis With EEG
Time-Frequency Analysis
A useful departure point for this discussion is to contrast
ERP analysis with modern event-related time-frequency
analysis of EEG. ERPs are systematic positive or nega-
tive voltage deflections evident in the averages of EEG
epochs time-locked to a class of repeated stimulus or
response events. As a result of averaging across a large
number of epochs, the ‘‘random’’ activity in the EEG
cancels out, approaching zero as the number of trials
increases. The waves that survive this averaging process,
known as ERP components, reflect deviations from a pre-
event baseline, and their peak amplitudes and latencies
are thought to index discrete sensory and cognitive pro-
cesses that unfold over time in response to a class of
events. The traditional view of ERPs, sometimes referred
to as the additive ERP model,
assumes that ERP com-
ponents reflect transient bursts of neuronal activity, time
locked to the eliciting event, that arise from one or more
neural generators subserving specific sensory and cogni-
tive operations during information processing. In this
view, ERPs are superimposed on, and imbedded in, on-
going background EEG ‘‘noise’’ with amplitude and
phase distributions that are completely unrelated to
processing of the task events.
This view of ERPs has been challenged on at least
2 counts. First, time-frequency analysis of single-trial
EEG epochs reveals that EEG does not simply reflect
random background noise; rather, there are event-related
changes in the magnitude and phase of EEG oscillations
at specific frequencies that support their role in the
event’s processing.
Second, ERPs themselves may repre-
sent transient phase resetting of ongoing EEG by exper-
imental events, leading to transient time- and phase
locking of frequency-specific oscillations with respect
to an event’s onset on trial after trial.
These phase-
synchronized oscillations survive cross-trial averaging
and are evident as waves in the average ERP. A related
alternative is that ERPs result from event-related partial
phase resetting of ongoing oscillatory activity along with
transient increases in the magnitude of oscillations that
are time-locked to the experimental events.
Makeig et al.
who have been at the forefront of chal-
lenging the traditional additive model of ERPs, have
developed an overarching approach for analysis of
event-related EEG data that they call ‘‘event-related
brain dynamics.’’ This approach emphasizes the spectral
decomposition of single-trial event-related EEG epochs
in order to separately examine event-related changes in
the magnitude and phase of oscillations at specific fre-
quencies. The approach also includes examination of
strategically sorted single trials of EEG in graphical
form (called ERP images) in order to reveal systematic
relationships between event-related amplitude changes
and other characteristics of the trials (eg, reaction times,
phase angles at specific frequencies).
In this way, the
approach provides a more refined and detailed account
of the brain’s event-related neurooscillatory activity,
relative to the more static view provided by traditional
ERP approach. Nonetheless, it is important to note
that despite the richness of the information provided
by time-frequency analyses, they are not able to unambig-
uously differentiate between the alternative models of
ERP generation discussed above, as was elegantly
demonstrated by Yeung et al.
While ERPs and time-frequency analysis of EEG both
provide a view of the serial or sequential events in the
brain’s information processing stream, an increment pro-
vided by time-frequency analysis of EEG, relative to
ERPs, is its potential to view the brain’s parallel process-
ing of information, with oscillations at various frequen-
cies reflecting multiple neural processes co-occurring and
in the service of integrative and dynamically
adaptive information processing. This incremental bene-
fit of EEG time-frequency analysis, relative to ERPs, may
also be manifested in greater sensitivity to the true nature
of the neuropathophysiological processes underlying
schizophrenia. For example, we have recently shown
with EEG data from a simple oddball paradigm that
both phase and power measures are more sensitive to
schizophrenia than traditional ERP components such
as the P300.
The Neuronal Basis of EEG
When a large number of parallel-oriented cortical neu-
rons receive the same repetitive synaptic input and/or
generate the same repetitive sequence of outputs, their
synchronous activity produces extracellular rhythmic
field potentials. These open electrical fields are propa-
gated or ‘‘volume conducted’’ throughout the body,
dropping off with increasing distance from the source.
Accordingly, stronger fields propagate further than
weaker fields. These open rhythmic field potentials can
B. J. Roach & D. H. Mathalon
be recorded as EEG from the scalp if they are strong
enough and have the right orientation (ie, perpendicular
or radially oriented fields with respect to the scalp surface
produce stronger scalp potentials than parallel or tangen-
tially oriented fields).
Thus, if the neural activity
recorded by scalp EEG electrodes were not already syn-
chronized and not already powerful, it would not be
evident at the scalp. Therefore, even before it is spectrally
decomposed, EEG at the scalp is prima facie evidence of
neural synchrony of cortical activity.
Time-frequency analyses of EEG provide additional
information about neural synchrony not apparent in
the ongoing EEG. They can tell us which frequencies
have the most power at specific points in time and space
and how their phase angles synchronize across time and
space. Because EEG rhythms are themselves the product
of synchronized activity among and within neuronal as-
semblies, it is often assumed that changes in EEG power
reflect underlying changes in neuronal synchrony, as
exemplified by the use of the terms ‘‘event-related syn-
chronization’’ or ‘‘event-related desynchronization’’ to
describe event-related changes in EEG power.
ever, it is not actually possible to know whether changes
in EEG power reflect changes in the magnitude of the
rhythmic field potentials or changes in their degree of
synchronization. Nonetheless, using time-frequency
analyses, we can assess changes in power and synchroni-
zation of EEG on a higher order, within or between spa-
tial locations across trials with respect to the onset of task
events. The methods providing these distinctions are
described below.
Modeling EEG in the Time and Frequency Domains
EEG is traditionally modeled as a series of sine waves of
different frequencies overlapping in time and with differ-
ent phase angles with respect to a stimulus. A sine wave
(figure 1A) is defined in terms of its frequency, its mag-
nitude, and its phase. The frequency of a sine wave refers
to the number of complete cycles or oscillations within
a 1-second time period and has the units of Hertz (Hz =
cycles per second). The magnitude refers to the maximum
height of the sine wave’s peaks (or valleys) with respect to
the x-axis. The phase refers to where specific time points
fall within a cycle of the sine wave, ranging from 180° to
180° or, when expressed in radians, ranging from p to p.
These concepts are illustrated in figure 1A for a 10-Hz
sine wave. This oscillation over time describes the signal
in the ‘‘time domain,’’ but the signal can also be repre-
sented in the ‘‘frequency domain’’ by means of a spectral
decomposition that extracts a complex number for one or
more frequencies. In time-frequency decompositions,
a complex number is estimated for each time point in
the time-domain signal, yielding both time and frequency
domain information.
Complex numbers comprise both real and imaginary
components that can be plotted on a 2-dimensional graph
with the x-axis representing the real component (r)
and the y-axis representing the imaginary component
(i) (see figure 1B). If a line is drawn from the origin of
this graph to the complex data point in the x-y (ie, r-i)
plane, 2 characteristics of the sine wave are defined for
the specific time point being evaluated: a magnitude value
and a phase angle (h). The magnitude is equal to the
length of the line (or ‘‘magnitude vector’’) connecting
the origin (0, 0) to the complex data point (r, i) and is
related to the amplitude, which is the square root of
the power, of the sine wave at that time point (The mag-
nitude is obtained by applying the Pythagorean theorem
þ b
= c
), where the real (a) and imaginary (b) values
are 2 legs of a right triangle. The magnitude is the hypot-
enuse (c). In this way, the magnitude for any time, fre-
quency, electrode, and trial can be calculated.). The
phase angle is equal to the angle formed by the magnitude
Fig. 1. Four cycles of a 10 Hz sine wave are plotted on the left (A) with vertical lines marking 4 different time points in the waveform.
Complex numbers decomposed from the 4 time points in the 10 Hz-sine wave are plotted on the right (B) with lines drawn from the
origin to depict magnitude and phase angle.
EEG Time-Frequency Analysis
vector and the x-axis and ranges in value from 180° to
180°. The complex numbers for 4 time points in the sine
wave shown in figure 1A are graphed as vectors depicting
their magnitudes and phase angles in figure 1B.
Just as described for this sine wave example, figure 2
shows that single-trial EEG epochs (figure 2A) can be
spectrally decomposed into complex numbers for each
EEG time point, providing estimates of the magnitude
and phase angles of the oscillations (figure 2C) at
any given frequency. This is accomplished through mul-
tiplication of the EEG with a windowed transformation
function (eg, Morlet wavelet transform, as shown in
figure 2B) centered on a segment of the EEG epoch,
an operation known as ‘‘convolution’’ that can be defined
as the multiplication of one series or ‘‘vector’’ of numbers
by another.
By sliding this windowed function across
the EEG time series one point at a time, a complex num-
ber at the window’s center point is estimated for each time
point in the EEG (figure 2C). When this is done for each
trial, the complex number values for a specific time point
relative to an event’s onset (eg, stimulus onset) are col-
lected across trials (figure 3A). At this point, it is possible
to independently isolate the magnitude or phase informa-
tion derived from these complex numbers. Thus, the
Fig. 2. Individual electroencephalography (EEG) trials (column A) are convolved with a complex Morlet wavelet (column B), containing
both real (solid line) and imaginary (dotted line) wave components, to produce a single, complex time-frequency data point (column C)
consisting of both real (axis, denoted r) and imaginary (y-axis, denoted i) parts. The length of the vector from the origin (0, 0) to the
complex data point (real, imaginary) depicts the signal magnitude, and the angle this vector forms with the x-axis depicts the phase
angle (h), for the 100-milliscond time point. The wavelet’s center time point (hatched vertical line, column B) is overlaid on the 100-millisecond
time point in the EEG epoch (hatched vertical line, column A) to perform this convolution.
B. J. Roach & D. H. Mathalon
magnitude length of the complex number vectors can be
extracted, squared, and averaged (figure 3B), yielding the
mean power for a given frequency at a particular time
point (figure 3D and 3F; see ‘‘Power Across Trials’’ sec-
tion below). Likewise, when each complex data point is
divided by its corresponding magnitude, a new series of
complex data points are generated where the phase angles
are preserved, but the magnitudes are transformed to one
(ie, unit normalized) (figure 3C). These magnitude-
normalized complex values can then be averaged, yield-
ing a measure of the cross-trial phase synchrony for a
particular frequency at a particular time point (figure 3E
and 3G; see ‘‘Phase Synchrony Between Trials’’ section
below). In short, once the distinct magnitude and phase
characteristics of EEG oscillations have been extracted,
they can be quantified in a variety of ways to elucidate
Fig. 3. A. single subject’s complex data points from 5 trials (each shown in different color) for the 40-Hz frequency and 100-millisecond
poststimulus time point, plotted on the real (x) and imaginary (y) axes. B. After removing the phase angles from the complex numbers,
remaining magnitude values are squared and then averaged (black line), providing an estimate of total power at 40 Hz and 100 milliseconds.
C. After removing the magnitude values from the complex numbers, remaining equal length vectors, which retain phase angle information,
are averaged to obtain the phase-locking factor (PLF) (length of vector shown in black). Repeating steps B and C for every trial, time,
and frequency point in the dataset yields a time-frequency matrix of total power values (D) and PLF values (E). More event-related
information is revealed on a different scale when total power values are transformed into dB values by normalizing to a prestimulus
baseline (F). Subtracting a prestimulus baseline from PLF values (G) results in less dramatic changes than those produced when total
power is baseline corrected.
EEG Time-Frequency Analysis
different aspects of dynamic brain function and neural
synchrony. A survey of these quantification approaches
is presented below.
Time-Frequency Transformation Methods
There are many approaches to time-frequency decompo-
sition of EEG data, including the short-term Fourier
transform (STFT),
or discrete
wavelet transforms, Hilbert transform
, and matching
A comprehensive survey of time-frequency de-
composition methods is beyond the scope of this article,
but some basic points about time-frequency transforma-
tions can be made that highlight differences among some
of the methods and also underscore some more general
considerations. Perhaps the most important overarching
principle is that all time-frequency decomposition meth-
ods strike some compromise between temporal resolution
and frequency resolution in resolving the EEG signals. In
general, the larger the time window used to estimate the
complex data for a given time point, the greater the fre-
quency resolution but the poorer the temporal resolution.
This trade-off between precision in the time domain vs
the frequency domain is formalized in the Heisenberg un-
certainty principle,
discussed again in a later section.
Short-Term Fourier Transform
A variant of the fast Fourier transform (FFT), known as
the STFT, or windowed Fourier transform
a Fourier transform within a time window that is moved
along the time series in order to characterize changes in
power and phase of EEG signals over time. Typically,
a fixed duration time window is applied to all frequencies.
The choice of time window constrains the frequency bin
size (ie, frequency resolution), which is uniform across all
frequencies, and also determines the lowest resolvable
frequency. The uniformity of the time window across fre-
quencies is a limitation of this approach because optimal
characterization of temporal changes in high-frequency
signals requires shorter time windows than those needed
to optimally characterize low-frequency signals. A more
flexible approach in which window size varies across
frequencies to optimize temporal resolution of different
frequencies is therefore desirable. Wavelet analysis pro-
vides such an approach.
Continuous Wavelet Transform
Continuous wavelet transforms describe a class of spec-
tral decomposition methods that are conceptually related
to the windowed short-term Fourier analysis described
above. Wavelets are waveforms of limited duration
that have an average value of zero. While any number
of waveforms can be considered a wavelet, to be useful
in modeling biological signals such as EEG, the wave-
forms contained in the wavelet must provide a biologi-
cally plausible fit to the signal being modeled. One
common type of biologically plausible wavelet, the
Morlet wavelet, is a Gaussian-windowed(seebelow) sinusoi-
dal wave segment comprising several cycles (figure 2B). A
family of wavelets, comprising compressed and stretched
versions of the ‘‘mother wavelet’’ to fit each frequency to
be extracted from the EEG, is traditionally constrained
to contain the same number of cycles across frequencies.
As a result, wavelet analyses utilize a different time win-
dow length for each frequency, with the longest windows
applied to the lowest frequencies and the shortest win-
dows applied to the highest frequencies. For example,
assuming a wavelet family contains 6 cycles of a sinusoi-
dal oscillation, the wavelet for the 10-Hz frequency
spans a time window of 600 milliseconds, whereas the
wavelet for the 40 Hz frequency spans a time window
of 150 milliseconds. This variation in the wavelet
from coarser to finer temporal resolution with increasing
frequency is achieved at the cost of diminishing fre-
quency resolution as frequency increases.
The sinusoidal waves contained in a wavelet are typi-
cally shaped by an envelope function (eg, a Gaussian
function), such that the wavelet has its largest magnitude
at the center time point and tapers off toward the edges of
the time window. Wavelets used in spectral decomposi-
tion are complex, containing both real and imaginary
sinusoids (see figure 2B). Each wavelet in a wavelet family
is convolved with the time series of EEG data, sliding the
wavelet time window across the time series, yielding a sep-
arate time series of complex wavelet coefficients for each
frequency. These complex coefficients, containing both
real and imaginary components, are used to derive a mag-
nitude and phase angle (figure 2C).
Contrasting the 2 methods, for high-frequency signals,
it is often assumed that the Morlet wavelet decomposi-
tion provides greater temporal resolution but poorer fre-
quency resolution than the STFT. However, while these
differences may be evident using the typical default set-
tings for each method, parameters can be adjusted across
frequencies in both methods such that they converge on
the same resolution.
Specifically, a modified STFT can
use a time window that decreases linearly as frequency
increases, rather than a fixed time window, as is imple-
mented in EEGLAB software (http://sccn.ucsd.edu/
eeglab/). Similarly, a modified wavelet approach can lin-
early increase the number of cycles used as frequency
increases, rather than using a fixed number of cycles,
as is implemented in Fieldtrip software (http://www.ru.
nl/fcdonders/fieldtrip/). More generally, by exercising
this kind of flexibility in the parameter settings for any
given time-frequency decomposition method, many of
the methods used can be shown to converge on the
same results.
Both EEGLAB and Fieldtrip toolboxes
are open source, free utilities that run within Matlab and
implement many of the measures of synchrony mentioned.
B. J. Roach & D. H. Mathalon
Regardless of the decomposition routine and associ-
ated analysis parameters selected, the output of spectral
decomposition analysis is a complex data point, consist-
ing of real and imaginary parts (figure 2C), for every
point in time and for each frequency, for each trial,
and for each electrode evaluated. These complex data
are the launching point for calculating numerous meas-
ures that appear in the research literature describing the
spectral characteristics of EEG, MEG, or intracranial
electrocorticography data.
Time-Frequency Analyses of EEG
Event-Related Power Across Trials
Power is calculated by squaring the magnitude (or length)
of the vector defined by plotting the complex number
coordinates, obtained from spectral decomposition of
an EEG time series, on the 2-dimensional, real-imaginary,
x-y plane. As such, it reflects the magnitude of the neuro-
electric oscillations at specific frequencies. Approaches to
calculation of power depend on the assumptions made
about the stability of the EEG signal during the time win-
dow of interest, as well as the assumptions about the con-
sistency of the phase angles of the oscillations across
Traditional Frequency Decomposition of EEG Power.
When EEG oscillations are assumed to be stable or
‘‘stationary’’ over time, the FFT is often used to spec-
trally decompose this (usually extended) period of
time-invariant EEG. This is done, for example, with rest-
ing EEG (also known as quantitative EEG
) or with
steady-state paradigms in which a stimulus is continu-
ously repeated at a fixed frequency for an extended
time period, driving the EEG at that specific fre-
The result is a single power spectrum that
captures the average magnitude of oscillations for indi-
vidual frequency bins integrated over the entire time pe-
riod analyzed. The frequency resolution is determined by
the rate at which the EEG time series was digitized and
hence the total number of time points contained in the
time window.
Modern Time-Frequency Decomposition of EEG Power.
When EEG activity cannot be assumed to be stable over
the time period of interest, as when it reflects the unfold-
ing sensory, perceptual, and cognitive stages of informa-
tion processing initiated by an event, the various
methods of time-frequency dec ompo siti on described
above are applied. These methods characterize event-
related changes in power, relative to a pre-event baseline
period, in EEG epochs time locked to task events
such as stimulus presentations or responses. When the
magnitude values are squared for each time-frequency
data point and then averaged over trials the result is
a 2-dimensional matrix containing total power of the
EEG at each frequency and time point. Total power cap-
tures the magnitude of the oscillations irrespective of
of even t-related oscillatory power, evoke d power and
induced power.
Evoked Power. Evoked power refers to event-related
changes in EEG power that are phase-locked with respect
to the event onset across trials. The phase-synchronized
oscillations in the EEG across trials are isolated by first
time domain averaging the event-locked EEG epochs to
derive the ERP. Frequencies that are phase synchronized
with respect to stimulus onset across repeated trials sur-
vive the averaging process and can be seen in the average
ERP. This is not the case for oscillations that are out of
phase with respect to stimulus onset across trials, which
cancel out toward zero during the averaging used to gen-
erate ERPs. Accordingly, evoked power is calculated by
spectral decomposition of an individual’s ERP, squaring
the magnitude values associated with each time and fre-
quency point in the time-frequency matrix. Evoked
power in specific frequencies, such as the gamma band,
have been linked to sensory registration
as well as
to top-down cognitive processing
of stimulus events
and generally occur within the first 200 milliseconds
following stimulus onset.
Induced Power. Induced power refers to event-related
changes in EEG power that are time-locked, but not
phase-locked, with respect to the event onset across trials.
Induced power, also known as ‘‘asynchronous power’’ or
‘‘phase-invariant power,’’ is contained within, and is
sometimes confused with, total power because the latter
is calculated from time-frequency decomposition of single-
trial EEG epochs using only the squared magnitude in-
formation without regard to the phase of the signal.
Similar measures are referred to as event-related desynch-
ronization or synchronization
or time-varying en-
When implemented in EEGLAB,
total power
is referred to as ‘‘event-related spectral perturbation.’’
Although these variously named total power measures
are considered to be insensitive to stimulus-evoked phase
locking, unless evoked power is explicitly removed from
measures of total power, they all actually contain both
phase-locked and non–phase-locked power. This may
be particularly true in the lower frequencies such as
the delta and theta bands, where phase-locked ERPs
may manifest as increases in total power. For example,
noted that the total power peak in the theta
band following auditory stimuli overlaps in both time
and frequency with ERP peaks, supporting the idea
that the early peak in theta power likely contains the en-
ergy from the phase-locked ERP as well as contributions
from trial-to-trial ERP variance. Thus, to isolate pure in-
duced power, evoked power must be removed from the
EEG Time-Frequency Analysis
single trial–based total power estimate. Unfortunately,
there is not agreement in the field as to how, or whether,
this subtraction should be performed.
Interest in induced power stems from early work by
Gray and Singer
involving recordings of multiunit ac-
tivity and local field potentials from cat visual cortex dur-
ing visual stimulus processing. This work showed that
interneuronal synchronization occurred on each trial,
but the latency of this synchronization with respect to
stimulus onset was variable across trials. This set the
stage for subsequent observations that perceptual pro-
cesses, such as the binding of disparate stimulus features
to form a percept,
and cognitive control processes, such
as working memory
or preparation to overcome a pre-
potent response tendency,
are often associated with
phase-asynchronous power changes that nonetheless
occur in approximately the same latency windows across
trials with respect to stimulus onset.
Other Sources of EEG Power. In addition to evoked and
induced power, other potential contributions to total
power come from background and spontaneous EEG
However, if these EEG power signals are
not event related, they are removed in the baseline cor-
rection and trial-averaging processes, respectively. The
comparison of figure 3D and 3F illustrates the impor-
tance of baseline correction to detect stimulus-related
changes in total power.
Event-Related Phase Locking Across Trials
Event-related phase consistency, or phase locking with
respect to an event’s onset, across trials can be calculated
within one electrode, complementing the total power
measure described above. To this end, we use the phase
information shown in figure 3C in which magnitude in-
formation has been unit normalized (ie, transformed
to 1). By averaging these normalized complex numbers
across trials for each time point and frequency bin,
a 2-dimensional matrix of time-frequency values describ-
ing the consistency of the phase angles with respect to an
event’s onset is obtained. Specifically, each value in this
time-frequency matrix is a real number (figure 3E) be-
tween zero and one, with zero reflecting a completely uni-
form random distribution of phase angles between trials
and with one reflecting identical, or perfectly synchro-
nized, phase angles across trials. The measure defined
by these values has been called phase-locking factor
or intertrial (phase) coherence (ITPC),
and it
represents one minus the circular variance of phases
(ie, phase variance
) for each time-frequency point ex-
amined. Event-related phase locking is an important
complement to total power because the complex number
magnitude values on which power calculations depend
have no influence on the phase angles used to calculate
phase locking.
The term ‘‘PLF’’ is unfortunately very similar to one of
the terms commonly used to describe the consistency of
phase differences between 2 electrodes across trials,
‘‘phase-locking value.’’
One of the challenges for the
field is to adopt consistent terminology that more sharply
distinguishes among the various types of synchrony
measures. Traditionally, the term ‘‘coherence’’ was
used in EEG to describe the consistency of the signals be-
tween 2 electrodes. Accordingly, to enhance the clarity of
our presentation, we adopt the term PLF,
rather than
to refer to event-related phase consistency
across trials within a single electrode, reserving the
term ‘‘coherence’’ for various measures of consistency
of the signals recorded from 2 channels (eg, electrodes,
MEG sensors, underlying regional brain sources) across
Event-Related Cross-Channel Coherence Across Trials
Traditional EEG Coherency and Coherence. Because of
the multichannel nature of EEG recordings, based on
arrays of electrodes sampling signals across the scalp,
there is a long tradition of analyzing the consistency
between the EEG from pairs of electrodes in an attempt
to address the brain’s regional connectivity and interre-
gional interaction.
The traditional approach to charac-
terizing the consistency of the EEG signals from 2
channels across trials involves calculating, for each fre-
quency, the linear relationship between the 2 complex sig-
nals derived from spectral decomposition of the EEG, in
a manner analogous to the Pearson product-moment-
correlation coefficient. When this EEG consistency mea-
sure is a complex coefficient, retaining both real and
imaginary components, it is known as ‘‘coherency,’’
whereas when the measure is based on isolating the mag-
nitude information from coherency, it is known as
To enhance insight into the nature of co-
herency and coherence coefficients, we start by recount-
ing the equation for the simple Pearson correlation
coefficient. The Pearson correlation between 2 paired
variables, x and y, can be defined as the standardized
covariance of x and y, with standardization achieved
by dividing the covariance by the product of the SDs
of x and y:
i = 1
Coherency is similarly defined as the standardized
cross-spectrum of complex signals X and Y across trials,
derived from spectral decompositions of the time series
(t) for a given frequency ( f), with standardization
achieved by dividing the cross-spectrum by the square
root of the product of the power spectrum of X and
B. J. Roach & D. H. Mathalon
the power spectrum of Y. The cross-spectrum, analogous
to the covariance in the Pearson correlation equation, is
defined as the expected value (over trials) of the product
of the complex signal X and the complex conjugate (The
complex conjugate of any complex number can be repre-
sented on the real-imaginary, x-y, plane as a reflection [ie,
a mirror flip] across the real axis [eg, the complex conju-
gate of 2 þ 3i = 2–3i].) (denoted by *) of the complex sig-
nal Y:
ð f ; tÞ = +
i = 1
X ð f ; tÞY *ð f ; tÞ
The power spectrum of signal X at a given frequency and
time across trials, analogous to the variance of x in the
Pearson correlation formula, is equivalent to the cross-
spectrum of X with itself and is defined as
ð f ; tÞ = S
f ; t
= +
i = 1
Xð f ; tÞX *
f ; t
Accordingly, coherency is defined as
ð f ; tÞ
i = 1
X ð f ; tÞY *ð f ; tÞ
i = 1
Xð f ; tÞX *ð f ; tÞ
i = 1
Yð f ; tÞY *ð f ; tÞ
Of note, the product of a complex number and its com-
plex conjugate yields a real number (ie, the squared mag-
nitude), whereas the product of 2 different complex
numbers, as is usually the case for the cross-spectrum
of X and Y (S
), yields a complex number. Therefore,
the power spectra are real numbers, but the cross-
spectrum, as well as coherency itself, is a complex num-
ber. As complex numbers, the cross-spectrum or the
coherency can be expressed in terms of their ‘‘cross-
magnitude’’ (ie, square root of the ‘‘cross-power’’) and
their ‘‘relative phase’’ (ie, the average phase difference
between the 2 channels across trials).
When the magnitude of coherency is isolated by taking
its absolute value (The absolute value of a complex num-
ber is equal to its magnitude, with phase information
dropping out.), the resulting coefficient is referred to
as ‘‘coherence,’’ which is a real, rather than a complex,
Unfortunately, terminology in the literature
is not used consistently, so in some descriptions
the term ‘‘coherence’’ is used to refer to the magnitude
of coherency squared. To minimize confusion, we refer
to this quantity as ‘‘magnitude squared coherence’’
(MS coherence), which is defined as the squared absolute
value (ie, magnitude) of the cross-spectrum divided by the
product of the power spectra of X and Y.
MS coherence
ð f ; t Þ = jCoherency
ð f ; tÞj
ðf ; tÞj
f ; t
f ; t
MS coherence is analogous to the squared Pearson cor-
relation, r
, which is the squared covariance divided by
the product of the variance of x and the variance of y.
Just as r
describes the proportion of variance in y
accounted for by a linear transformation of x, the mag-
nitude squared coherence reflects the proportion of var-
iance of channel X at frequency ( f) that can be accounted
for by a constant linear transformation of the complex
spectral coefficients derived from channel Y.
As with
other correlation coefficients, the traditional coherence
measure has a skewed sampling distribution that is typ-
ically normalized using a Fisher z transform.
MS coherence has combined sensitivity to both mag-
nitude and phase synchrony between 2 channels. How-
ever, MS coherence is more influenced by phase
relationships than magnitude relationships in that it
approaches zero when the distribution of the phase differ-
ences between channels is randomly uniform across trials,
whereas consistent phase differences and unrelated cross-
channel magnitudes across trials yields non-zero MS
coherence values. In effect, MS coherence is a measure
of the consistency of phase differences between 2 chan-
nels weighted by the product of their respective magni-
tudes. This has been regarded as a strength of the
traditional coherence measure, in that less weight is given
to phase differences when the magnitudes of the signals
are weak.
Nonetheless, the sensitivity of MS coherence
to both magnitude and phase relationships has also been
regarded as a limitation of the measure because the par-
tial confounding of magnitude and phase makes its inter-
pretation somewhat ambiguous. Moreover, the changes
induced in the magnitude and phase of neurooscillations
by events are dissociable, both in theory
and empiri-
, and are likely subserved by distinct neurobiolog-
ical mechanisms (eg, Pinto et al
). These considerations
have motivated the development of measures that sepa-
rately quantify the consistency of cross-trial phase differ-
ences between 2 channels as well as the correlation of
their magnitudes across trials.
Event-Related Phase Coherence Across Trials
When the magnitudes of the frequency- and time-specific
complex numbers, derived from spectral decomposition
of single-trial EEG epochs, are unit normalized (ie, set
to 1) prior to calculation of coherency, the resulting co-
herency estimate provides a measure of the consistency of
phase differences between the channels across trials, un-
weighted by magnitude. This special case of coherency is
EEG Time-Frequency Analysis
known by different names in the literature, including
‘‘phase coherence,’’
‘‘phase consistency,’’
locking value,’’
‘‘phase synchronization,’’
or simply
‘‘phase synchrony.’’
Because we adopted the conven-
tion of reserving the term ‘‘coherence’’ to refer to between
channel consistency of EEG, we will use the term ‘‘phase
coherence’’ to refer to this measure of consistency of
phase differences between channels.
The magnitude-normalized complex data shown in fig-
ure 3C, which were used to calculate PLF, are also used to
calculate the phase coherence, except that such data are
obtained from 2 recording sites. Next, the difference
between the phase angles of the signals from each elec-
trode is calculated for each time-frequency data point
and for every trial. The single-trial phase differences, rep-
resented by complex numbers, are then averaged across
trials. The absolute value of this complex average yields
the magnitude value that defines the phase coherence.
Phase coherence = 0 indicates completely uniform ran-
dom phase angle differences across trials, whereas phase
coherence = 1 indicates completely consistent phase
angle differences across trials. This pairwise phase coher-
ence is sometimes calculated for every unique electrode-
pair combination available in a given scalp electrode
montage then averaged across all pairs, yielding a single,
2-dimensional phase coherence matrix summarizing the
overall pair-wise phase coherence across the entire elec-
trode montage.
Such an overall phase coherence mea-
sure is sometimes accompanied by a scalp map of the
EEG electrodes with lines connecting all electrode pairs
whose coherence has exceeded some statistical signifi-
cance threshold within a specific frequency band and
time window.
Particularly because there are now studies document-
ing schizophrenia-related deficits in cross-trial consis-
tency of phase differences across recording sites using
phase coherence
and cross-trial consistency of phase
within recording sites using PLF,
it is important to
emphasize the complete dissociability and complemen-
tarity of these 2 measures. High phase coherence suggests
that the difference in phase angles between signals from
sites A and B are consistent from trial to trial, but the
actual phase angles across trials from site A (or site B)
need not show high cross-trial consistency, ie, the PLF
within an electrode site may be as small as zero. The dif-
ference between phase coherence and PLF measures can
be made clear if we consider the location of the hour and
minute hands on a clock to represent the phase angles
(ranging from 180° to 180°) from 2 electrode sites, re-
spectively, for a specific time-frequency data point on
a single trial. Consider 4 unique ‘‘trials’’ represented
by the times 12:15, 3:30, 6:45, and 9:00. The phase angle
difference between the hour and minute hands across
these 4 trials is always 90°. Therefore, the phase coher-
ence across these trials equals one, indicating perfectly
synchronous phase differences between the sites across
trials. However, the PLF for the hour hand and the
PLF for the minute hand is essentially zero because
the phase angles for the individual hands are inconsistent
across trials. Now consider another set of 4 trials repre-
sented by the times 12:14, 12:15, 12:16, and 12:17 on our
hypothetical phase angle ‘‘clock’’. Again, the phase angle
difference between the hour and minute hands across
these new trials is very close to 90°, which would produce
a phase coherence that is very close to one. This set would
also produce a PLF very close to one for the hour hand
(site A) and the minute hand (site B) because their indi-
vidual phases are much more consistent across trials than
in the first example. Thus, phase coherence and PLF are
completely dissociable measures that reflect very differ-
ent types of phase synchrony.
One caution that applies equally to PLF and to phase
coherence is the importance of having similar numbers of
trials contributing to calculations when comparing 2 con-
ditions. PLF and phase coherence are sensitive to the
number of trials included, particularly when the trial
number is small. In the extreme case, the PLF or phase
coherence involving only one trial yields a value = 1, and
experimental conditions containing fewer trials will gen-
erally have higher PLF or phase coherence than condi-
tions containing more trials.
Event-Related Magnitude Correlation Across Trials
Just as phase coherence calculates phase consistency be-
tween channels across trials, there are algorithms to cal-
culate ‘‘pure’’ cross-channel consistency of EEG
magnitudes (or magnitude squared, ie, power) across
trials. Because magnitude values can be obtained from
complex numbers (as described in the total power section
above), one approach used to estimate ‘‘magnitude-only’’
cross-channel consistency is to extract these real magni-
tude values, at a specific frequency and time point in the
event-related epoch, for each electrode pair across all
trials, and then to correlate them using the Pearson
correlation. However, it has been argued that EEG mag-
nitudes can vary slowly (ie, over minutes) across trials
and brain regions as a subject’s state of arousal drifts
over time, attenuating the magnitude correlation across
trials. Accordingly, one alternative measure, the ampli-
tude envelope correlation (AEC),
focuses, for each fre-
quency of interest, on the correlation of the EEG
magnitudes contained within a short time window (ie,
the amplitude envelope) within an epoch. This time win-
dow is moved across the epoch to provide time-specific
correlation values. These correlation values are normal-
ized using Fisher’s r-to-z transformation and then aver-
aged across trials. Unlike MS coherence, AEC values can
be very high even when phase differences are randomly
distributed, and 2 signals have low MS coherence. This
also means that AEC and phase coherence measures
provide independent complementary measures of the
B. J. Roach & D. H. Mathalon
synchrony of magnitude and phase, respectively, between
2 recording sites.
Spatial EEG Coherence in Source Space Vs Sensor Space
EEG signals are transmitted from sources in the brain to
the scalp surface in ways that reflect the geometry of the
cortical folds and the orientation of the dipoles generated
by changes in excitatory and inhibitory postsynaptic
potentials within neuronal assemblies. These electrical
currents are volume conducted through the brain’s tissue
and spatially smeared as they are conducted through the
cerebrospinal fluid, dura mater, skull, and scalp. The re-
sult is that EEG activity seen at one scalp electrode does
not necessarily reflect the activity of the directly under-
lying cortex; rather, it reflects the summated activity
from multiple sources volume conducted across variable
distances to reach the electrode. Just as importantly,
EEG activity from a particular source is transmitted to
multiple electrodes across the scalp, depending on the
orientation and strength of the dipoles comprising the
source activity. Consequently, spatial coherence analyses
between electrode sites can be confounded by shared
activity from a third source, creating essentially spurious
coherence between sites. While this may be less problem-
atic, the further apart electrodes are in space, a source
near the rostral vertex of the cortex with a transverse an-
terior to posterior dipole orientation with respect to the
scalp surface can transmit its signals to both the anterior
and posterior scalp sites without being evident in the elec-
trodes directly over the source itself. Thus, even electro-
des that are relatively far apart can largely reflect activity
from the same underlying source. Related to the ‘‘shared
source’’ problem is the fact that the electrical activity cap-
tured by EEG electrodes reflects voltage differences with
respect to a common reference electrode or set of refer-
ence electrodes. Accordingly, the activity in the reference
electrode can also introduce spurious coherence between
EEG channels.
This is not a problem for MEG
recordings, which provides reference-free measures of
magnetic fields.
To address the problem of single source contamination
of multiple sensors via volume conduction, some have ad-
vocated for methods that reduce the spatial smoothing
and smearing of scalp EEG activity, such as Laplacian
transforms used to generate current source density
(CSD) waveforms.
These CSD waveforms reflect
what is unique to each electrode while minimizing activity
that is broadly distributed across multiple electrodes.
Another approach involves isolating statistically inde-
pendent waveforms from the scalp EEG data using inde-
pendent component analysis, followed by assessment of
MS coherence and/or phase coherence between indepen-
dent components.
Because of the contamination of elec-
trodes or sensors by volume-conducted signals, the
absolute value of phase coherence between sites is prob-
ably less meaningful than a relative comparison of phase
coherence between 2 experimental conditions. However,
even here, caution is required because when a third source
is active in one experimental condition, but not another,
it can create the spurious impression that one condition is
associated with increased coherence between sites, rela-
tive to the second condition.
Distinct from methods that attempt to isolate more lo-
calized or independent activity within the array of scalp
sensors are methods that attempt to isolate the underly-
ing neural sources of scalp-recorded activity. These
source methods examine spatial synchronization of oscil-
lations between brain sources, in ‘‘source space’’ rather
than in ‘‘sensor space.’’
This requires source mod-
eling to solve the so-called inverse problem, modeling the
location and number of sources that give rise to the EEG
distributions across the scalp surface. This problem is ‘‘ill
posed’’ in that multiple source model solutions can give
rise to the same scalp data; the problem cannot be
uniquely solved but requires the investigator to make
assumptions about the number and general location of
sources or to use approaches such as minimum-norm
that allocate EEG activity to thousands of
small sources across the entire cortex and subcortical
brain regions. Phase coherence between source wave-
forms is implemented in software packages such as
Some have even argued that modeling source
activity does not eliminate the possibility that 2 sources
are spuriously coherent because they are contaminated
by activity from a third source.
Accordingly, other
alternatives have been proposed such as examination
of coherence between only the imaginary component
of the complex data estimated for each source
, deriving
a coherency measure that is insensitive to phase-coherent
oscillations involving signals with a zero phase lag be-
tween them. Zero phase lag between phase-coherent sig-
nals is presumed to reflect activity from the same source
because communication between sources takes time,
resulting in a phase lag between the synchronous oscilla-
tions. Of note, studies of spatial phase coherence in
schizophrenia published to date
have been based
on analyses of spatially untransformed EEG data in scalp
sensor space, not source space, and therefore, results are
potentially influenced by spurious phase coherence aris-
ing from contamination of the scalp sensors by activity
from the same underlying source(s).
Magnitude and/or Phase Coupling Between Frequencies
The measures described so far characterize the synchro-
nization of phase and power with respect to an eliciting
event or between 2 spatially segregated signals but
always within the same frequency or frequency band.
In contrast, there is another class of measures, broadly
referred to as cross-frequency ‘‘coupling’’ of EEG power
or phase. Coupling describes synchronous activity between
EEG Time-Frequency Analysis
magnitude and/or phase components of data in 2 differ-
ent frequencies. It has been defined as a cross-frequency
relationship between 2 distinct frequencies in the contin-
uous, recorded signal.
Coupling measures deviate from
all previous measures discussed above because they ex-
amine relationships between different frequencies, time
locked to features of the phase or magnitude of one of
the frequencies. Theta-gamma coupling is described in
detail by Lisman and Buszaki.
Cross-frequency coupling can be estimated for phase-
magnitude, phase-phase, or magnitude-magnitude data
from pairs of frequencies. Beyond studying theta-gamma
coupling, a computational problem quickly arises if there
is no predetermined notion of the coupling type and spe-
cific frequencies to examine. Looking for all 3 types of
coupling between 50 measured frequencies at 32 electrode
sites quickly leads to over 100 000 comparisons for a sin-
gle time sample. Thus, the question of where to look for
coupling is an important consideration.
One MEG study of phase-phase coupling (called ‘‘n:m
phase synchronization’’) restricted the number of com-
parisons by examining relationships between phases
of a base frequency and its harmonic frequencies (ie,
n = 5, m = 10 or any other multiple of 5) only.
study attempted to link the phases of a coordinated mo-
tor behavior (hand tremor in a patient with Parkinson
disease) with the phases of coordinated cortical activity
by designating the frequency of the tremor (n = 5–7
Hz) as the base frequency and then searching for phase
coupling in the MEG data from sensorimotor and pre-
motor areas specifically in the harmonic frequencies of
interest (m = 10–14 Hz).
Another proposed method
to deal with the compu-
tational complexity of coupling analysis is to examine
the coupling between the phase of total power fluctua-
tions of a high-frequency band and the phase of a low
frequency EEG oscillation over the same time window.
This is accomplished by performing an FFT on the
time series of total power values for a higher frequency
band of interest and then designating the peak frequency
from the FFT as the lower frequency of interest to be
extracted over the same time period from the EEG.
The phase of the low frequency EEG oscillation is
then examined for coupling with the phase of the higher
frequency’s power oscillation.
Measures of coupling and procedures to define com-
parison frequencies are certainly not limited to those
mentioned in this section, and further investigations
may help to reduce the frequency selection problem of
coupling analysis.
Baseline Correction of Event-Related Time-Frequency
In all the event-related time-frequency measures de-
scribed above, the question arises as to whether, or
how, to take pre-event baseline activity into consider-
ation. Because our interest is in capturing event-related
changes in brain activity, baseline correction is generally
implemented to adjust post-stimulus values for values
present in the baseline period. Some measures, like
PLF, or phase coherence, may not have significantly
large values in the pre-event baseline period, and there-
fore, baseline correction may negligibly change the
results. When baseline values are large and/or variable
across trials, detection of event-related changes will gen-
erally benefit from baseline correction. However, there
are a variety of approaches to performing baseline cor-
rection and some important considerations in choosing
a baseline when analyzing time-frequency data. It is im-
portant to understand that the choices made in imple-
menting baseline correction can influence the results of
analyses and that differences in the baseline correction
procedure may be one reason for inconsistent results
across studies.
In general, for each frequency in a time-frequency ma-
trix resulting from any of the methods described above,
a baseline period is defined by the average of the values
within a time window preceding the time-locking event.
There are at least 4 common methods for baseline correc-
tion in time-frequency analyses. One method involves
a simple subtraction of baseline values from all the values
in the epoch.
This is the most common approach to
baseline correction of ERP data. A second method
involves dividing the baseline-subtracted values by the
baseline, producing a ‘‘percent change from baseline’’
. A third related method involves dividing the
value at each time point in the epoch is by the baseline
value and then taking the log
transform of this quotient
and multiplying it by 20, yielding values expressed in
units of decibels (dB)
(figure 2F). A fourth method
involves subtracting the baseline from each value then
dividing this difference by the SD of the values contained
in the baseline period, yielding baseline-adjusted z
Methods 2 through 4 have the advantage
of removing overall scale differences between frequencies
and between individuals, rendering them more directly
comparable. Method 4, which expresses the deviations
from baseline in SD units that take into account the var-
iability in the baseline period, may be particularly sensi-
tive to small changes, relative to a simple unstandardized
baseline subtraction method.
Concerning baseline correction, whether by division
(as in the dB scale transform) or by subtraction, it is im-
portant to take into consideration the length of the tem-
poral window used in time-frequency decomposition (eg,
STFT or wavelet window). Because the complex value
estimated at any given center time point within the
time window is influenced by all of the points encom-
passed by the window, half of the time points influencing
the complex value estimate at an event’s onset (time = 0
milliseconds) actually follow its onset, whereas the other
B. J. Roach & D. H. Mathalon
half precede it. Other complex values at time points pre-
ceding an event’s onset are influenced by post-onset data
up until the time point corresponding to one-half the
length of the STFT or wavelet window. In order to min-
imize the temporal smearing of post-onset activity into
the baseline, some
recommend that the baseline period
should end no closer to the event’s onset than one-half the
length of the wavelet or STFT window. However, inas-
much as the sliding temporal windows used in most spec-
tral decomposition methods are weighted by tapered
envelopes (eg, Gaussian, Hanning, Hamming, triangu-
lar), minimizing the influence of data points furthest
from the window’s center time point, studies commonly
extend the baseline period all the way to an event’s onset
without serious consequence.
Perhaps more important than the endpoint of a base-
line period relative to an event’s onset is the proximity of
the baseline’s starting point relative to the beginning of
the EEG epoch. A baseline period should begin in the
epoch after at least one-half the length of the temporal
window used in time-frequency decomposition in order
to avoid ‘‘edge effects’’ (ie, distortions resulting from
convolution of the temporal windowing function with
a data time series that does not extend over the full length
of the temporal window).
A similar consideration
applies in choosing the last post-event time point ana-
lyzed relative to the end of the epoch.
Another important consideration in defining pre-event
baselines is that the duration of the baseline itself should
be influenced by the EEG frequency being analyzed.
Slower frequencies will benefit from longer baselines in
order to capture a reasonably stable period of baseline
activity. Although there are no widely accepted rules
or conventions about this, if one were to adopt the con-
vention that the baseline duration should be at least long
enough to capture a full cycle of the frequency of interest,
then the baseline duration for a 4 Hz frequency, for ex-
ample, would need to be at least 250 milliseconds.
General Hardware Considerations for EEG Time-Frequency
Amplifier and filter settings for EEG data acquisition
must attend to some important considerations in order
to record data suitable for time-frequency analysis.
The EEG signal must be sampled at a fast enough rate
to avoid frequency aliasing of the signal. Aliasing is
the misrepresentation of a high-frequency signal as
a lower frequency signal due to temporal undersampling.
The minimum sampling rate needed to avoid aliasing,
known as the Nyquist rate, is twice as fast as the highest
frequency of interest, although most EEG acquisition
software imposes an even higher standard such as a sam-
pling rate that is 4 times the highest frequency of interest.
In addition, if data are acquired with a bandpass filter
setting, it is important to set the low-pass filter above
the highest frequency of interest so that oscillation fre-
quencies of interest are not removed from the data.
This issue comes up because low-pass filters were often
set to cut-offs between 30 and 50 Hz for traditional
ERP paradigms in order to eliminate 60 Hz (50 Hz)
line noise from the acquired EEG data. While this
worked well for ERP analysis, it usually precluded any
meaningful time-frequency analysis.
Time-Frequency Methods and Measures in Practice
Evoked Gamma Response to Standard Tones From
Auditory Oddball Task
To further support the concepts described above, a time-
frequency analysis of EEG data from an auditory oddball
paradigm is presented below. The purpose of this presen-
tation is 2-fold: First, we conduct a Morlet wavelet anal-
ysis on the data from healthy control subjects in order to
provide a detailed explanation of the wavelet procedure
and to illustrate the impact of different parameter
choices on the resulting spectral decomposition of the
EEG data. Our points are illustrated by focusing on
the well-characterized gamma response
evoked by
auditory stimuli, in this case by the standard tones,
occurring about 50 milliseconds post-stimulus onset.
Second, the PLF values that quantify the phase locking
of this evoked gamma response are compared in healthy
controls and patients with schizophrenia. The few pub-
lished reports that have examined this auditory evoked
gamma response in schizophrenia patients have generally
not found significant abnormalities,
despite evi-
dence that schizophrenia patients show reduced auditory
evoked gamma responses to 40-Hz click trains during
auditory steady-state driving paradigms
less, the dependence of gamma oscillations on neuro-
transmitter systems and circuits implicated in the
pathophysiology of schizophrenia
led us to hypothe-
size that the phase locking of the 50-millisecond post-
stimulus gamma response to auditory stimuli would be
reduced in patients with schizophrenia. Details of the
task, subject samples, ERPs, and time-frequency analyses
from this study are described in more detail elsewhere,
although the analysis of the 50-millisecond evoked audi-
tory gamma response to standard tones was not previ-
ously reported.
Subjects. The healthy control group (HC; n = 22) com-
prised 13 men and 9 women recruited by newspaper ad-
vertisement from the community. The HC had no prior
history of a major Axis I psychiatric disorder, including
alcohol or drug abuse, based on the screening questions
from the Structured Clinical Interview for Diagnostic and
Statistical Manual of Mental Disorders, Fourth Edition
In addition, the HC had no history of psy-
chotic disorders in first-degree relatives. The majority of
EEG Time-Frequency Analysis
the HC group was right-handed (right-handed, n = 19;
left-handed, n = 2; ambidextrous, n = 1).
The schizophrenia patient group (SZ; n = 21) com-
prised 4 women and 17 men recruited from our local out-
patient clinics. All patients met DSM-IV criteria for
schizophrenia (paranoid subtype, n = 18; undifferenti-
ated subtype, n = 3) based on a Structured Clinical Inter-
view for DSM-IV, and all were on stable doses of
antipsychotic medication (atypical agent, n = 17; typical
agent, n = 1; both atypical and typical agent, n = 3). The
majority of the SZ group was right-handed (right-
handed, n = 20; left-handed n = 1). Patients were ex-
cluded if they met criteria for DSM-IV alcohol or drug
abuse within the 30 days prior to study participation.
The groups were matched on age (mean
6 SD:
HC = 37.3
6 12.6 years, SZ = 39.2 6 10.4, difference
not significant) and parental socioeconomic status
6 SD: HC = 34.6 6 15.2, SZ = 38.3 6 19.7, differ-
ence not significant), but the HC group had significantly
(P < .0001) more years of education than the SZ group
(HC = 16.2
6 2.8 years, SZ = 13.3 6 2.1 years). Exclusion
criteria for both groups included any significant history
of head injury, neurological disorders, or other medical
illnesses compromising the central nervous system. The
study was approved by the institutional review boards
of Yale University School of Medicine and the VA Con-
necticut Healthcare system, and all subjects provided
written informed consent prior to being enrolled in the
Task Description. Subjects were presented with a pseu-
dorandom sequence of 210 (P = .70) standard tones (500
Hz, 10-millisecond rise and fall time, 50-millisecond
duration), 45 (P = .15) novel sounds, and 45 (P = .15)
target tones, played at 80-dB SPL via headphones with
an intertrial interval of 1250 milliseconds. Subjects
responded to target tones with a button press.
Preprocessing EEG Data for Time-Frequency Analysis.
EEG data were continuously recorded from 26 sites, ref-
erenced to linked earlobes, although only the data from
electrode Fz are presented for the demonstration of pa-
rameter influences on the wavelet analysis. For the group
comparisons, electrodes F3, Fz, F4, C3, Cz, and C4 were
analyzed. EEG data were digitized at a rate of 1 kHz with
a 0.05- to 100-Hz bandpass filter. No additional filters
were applied to the data offline. EEG associated with
standard tone trials were segmented into epochs spanning
500 milliseconds before the tone onset to 600 milliseconds
after it. Trials where the subject responded within 1200
milliseconds of the standard tone were considered false
alarm errors and discarded.
EEG trial epochs were corrected for eye movements
and blinks based on the vertical and horizontal electro-
oculogram channels using a regression approach.
Epochs were then baseline corrected by subtracting
the 100 to 0 milliseconds prestimulus baseline from
all data points in the epoch. Finally, trials containing arti-
facts exceeding
6100 lV were discarded, and the number
discarded did not differ significantly (P = .23) between
the groups (mean
6 SD trials surviving artifact rejection,
HC = 202
6 14 trials, SZ = 196 6 18 trials).
Time-Frequency Analysis of EEG Epochs. Standard tone
EEG epochs were analyzed with a complex Morlet wave-
let decomposition
using freely distributed FieldTrip
(http://www.ru.nl/fcdonders/fieldtrip/) software in Mat-
lab. This is by no means the only approach to wavelet
analysis or to time-frequency decomposition of EEG.
However, we focus on this method in order to provide
a more detailed example of how different parameter
choices influence the results of time-frequency analyses.
Morlet Wavelet Transform. The Morlet wavelet trans-
form is defined by setting parameters for the general
‘‘mother wavelet,’’ which is then used to generate the
family of wavelets covering the frequencies to be
extracted during the spectral decomposition of EEG
data. The Morlet wavelet is a complex wavelet, compris-
ing real and imaginary sinusoidal oscillations, that is con-
volved with a Gaussian envelope so that the wavelet
magnitude is largest at its center and tapered toward
its edges (see figure 4). The wavelet’s Gaussian distribu-
tion around its center time point has a SD of r
. The
wavelet also has a Gaussian shaped spectral bandwidth
around its center frequency, f
, that has a SD of r
The temporal SD, r
, is inversely proportional to r
(ie, r
; 1/r
), consistent with the Heisenberg uncertainty
principle described earlier that as temporal precision
increases (ie, shorter r
) frequency precision decreases
(ie, larger r
). The exact relationship between them is
defined by the formula r
= 1/(2pr
). Furthermore,
a wavelet is defined by a constant ratio of the center fre-
quency, f
(ie, f
= c), such that r
and r
with the center frequency, f
. This constant, c, is typically
recommended to be greater than 5,
and is often set to
values of 6 or 7, which corresponds to a r
that encom-
passes at least one full sinusoidal cycle for any particular
frequency. In addition to setting the value for this con-
stant, the investigator must also specify a factor, m,
that, when multiplied by the product of r
and the center
frequency, f
, defines the number of cycles to be included
in the mother wavelet (number of cycles = mr
). Often
6 cycles are recommended,
but fewer cycles such as
or 2
have been used to the benefit of temporal res-
olution but at the expense of frequency resolution. Thus,
the temporal window of a Morlet wavelet for any given
frequency is mr
and the spectral bandwidth around any
given center frequency is mr
. Morlet wavelets are usually
normalized to have a total energy equal to 1 for each fre-
quency prior to convolution with the EEG data, allowing
direct comparisons between the magnitude values output
B. J. Roach & D. H. Mathalon
for different frequencies.
In order for the Morlet-
derived magnitude values to be directly related to the
raw voltage values for each frequency, a different normal-
ization factor is required.
Morlet Wavelet Analysis of Standard Tone EEG Data
in Healthy Controls. We applied a Morlet wavelet
analysis to the standard tone EEG epochs to examine
the evoked gamma (;40 Hz) response to the tone in
the 50–100 millisecond post-tone onset time range. In
order to focus on the gamma band and its neighboring
frequencies, we limited the frequency range examined
to 20–60 Hz. We also limited the time period of interest
to a range beginning at 150 milliseconds prestimulus to
200 milliseconds poststimulus. The length of the EEG
epochs ( 500 to 600 milliseconds) encompassed time
points beyond the period of interest in order to provide
the wavelet at the lowest frequency examined (20 Hz) suf-
ficient time samples at the edges of the period of interest
(150 and 200 milliseconds) to calculate the complex
data for the wavelet’s center point via convolution.
Because our focus was on the evoked (ie, phase synchro-
nized) gamma response at 50 milliseconds post-stimulus,
we extracted the phase angles from the complex data to
Fig. 4. Here we show 6 different results from one dataset. Grand average phase-locking factor (PLF) plots for standard tones from an oddball
task based on N 5 22 subjects. PLF values were derived from Morlet wavelet transforms of single-trial electroencephalography epochs
(shown for one subject in center row of graph) based on 6 different combinations of 2 wavelet parameters, c and m. The Morlet wavelet
constant, c, which equals f
, is set to 7 (top panel) or 14 (bottom panel). The multiplication factor, m, which influences the wavelet’s
temporal window size (window size 5 mr
) and spectral bandwidth (spectral bandwidth 5 mr
), is set to 2 (left column), 4 (middle column),
or 6 (right column). Beneath the top row, and above the bottom row, of PLF plots are the Morlet wavelets corresponding to the 40-Hz
frequency for each set of parameter combinations. Note that the number of cycles contained in the wavelet increases as c and m increase,
leading to better frequency resolution but poorer temporal resolution of the evoked gamma band (30–50 Hz) response occurring between 50
and 100 milliseconds following the tone onset.
EEG Time-Frequency Analysis
estimate the cross-trial phase consistency (PLF) for all
frequencies and time points in our time-frequency matrix.
Our purpose in this set of analyses is to demonstrate the
impact of different Morlet wavelet parameter choices on
the resulting PLF values describing the same raw data.
We varied 2 parameters, c and m, repeating the Morlet
transform for 6 different c and m combinations. The con-
stant, c, was set to values of 7 or 14. Based on the formu-
las provided above, the doubling of c doubles the
temporal size of the SD of the Gaussian time envelope,
, that shapes the wavelet. The multiplication factor,
m, which determines the number of these r
SDs encom-
passed by the wavelet, was set to values of 2, 4, or 6. Note
that the number of cycles contained within the mother
wavelet increase as either one of these parameters
The PLF plots resulting from the wavelet analyses us-
ing the 6 c and m parameter combinations are presented
in figure 4, along with the associated Morlet wavelet used
at the 40-Hz frequency bin. Although the plots depict the
group mean PLFs (averaged over 22 subjects), we
also present for purposes of illustration the overlays of
210 EEG trial epochs from one subject in the center of
the figure. As can be seen in the figure, at either value
of the constant, c,asm increases from 2 to 4 to 6, the
wavelet expands in its temporal width, encompassing
additional cycles within the tapering tails of the wavelet’s
Gaussian temporal envelope. Of note, when c = 7, the
value of m closely corresponds to the number of cycles,
such that the wavelet contains 2.23 cycles when m = 2 and
6.68 cycles when m = 6. When c is doubled to 14, the num-
ber of cycles contained in the wavelet at each level of m is
also doubled, leading to 4.46 cycles when m = 2 and 13.37
cycles when m = 6. The PLF plots show that at the small-
est temporal width of the 40-Hz wavelet, the PLF values
in the gamma band are blurred across a broad frequency
range, from 20 to nearly 60 Hz, but with relatively tight
temporal specificity showing essentially 2 temporal
bands, one centered at about 50 milliseconds and one
at about 75 milliseconds (figure 4, top left PLF plot).
This temporal specificity blurs into a single burst of
gamma phase locking spanning between 40 and 80 milli-
seconds, but with a much narrower gamma range cen-
tered on about 42 Hz and spreading between 36 and
48 Hz (top right PLF Plot). For any given value of the
multiplication factor, m, the increase in the constant, c,
from 7 to 14 is associated with a wavelet with a stretched
Gaussian envelope that encompasses twice the number of
cycles and a more slowly declining taper toward the
wavelet’s edges. As a result, doubling the constant broad-
ens the temporal smearing while also tightening the
gamma frequency range showing enhanced PLF, as is
most evident in the bottom right PLF plot. These figures
are consistent with the estimates of the temporal windows
) and spectral bandwidths (mr
) associated with each
of the 6 parameter combinations (see table 1).
Which of these time-frequency decompositions best
capture the ‘‘true’’ nature of the gamma synchronization
evoked by auditory tones? The answer, of course, is none
of them. Each is as ‘‘true’’ as the other but reflects inves-
tigator judgments about the best compromise to strike
between time resolution and frequency resolution. The
fact that gamma PLF cannot be simultaneously pin-
pointed in time and in frequency, but instead is more pre-
cise in one dimension at the expense of precision in
the other dimension, has been related to the well-known
Heisenberg uncertainty principle derived from quantum
Group Comparison of the Phase Locking of the Evoked
Gamma Response. For the group comparison, we
used the PLF values based on a wavelet constant c = 7
and multiplication factor of m = 4. The time-frequency
plots of the PLF values for the HC and SZ groups are
presented in figure 5. The evoked gamma response was
most evident in PLF values of the HC group between
Table 1. Temporal Window Size and Spectral Bandwidth at the 40-Hz Frequency of the Morlet Wavelet Transform Using Different
Wavelet Parameters
40-Hz Frequency
Multiplication Factor
m = 2 m = 4 m = 6
Bandwidth (Hz)
Window (ms)
Bandwidth (Hz)
Window (ms)
Bandwidth (Hz)
Window (ms)
c = 7 mr
= 11.43 mr
= 55.7 mr
= 22.86 mr
= 111.4 mr
= 34.29 mr
= 167.1
c = 14 mr
= 5.71 mr
= 111.4 mr
= 11.43 mr
= 222.8 mr
= 17.14 mr
= 334.2
Note: m refers to a factor by which r
, r
, and (r
) are multiplied to yield the temporal window size, the spectral bandwidth, and the
number of cycles contained in the wavelet, respectively. c refers to the wavelet constant ratio, which equals f
for all center
frequencies in a wavelet family. Thus, c defines the SD of the Gaussian bandwidth, r
, bounding any given center frequency, f
. Because
= 1/2pr
, c also determines the SD of the Gaussian temporal envelope containing the wavelet for any given frequency.
B. J. Roach & D. H. Mathalon
20 and 60 milliseconds in a frequency band of 35–50 Hz,
as shown in figure 5. Accordingly, the PLF values in this
time-frequency window were averaged in each group and
analyzed in a group (HC vs SZ)
3 frontal-central (F3, Fz,
F4 vs C3, Cz, C4)
3 laterality (F3, C3 vs Fz, Cz vs F4, C4)
repeated-measures analysis of variance. The results
showed a significant overall reduction of the gamma
PLF in SZ relative to HC (F
= 5.01, P = .031), as
well as significantly larger gamma PLF in frontal relative
to central electrodes (F
= 29.91, P < .0001) and in
midline relative to off-midline electrodes (F
= 19.93,
P < .0001). There was also a trend for SZ to exhibit
greater reductions than HC in midline relative to lateral
electrodes (F
= 3.07, P = .057, Greenhouse-Geisser
adjusted). No other interaction effects were significant.
These results suggest that chronic medicated patients
with schizophrenia exhibit deficient phase synchroniza-
tion of the frontally distributed gamma oscillation
evoked by an auditory standard tone in an oddball target
detection task. While it is not clear why we observed this
difference when others examining the same auditory
evoked gamma response did not,
we speculate
that task differences may account for the discrepant
results. In particular, our standard tones were imbedded
in a 3-stimulus oddball paradigm involving both infre-
quent task-relevant target tones and infrequent task-
irrelevant novel sounds. The presence of novel distractors
may have heightened our task’s attentional demands, rel-
ative to simpler 2-tone oddball tasks, unmasking the
schizophrenia deficit in the evoked gamma response.
Of note, the auditory gamma response evoked around
50 milliseconds following auditory stimuli has been
shown to be modulated by top-down attentional control
consistent with the idea that the reduced
gamma phase locking in the SZ group in our study
may have arisen from task-related deficits in attentional
state, relative to the HC group. Further work is needed
to clarify under what conditions this early-evoked
gamma response is reduced or intact in patients with
There is growing recognition, from both basic and sys-
tems neuroscience, that the brain organizes and coordi-
nates the information it processes through synchronized
oscillatory activity among and between neuronal assem-
blies. This recognition has breathed new life into the
relatively old technology of EEG recorded from the
scalp. Furthermore, the development of mathematical
algorithms and ready access to computational hardware
and software that easily implements these algorithms has
set the stage for a new era of EEG-based data analyses
that are poised to elucidate the role of frequency-specific
neuronal oscillations and their synchronization in brain
functions ranging from simple sensory processing to
higher order cognition. A natural extension of these
methods to neuropathological conditions provides new
leverage for understanding the pathophysiology of com-
plex neuropsychiatric disorders such as schizophrenia.
This is a timely development in that other aspects of
the clinical neuroscience of schizophrenia increasingly
point to disruptions in connectivity and coordination
among brain regions, processes that depend on synchro-
nized neuronal oscillations. Furthermore, schizophrenia
is associated with compromise of neuronal elements that
subserve these oscillations, such as abnormalities in par-
valbumin-expressing c-aminobutyric acidergic interneur-
in N-methyl-D-aspartate glutamate receptors.
a result, there is a growing literature using EEG (and
MEG) to study abnormal brain dynamics, synchroniza-
tion, and connectivity in schizophrenia. Accordingly, in
order for the schizophrenia neuroscience community to
be able to synthesize the results from these studies, a wider
segment of this community will need to develop a basic
understanding of the methods being used for spectral de-
composition of EEG, the dependence of results on the
parameter settings chosen, and the variation across stud-
ies in how the concept of neural synchrony is addressed.
Toward this end, we have provided a basic overview of
spectral decomposition methods and neural power and
Fig. 5. Group average phase-locking factor (PLF) values between 20
and 60 Hz are shown over the first 200 milliseconds following the
onset (time 5 0) of standard tones presented during the auditory
oddball task. PLF plots are presented for healthy controls (left) and
patients with schizophrenia (right), for frontal (top row) and central
(bottom row) midline electrodes. The dashed line rectangle shows
the time window and frequency band in which the evoked gamma
response was most evident. Values within this window were
averaged for each subject and analyzed in group 3 frontal-central 3
laterality repeated-measures analysis of variance. The phase locking
of this evoked gamma band response was significantly (P 5 .031)
reduced in patients with schizophrenia, relative to healthy controls.
EEG Time-Frequency Analysis
synchrony measures, most of which have already been
implemented in recent event-related EEG studies of
schizophrenia. These methods and measures, and the
names assigned to them, can be a source of confusion
in the research literature. All the measures make use of
the magnitude and/or phase angle information derived
from the complex data extracted from the EEG during
spectral decomposition. Some measures estimate the
magnitude or phase consistency of the EEG within one
channel across trials, whereas others (sometimes with
similar names) estimate the consistency of the magnitude
or phase differences between channels across trials.
Beyond these 2 families of calculations, there are also mea-
trials and within recording sites. Of course, in the realm of
time-frequency analysis, many types of relationships can
be examined beyond those already mentioned, and new
measures are still being created and explored.
This work was supported by the Department of Veterans
Affairs and grants from the National Institute of Mental
Health (MH058262) and the National Alliance for Re-
search in Schizophrenia and Affective Disorders.
The authors thank the two reviewers for their helpful
1. Ford JM, Krystal JH, Mathalon DH. Neural synchrony in
schizophrenia: from networks to new treatments. Schizophr
Bull. 2007;33:848–852.
2. Lewis DA, Hashimoto T, Volk DW. Cortical inhibitory neu-
rons and schizophrenia. Nat Rev Neurosci. 2005;6:312–324.
3. Gonzalez-Burgos G, Lewis DA. GABA neurons and the
mechanisms of network oscillations: implications for under-
standing cortical dysfunction in schizophrenia. Schizophr
Bull. June 26, 2008; doi:10.1093/schbul/sbn070.
4. Lisman J, Buzsaki G. A neural coding scheme formed by the
combined function of gamma and theta oscillations. Schiz-
ophr Bull. June 16, 2008; doi:10.1093/schbul/sbn060.
5. Roopun A, Cunningham MO, Racca C, Alter K, Traub RD,
Whittington MA. Region-specific changes in gamma and
beta2 rhythms in NMDA receptor dysfunction models of
schizophrenia. Schizophr Bull. In press.
6. Uhlhaas PJ, Haenschel C, Nikolic D, Singer W. The role of
oscillations and synchrony in cortical networks and their pu-
tative relevance for the pathophysiology of schizophrenia.
Schizophr Bull. In press.
7. Makeig S, Debener S, Onton J, Delorme A. Mining event-
related brain dynamics. Trends Cogn Sci. 2004;8:204–210.
8. Makeig S, Westerfield M, Jung TP, et al. Dynamic brain
sources of visual evoked responses. Science. 2002;295:
9. Luu P, Tucker DM. Regulating action: alternating activation
of midline frontal and motor cortical networks. Clin Neuro-
physiol. 2001;112:1295–1306.
10. Delorme A, Makeig S. EEGLAB: an open source toolbox for
analysis of single-trial EEG dynamics including independent
component analysis. J Neurosci Methods. 2004;134:9–21.
11. Yeung N, Bogacz R, Holroyd CB, Cohen JD. Detection of
synchronized oscillations in the electroencephalogram: an
evaluation of methods. Psychophysiology. 2004;41:822–832.
12. Yeung N, Bogacz R, Holroyd CB, Nieuwenhuis S, Cohen JD.
Theta phase resetting and the error-related negativity. Psy-
chophysiology. 2007;44:39–49.
13. Ford JM, Roach BJ, Hoffman RS, Mathalon DH. The
dependence of P300 amplitude on gamma synchrony breaks
down in schizophrenia [published online ahead of print
June 25, 2008]. Brain Res. doi:10.1016/j.brainres.2008.06.048.
14. Nunez PL, Srinivasan R. Electric Fields of the Brain: The
Neurophysics of EEG. 2nd ed. Oxford, NY: Oxford Univer-
sity Press; 2006:611.
15. Whittington MA. Can brain rhythms inform on underlying
pathology in schizophrenia? Biol Psychiatry. 2008;63:728–729.
16. Pfurtscheller G, Aranibar A. Event-related cortical desynch-
ronization detected by power measurements of scalp EEG.
Electroencephalogr Clin Neurophysiol. 1977;42:817–826.
17. Pfurtscheller G. Graphical display and statistical evaluation
of event-related desynchronization (ERD). Electroencepha-
logr Clin Neurophysiol . 1977;43:757–760.
18. Bracewell R, Kahn PB. The Fourier transform and its appli-
cations. Am J Phys. 1966;34:712.
19. Gabor D. Theory of Communication. J. Inst. Electr. Engrs.
20. Daubechies I. Ten Lectures on Wavelets. Philadelphia, Pa: So-
ciety for Industrial and Applied Mathematics; 1992:357.
21. Combes JM, Grossmann A, Tchamitchian P. Wavelets: Time-
Frequency Methods and Phase Space—Proceedings of the In-
ternational Conference; December 14–18, 1987; Marseille,
22. Mallat SG. A theory for multiresolution signal decomposi-
tion: the wavelet representation. IEEE Trans Pattern Anal
Mach Intell. 1989;11:674–693.
23. Lyons RG. Understanding Digital Signal Processing. 2nd ed.
Upper Saddle River, NJ: Prentice Hall PTR; 2004:688.
24. Mallat S, Zhang Z. Matching pursuits with time-frequency
dictionairies. IEEE Trans. Signal Proc. 1993;41(12):3397–3415.
25. Folland GB, Sitaram A. The uncertainty principle: a mathe-
matical survey. J Fourier Anal Appl. 1997;3:207–233.
26. Bruns A. Fourier-, hilbert- and wavelet-based signal analysis:
are they really different approaches? J Neurosci Methods.
27. Le Van Quyen M, Foucher J , Lachaux J, et al. Comparison
of hilbert transform and wavelet methods for the analysis of
neuronal sync hrony . J Neuro sci Method s. 2001;111 :83–98.
28. Quiroga Q, Kraskov A, Kreuz T, Grassberger P. Perfor-
mance of different synchronization measures in real data:
a case study on electroencephalographic signals. Physical Re-
view. 2002;65:14.
29. John ER, Prichep LS, Fridman J, Easton P. Neurometrics:
computer-assisted differential diagnosis of brain dysfunc-
tions. Science. 1988;239:162–169.
30. Galambos R, Makeig S, Talmachoff PJ. A 40-hz auditory po-
tential recorded from the human scalp. Proc Natl Acad Sci
USA. 1981;78:2643–2647.
B. J. Roach & D. H. Mathalon
31. Plourde G, Stapells DR, Picton TW. The human auditory
steady-state evoked potentials. Acta Otolaryngol Suppl.
1991;491:153–159; discussion 160.
32. Tallon-Baudry C, Bertrand O, Delpuech C, Pernier J. Stimu-
lus specificity of phase-locked and non-phase-locked 40 hz vi-
sual responses in human. J Neurosci. 1996;16:4240–4249.
33. Fries P, Reynolds J, Rorie A, Desimone R. Modulation of os-
cillatory neuronal synchronization by selective visual atten-
tion. Science. 2001;291:1560–1563.
34. Spencer KM, Niznikiewicz MA, Shenton ME, McCarley
RW. Sensory-evoked gamma oscillations in chronic schizo-
phrenia. Biol Psychiatry. 2007;63:744–747.
35. Debener S, Herrmann CS, Kranczioch C, Gembris D, Engel
AK. Top-down attentional processing enhances auditory
evoked gamma band activity. Neuroreport. 2003;14:683–686.
36. Tiitinen H, Sinkkonen J, Reinikainen K, Alho K, Lavikainen J,
Naatanen R. Selective attention enhances the auditory 40-hz
transient response in humans. Nature. 1993;364:59–60.
37. Sinkkonen J, Tiitinen H, Naatanen R. Gabor filters: an infor-
mative way for analysing event-related brain activity. J Neu-
rosci Methods. 1995;56:99–104.
38. Tallon-Baudry C, Bertrand O, Delpuech C, Permier J. Oscil-
latory gamma-band (30-70 hz) activity induced by a visual
search task in humans. J Neurosci. 1997;17:722–734.
39. Makeig S. Auditory event-related dynamics of the EEG spec-
trum and effects of exposure to tones. Electroencephalogr Clin
Neurophysiol. 1993;86:283–293.
40. David O, Kilner JM, Friston KJ. Mechanisms of evoked and in-
duced responses in MEG/EEG. Neuroimage. 2006;31:1580–1591.
41. Bertrand O, Tallon-Baudry C. Oscillatory gamma activity in
humans: a possible role for object representation. Int J Psy-
chophysiol. 2000;38:211–223.
42. Truccolo WA, Ding M, Knuth KH, Nakamura R, Bressler
SL. Trial-to-trial variability of cortical evoked responses:
implications for the analysis of functional connectivity. Clin
Neurophysiol. 2002;113:206–226.
43. Gray CM, Singer W. Stimulus-specific neuronal oscillations
in orientation columns of cat visual cortex. Proc Natl Acad
Sci USA . 1989;86:1698–1702.
44. Tallon-Baudry C, Bertrand O. Oscillatory gamma activity in
humans and its role in object representation. Trends Cogn Sci.
45. Howard MW, Rizzuto DS, Caplan JB, et al. Gamma oscilla-
tions correlate with working memory load in humans. Cereb
Cortex. 2003;13:1369–1374.
46. Cho RY, Konecky RO, Carter CS. Impairments in frontal
cortical gamma synchrony and cognitive control in schizo-
phrenia. Proc Natl Acad Sci U S A. 2006;103(52):19878–19883.
47. Herrmann CS, Grigutsch M, Busch NA. EEG oscillations
and wavelet analysis. In: Handy TC, ed. Event-Related Poten-
tials: A Methods Handbook. Cambridge, Mass: MIT Press;
48. Fisher NI. Statistical Analysis of Circular Data. Cambridge,
Mass: Cambridge University Press; 1996:295.
49. Lachaux JP, Rodriguez E, Martinerie J, Varela FJ. Measur-
ing phase synchrony in brain signals. Hum Brain Mapp.
50. Nunez PL, Srinivasan R, Westdorp AF, et al. EEG coher-
ency. I: statistics, reference electrode, volume conduction, lap-
lacians, cortical imaging, and interpretation at multiple scales.
Electroencephalogr Clin Neurophysiol. 1997;103:499–515.
51. Nolte G, Bai O, Wheaton L, Mari Z, Vorbach S, Hallett M.
Identifying true brain interaction from EEG data using the
imaginary part of coherency. Clin Neurophysiol. 2004;115:
52. Benignus V. Estimation of the coherence spectrum and its
confidence interval using the fast Fourier transform. IEEE
Trans Audio Electroacoustics . 1969;17:145–150.
53. Pinto DJ, Hartings JA, Brumberg JC, Simons DJ. Cortical
damping: analysis of thalamocortical response transforma-
tions in rodent barrel cortex. Cereb Cortex. 2003;13:33–44.
54. Rodriguez E, George N, Lachaux JP, Martinerie J, Renault
B, Varela FJ. Perception’s shadow: long-distance synchroni-
zation of human brain activity. Nature. 1999;397:430–433.
55. Rosenblum MG, Pikovsky AS, Kurths J. Phase synchroniza-
tion of chaotic oscillators. Phys Rev Lett. 1996;76:1804–1807.
56. Uhlhaas PJ, Linden DE, Singer W, et al. Dysfunctional long-
range coordination of neural activity during gestalt percep-
tion in schizophrenia. J Neurosci . 2006;26:8168–8175.
57. Spencer KM, Nestor PG, Niznikiewicz MA, Salisbury DF,
Shenton ME, McCarley RW. Abnormal neural synchrony
in schizophrenia. J. Neurosci. 2003;23:7407–7411.
58. Spencer KM, Nestor PG, Perlmutter R, et al. Neural syn-
chrony indexes disordered perception and cognition in schizo-
phrenia. Proc Natl Acad Sci USA. 2004;101:17288–17293.
59. Light GA, Hsu JL, Hsieh MH, et al. Gamma band oscillations
reveal neural network cortical coherence dysfunction in schizo-
phrenia patients. Biol Psychiatry. 2006;60:1231–1240.
60. Ford JM, Roach BJ, Faustman WO, Mathalon DH. Synch
before you speak: auditory hallucinations in schizophrenia.
Am J Psychiatry . 2007;164:458–466.
61. Ford JM, Roach BJ, Faustman WO, Mathalon DH. Out-of-
synch and out-of-sorts: dysfunction of motor-sensory commu-
nication in schizophrenia. Biol Psychiatry. 2007;63(8):736–743.
62. Bruns A, Eckhorn R, Jokeit H, Ebner A. Amplitude envelope
correlation detects coupling among incoherent brain signals.
Neuroreport. 2000;11:1509–1514.
63. Fein G, Raz J, Brown FF, Merrin EL. Common reference co-
herence data are confounded by power and phase effects.
Electroencephalogr Clin Neurophysiol. 1988;69:581–584.
64. Guevara R, Velazquez JL, Nenadovic V, Wennberg R,
Senjanovic G, Dominguez LG. Phase synchronization meas-
urements using electroencephalographic recordings: what
can we really say about neuronal synchrony? Neuroinfor-
matics. 2005;3:301–314.
65. Perrin F, Pernier J, Bertrand O, Echallier JF. Spherical
splines for scalp potential and current density mapping. Elec-
troencephalogr Clin Neurophysiol. 1989;72:184–187.
66. Scherg M, Von Cramon D. Two bilateral sources of the late
AEP as identified by a spatio-temporal dipole model. Electro-
encephalogr Clin Neurophysiol. 1985;62:32–44.
67. Sarvas J. Basic mathematical and electromagnetic concepts of
the biomagnetic inverse problem. Phys Med Biol. 1987;32:
68. Pascual-Marqui RD, Michel CM, Lehmann D. Low resolu-
tion electromagnetic tomography: a new method for local-
izing electrical activity in the brain. Int J Psychophysiol.
69. Hoechstetter K, Bornfleth H, Weckesser D, Ille N, Berg P,
Scherg M. BESA source coherence: a new method to study
cortical oscillatory coupling. Brain Topogr. 2004;16:233–238.
70. Hoogenboom N, Schoffelen JM, Oostenveld R, Parkes LM,
Fries P. Localizing human visual gamma-band activity in fre-
quency, time and space. Neuroimage. 2006;29:764–773.
71. Haig AR, Gordon E, De Pascalis V, Meares RA, Bahramali
H, Harris A. Gamma activity in schizophrenia: evidence of
EEG Time-Frequency Analysis
impaired network binding? Clin Neurophysiol. 2000;111:
72. Canolty RT, Edwards E, Dalal SS, et al. High gamma power
is phase-locked to theta oscillations in human neocortex. Sci-
ence. 2006;313:1626–1628.
73. Tass P, Rosenblum M, Weule J, Kurths J. Detection of n: M
phase locking from noisy data: application to magnetoence-
phalography. Phys Rev Lett. 1998;81(15):3291–3294.
74. Cohen MX. Assessing transient cross-frequency coupling in
EEG data. J Neurosci Methods. 2007.
75. Debener S, Ullsperger M, Siegel M, Fiehler K, von Cramon
DY, Engel AK. Trial-by-trial coupling of concurrent
electroencephalogram and functional magnetic resonance im-
aging identifies the dynamics of performance monitoring.
J Neurosci. 2005;25:11730–11737.
76. Gallinat J, Winterer G, Herrmann CS, Senkowski D. Re-
duced oscillatory gamma-band responses in unmedicated
schizophrenic patients indicate impaired frontal network pro-
cessing. Clin Neurophysiol. 2004;115:1863–1874.
77. Brenner CA, Sporns O, Lysaker PH, O’Donnell BF. EEG
synchronization to modulated auditory tones in schizophre-
nia, schizoaffective disorder, and schizotypal personality dis-
order. Am J Psychiatry. 2003;160:2238–2240.
78. Kwon JS, O’Donnell BF, Wallenstein GV, et al. Gamma fre-
quency-range abnormalities to auditory stimulation in schizo-
phrenia. Arch Gen Psychiatry. 1999;56:1001–1005.
79. Spencer KM, Salisbury DF, Shenton ME, McCarley RW.
Gamma-band auditory steady-state responses are impaired
in first episode psychosis [published online ahead of print
April 7, 2008]. Biol Psychiatry. doi:10.1016/j.biopsych.
80. First MB, Spitzer RL, Gibbon M, Williams JB. Structured
clinical interview for DSM-IV axis I disorders. New York,
NY: Biometrics Research Department, New York State
Psychiatric Institute; 2002.
81. Gratton G, Coles MG, Donchin E. A new method for off-line
removal of ocular artifact. Electroencephalogr Clin Neurophy-
siol. 1983;55:468–484.
82. Krystal JH, Karper LP, Seibyl JP, et al. Subanesthetic
effects of the noncompetitive NMDA antagonist, ketamine,
in humans. psychotomimetic, perceptual, cognitive, and
neuroendocrine responses. Arch Gen Psychiatry. 1994;51:
B. J. Roach & D. H. Mathalon
    • "These components could be easily calculated simply by subtracting the classic ERP from the EEG signal of each channel and re-analyzing the new data using the GW6 method or by filtering the EEG signal in several sub-bands. According to Roach and Mathalon [24], we suppose that an inter-neuronal synchronization occurs on each stimulus trial, but the latency with respect to stimulus is variable across trails. In general, it is easy to explain because the great majority of ERP components are in the lower band frequency (0.5–8 Hz). "
    [Show abstract] [Hide abstract] ABSTRACT: Event-related potentials (ERPs) are widely used in brain-computer interface applications and in neuroscience. Normal EEG activity is rich in background noise, and therefore, in order to detect ERPs, it is usually necessary to take the average from multiple trials to reduce the effects of this noise. The noise produced by EEG activity itself is not correlated with the ERP waveform and so, by calculating the average, the noise is decreased by a factor inversely proportional to the square root of N, where N is the number of averaged epochs. This is the easiest strategy currently used to detect ERPs, which is based on calculating the average of all ERP’s waveform, these waveforms being time- and phase-locked. In this paper, a new method called GW6 is proposed, which calculates the ERP using a mathematical method based only on Pearson’s correlation. The result is a graph with the same time resolution as the classical ERP and which shows only positive peaks representing the increase—in consonance with the stimuli—in EEG signal correlation over all channels. This new method is also useful for selectively identifying and highlighting some hidden components of the ERP response that are not phase-locked, and that are usually hidden in the standard and simple method based on the averaging of all the epochs. These hidden components seem to be caused by variations (between each successive stimulus) of the ERP’s inherent phase latency period (jitter), although the same stimulus across all EEG channels produces a reasonably constant phase. For this reason, this new method could be very helpful to investigate these hidden components of the ERP response and to develop applications for scientific and medical purposes. Moreover, this new method is more resistant to EEG artifacts than the standard calculations of the average and could be very useful in research and neurology. The method we are proposing can be directly used in the form of a process written in the well-known Matlab programming language and can be easily and quickly written in any other software language. Electronic supplementary material The online version of this article (doi:10.1186/s13637-016-0043-z) contains supplementary material, which is available to authorized users.
    Full-text · Article · Dec 2016
    • "Accordingly, individual differences in task-related ERP measures, as well as group-wise differences, could be influenced by features of neural oscillatory activity that are inadvertently excluded from conventional ERP analysis. Increased use of time-frequency analysis over the past 10 years [3, 4] , and associated measures of coherence and phase synchrony, further extend the range of features that can be extracted from standard ERP experiments and the number of variables that can potentially be submitted to statistical analysis. Given the many sources on information that can be gleaned through various signal processing approaches, there is increased need for computational frameworks capable of mining large datasets to identify features most relevant to questions asked of EEG data. "
    [Show abstract] [Hide abstract] ABSTRACT: Background: With millisecond-level resolution, electroencephalographic (EEG) recording provides a sensitive tool to assay neural dynamics of human cognition. However, selection of EEG features used to answer experimental questions is typically determined a priori. The utility of machine learning was investigated as a computational framework for extracting the most relevant features from EEG data empirically. Methods: Schizophrenia (SZ; n = 40) and healthy community (HC; n = 12) subjects completed a Sternberg Working Memory Task (SWMT) during EEG recording. EEG was analyzed to extract 5 frequency components (theta1, theta2, alpha, beta, gamma) at 4 processing stages (baseline, encoding, retention, retrieval) and 3 scalp sites (frontal-Fz, central-Cz, occipital-Oz) separately for correctly and incorrectly answered trials. The 1-norm support vector machine (SVM) method was used to build EEG classifiers of SWMT trial accuracy (correct vs. incorrect; Model 1) and diagnosis (HC vs. SZ; Model 2). External validity of SVM models was examined in relation to neuropsychological test performance and diagnostic classification using conventional regression-based analyses. Results: SWMT performance was significantly reduced in SZ (p < .001). Model 1 correctly classified trial accuracy at 84 % in HC, and at 74 % when cross-validated in SZ data. Frontal gamma at encoding and central theta at retention provided highest weightings, accounting for 76 % of variance in SWMT scores and 42 % variance in neuropsychological test performance across samples. Model 2 identified frontal theta at baseline and frontal alpha during retrieval as primary classifiers of diagnosis, providing 87 % classification accuracy as a discriminant function. Conclusions: EEG features derived by SVM are consistent with literature reports of gamma's role in memory encoding, engagement of theta during memory retention, and elevated resting low-frequency activity in schizophrenia. Tests of model performance and cross-validation support the stability and generalizability of results, and utility of SVM as an analytic approach for EEG feature selection.
    Full-text · Article · Dec 2016
    • "Stimulus-locked analysis can dissociate processes involved in attentional and memory integration, while response-locked analysis can dissociated processes involved in accumulation and integration of memory information that will lead to a decision (Werkle-Bergner et al., 2014). Since electrophysiological responses may contain both evoked (phase-locked) and induced (oscillatory but not phase-locked) neural activity, we used trial-based power spectral analysis, which can report on both types of neural responses (Cohen, 2014; Roach and Mathalon, 2008). This time-frequency power analysis allowed us to detect and evaluate EEG synchronization (increase in power compared to baseline) and desynchronization (decrease in power compared to baseline), that represents coupling and uncoupling, respectively, of multiple neuronal populations that are involved in retrieval of object memory (Pfurtscheller and Lopes, 1999). "
    [Show abstract] [Hide abstract] ABSTRACT: (free download: http://authors.elsevier.com/a/1THEecAwkKMHN) Abstract How the brain combines the neural representations of features that comprise an object in order to activate a coherent object memory is poorly understood, especially when the features are presented in different modalities (visual vs. auditory) and domains (verbal vs. nonverbal). We examined this question using three versions of a modified Semantic Object Retrieval Test, where object memory was probed by a feature presented as a written word, a spoken word, or a picture, followed by a second feature always presented as a visual word. Participants indicated whether each feature pair elicited retrieval of the memory of a particular object. Sixteen subjects completed one of the three versions (N = 48 in total) while their EEG were recorded simultaneously. We analyzed EEG data in four separate frequency bands (delta: 1-4 Hz, theta: 4-7 Hz; alpha: 8-12 Hz; beta: 13-19 Hz) using a multivariate data-driven approach. We found that alpha power time-locked to response was modulated by both cross-modality (visual vs. auditory) and cross-domain (verbal vs. nonverbal) probing of semantic object memory. In addition, retrieval trials showed greater changes in all frequency bands compared to non-retrieval trials across all stimulus types in both response-locked and stimulus-locked analyses, suggesting dissociable neural subcomponents involved in binding object features to retrieve a memory. We conclude that these findings support both modality/domain-dependent and modality/domain-independent mechanisms during semantic object memory retrieval. (free download: http://authors.elsevier.com/a/1THEecAwkKMHN)
    Article · Jun 2016
Show more

    Recommended publications

    Discover more