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

**Abstract**

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

2

and Daniel H. Mathalon

1–3

2

Mental Health Service, Veterans Affairs Medical Center and

Northern California Institute for Research and Education, San

Francisco, CA;

3

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.

1–6

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,

6

it is important

to maintain an appreciation of the distinctions among the

measures used and their mathematical underpinnings.

1

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

doi:10.1093/schbul/sbn093

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.

907

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,

7

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.

7

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.

7,8

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.

7,9

Makeig et al.

7

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).

10

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.

11,12

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

interacting

4

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.

13

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

908

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).

14,15

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.

16,17

How-

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

(a

2

þ b

2

= c

2

), 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.

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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.

18

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.

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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.

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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),

19

continuous

20,21

or discrete

22

wavelet transforms, Hilbert transform

23

, and matching

pursuits.

24

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,

25

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

19

performs

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.

26

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.

26–28

Both EEGLAB and Fieldtrip toolboxes

are open source, free utilities that run within Matlab and

implement many of the measures of synchrony mentioned.

912

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

trials.

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

29

) 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-

quency.

30,31

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

theirphaseangles.Assuch,itcomprises2majorsources

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

32–34

as well as

to top-down cognitive processing

35,36

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.

37

Similar measures are referred to as event-related desynch-

ronization or synchronization

16,17

or time-varying en-

ergy.

38

When implemented in EEGLAB,

10

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,

Makeig

39

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

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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.

39–42

Interest in induced power stems from early work by

Gray and Singer

43

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,

44

and cognitive control processes, such

as working memory

45

or preparation to overcome a pre-

potent response tendency,

46

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

power.

40,44,47

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

(PLF)

38

or intertrial (phase) coherence (ITPC),

10

and it

represents one minus the circular variance of phases

(ie, phase variance

48

) 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.’’

49

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,

38

rather than

‘‘ITPC,’’

10

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

trials.

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.

50

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

‘‘coherence.’’

51

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:

r

xy

=

+

N

i = 1

ðx

i

xÞðy

i

yÞ

N

r

x

r

y

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

914

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:

S

XY

ð f ; tÞ = +

N

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

P

X

ð f ; tÞ = S

XX

f ; t

= +

N

i = 1

Xð f ; tÞX *

f ; t

Accordingly, coherency is defined as

Coherency

xy

ð f ; tÞ

=

+

N

i = 1

X ð f ; tÞY *ð f ; tÞ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

+

N

i = 1

Xð f ; tÞX *ð f ; tÞ

+

N

i = 1

Yð f ; tÞY *ð f ; tÞ

s

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

XY

), 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,

number.

51

Unfortunately, terminology in the literature

is not used consistently, so in some descriptions

10,14

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

xy

ð f ; t Þ = jCoherency

xy

ð f ; tÞj

2

=

j

S

XY

ðf ; tÞj

2

P

X

ð

f ; t

Þ

P

Y

ð

f ; t

Þ

MS coherence is analogous to the squared Pearson cor-

relation, r

2

, which is the squared covariance divided by

the product of the variance of x and the variance of y.

Just as r

2

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.

14

As with

other correlation coefficients, the traditional coherence

measure has a skewed sampling distribution that is typ-

ically normalized using a Fisher z transform.

52

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.

14

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

7

and empiri-

cally

8

, and are likely subserved by distinct neurobiolog-

ical mechanisms (eg, Pinto et al

53

). 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

915

EEG Time-Frequency Analysis

known by different names in the literature, including

‘‘phase coherence,’’

14,51

‘‘phase consistency,’’

26

‘‘phase-

locking value,’’

49,54

‘‘phase synchronization,’’

55

or simply

‘‘phase synchrony.’’

27

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.

56

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

56,57

and cross-trial consistency of phase

within recording sites using PLF,

13,58–61

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),

62

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

916

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.

14,63,64

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.

50,65

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.

10

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.’’

50,66,67

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

methods

68

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

BESA.

69,70

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.

51

Accordingly, other

alternatives have been proposed such as examination

of coherence between only the imaginary component

of the complex data estimated for each source

51

, 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

57,71

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

917

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.

72

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.

4

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.

72

The

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

74

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

Measures

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.

58

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’’

value

70

. 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

10

transform of this quotient

and multiplying it by 20, yielding values expressed in

units of decibels (dB)

10

(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

scores.

27,49,54,72

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

918

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

47

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).

47,75

A similar consideration

applies in choosing the last post-event time point ana-

lyzed relative to the end of the epoch.

47

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

Studies

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

30,34

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,

34,71,76

despite evi-

dence that schizophrenia patients show reduced auditory

evoked gamma responses to 40-Hz click trains during

auditory steady-state driving paradigms

58,77–79

Nonethe-

less, the dependence of gamma oscillations on neuro-

transmitter systems and circuits implicated in the

pathophysiology of schizophrenia

3–6

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,

13

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

(DSM-IV).

80

In addition, the HC had no history of psy-

chotic disorders in first-degree relatives. The majority of

919

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

(mean

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

study.

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.

81

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

38,41

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

t

. The

wavelet also has a Gaussian shaped spectral bandwidth

around its center frequency, f

0

, that has a SD of r

f

.

The temporal SD, r

t

, is inversely proportional to r

f

(ie, r

t

; 1/r

f

), consistent with the Heisenberg uncertainty

principle described earlier that as temporal precision

increases (ie, shorter r

t

) frequency precision decreases

(ie, larger r

f

). The exact relationship between them is

defined by the formula r

t

= 1/(2pr

f

). Furthermore,

a wavelet is defined by a constant ratio of the center fre-

quency, f

0

,tor

f

(ie, f

0

/r

f

= c), such that r

f

and r

t

vary

with the center frequency, f

0

. This constant, c, is typically

recommended to be greater than 5,

21

and is often set to

values of 6 or 7, which corresponds to a r

t

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

t

and the center

frequency, f

0

, defines the number of cycles to be included

in the mother wavelet (number of cycles = mr

t

f

0

). Often

6 cycles are recommended,

47

but fewer cycles such as

4

13,61

or 2

38

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

t,

and the spectral bandwidth around any

given center frequency is mr

f

. 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

920

B. J. Roach & D. H. Mathalon

for different frequencies.

38,47

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.

47

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

0

/r

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

t

) and spectral bandwidth (spectral bandwidth 5 mr

f

), 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.

921

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,

r

t

, that shapes the wavelet. The multiplication factor,

m, which determines the number of these r

t

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

increase.

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

(mr

t

) and spectral bandwidths (mr

f

) 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

physics.

25

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

Spectral

Bandwidth (Hz)

Temporal

Window (ms)

Spectral

Bandwidth (Hz)

Temporal

Window (ms)

Spectral

Bandwidth (Hz)

Temporal

Window (ms)

c = 7 mr

f

= 11.43 mr

t

= 55.7 mr

f

= 22.86 mr

t

= 111.4 mr

f

= 34.29 mr

t

= 167.1

c = 14 mr

f

= 5.71 mr

t

= 111.4 mr

f

= 11.43 mr

t

= 222.8 mr

f

= 17.14 mr

t

= 334.2

Note: m refers to a factor by which r

t

, r

f

, and (r

t

f

0

) 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

0

/r

f

for all center

frequencies in a wavelet family. Thus, c defines the SD of the Gaussian bandwidth, r

f

, bounding any given center frequency, f

0

. Because

r

t

= 1/2pr

f

, c also determines the SD of the Gaussian temporal envelope containing the wavelet for any given frequency.

922

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

1,41

= 5.01, P = .031), as

well as significantly larger gamma PLF in frontal relative

to central electrodes (F

1,41

= 29.91, P < .0001) and in

midline relative to off-midline electrodes (F

1,41

= 19.93,

P < .0001). There was also a trend for SZ to exhibit

greater reductions than HC in midline relative to lateral

electrodes (F

1,41

= 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,

34,71,76

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

processes,

35,36

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

schizophrenia.

Conclusion

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-

ons

2

in N-methyl-D-aspartate glutamate receptors.

82

As

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.

923

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-

suresthatexaminethecouplingbetweenfrequencies,within

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.

Funding

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.

Acknowledgments

The authors thank the two reviewers for their helpful

comments.

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- CitationsCitations199
- ReferencesReferences113

- "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.- "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.- "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)

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