Time and frequency weightings and the assessment of sound exposure

Abstract

Since the development of averaging/integrating sound level meters and frequency weighting networks in the 1950's, measurement of the physical characteristics of sound has not changed a great deal. Advances have occurred in how the measured values are used (day-night averages, limit and action values, etc.), but in essence the measurement principle remains the same. There are advantages of having a well established, world-wide methodology, such as: uniformity of measurements, wide variety of measurement equipment, experience based knowledge, etc. The problem arises from the ambiguity of the measure, where a wide variety of sound characteristics that have different effects on the hearing lead to the same result. Today, the technological advances permit precise measurements of the time and frequency characteristics of sound, which can be stored and analyzed to give a better description of the exposure. This information is being used to investigate metrics that can differentiate temporal characteristics (impulsive, fluctuating) as well as frequency characteristics (narrow-band or tonal dominance) of sound exposures. This presentation gives an overview of the existing sound measurement and analysis methods, that can provide a better representation of the effects of sound exposures on the hearing system.

Full text

TIME AND FREQUENCY WEIGHTINGS AND THE
ASSESSMENT OF SOUND EXPOSURE
Rodigo Ordoñez1, Miguel Angel Aranda de Toro, and Dorte Hammershøi1
Affiliation: 1Acoustics, Institute of Electronic Systems, Aalborg University
e-mail: rop@es.aau.dk; dh@es.aau.dk
Abstract
Since the development of averaging/integrating sound level meters and frequency weighting
networks in the 1950’s, measurement of the physical characteristics of sound has not changed
a great deal. Advances have occurred in how the measured values are used (day-night
averages, limit and action values, etc.), but in essence the measurement principle remains
the same. There are advantages of having a well established, world-wide methodology, such
as: uniformity of measurements, wide variety of measurement equipment, experience based
knowledge, etc. The problem arises from the ambiguity of the measure, where a wide variety
of sound characteristics that have different effects on the hearing lead to the same result.
Today, the technological advances permit precise measurements of the time and frequency
characteristics of sound, which can be stored and analyzed to give a better description of the
exposure. This information is being used to investigate metrics that can differentiate temporal
characteristics (impulsive, fluctuating) as well as frequency characteristics (narrow-band or
tonal dominance) of sound exposures.
This presentation gives an overview of the existing sound measurement and analysis meth-
ods, that can provide a better representation of the effects of sound exposures on the hearing
system.
Keywords: Sound exposure, Equivalent levels, Time and frequency weightings
1 Introduction
Currently the assessment of sound exposure to determine risk of hearing damage, is done
world-wide through the Equivalent Energy Hypothesis (EEH). The sound exposure energy is
obtained using the equivalent continuous sound pressure levels and the A-weighting curve,
denoted LAeq,T [1]. The working assumption of the EEH is that hearing damage is a monotonic
function of the amount of A-weighted energy that reaches the cochlea throughout its life time.
This approach yields a single number that represents the energy of the signal integrated over
time. Sounds with large differences in peak sound pressure level and time distribution, as
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well as different frequency content can have the same energy, and therefore, lead to the
same exposure rating. Figure 1 shows a segment of 10 seconds of a broad-band continuous
signal (shown in black and denoted as cont in the figure), and the same signal combined
with a series of impact sounds (shown in grey and denoted imp+cont). Both signals have
an equivalent continuous A-weighted sound pressure level of LAeq,3min = 90 [dB], but differ
considerably in their peak levels (here all dB values are given with respect to the reference
effective pressure p0= 20 [µP a]).
0 1 2 3 4 5 6 7 8 9 10
−12
−8
−4
0
4
8
12
Time [s]
Amplitude [Pa]
cont
imp+cont
Figure 1: Sound pressure as a function of time, for a broad-band con-
tinuous signal (in black), and for the same signal mixed with impact
sounds at a repetition rate of 0.5 impacts/seconds with a maximum
peak level 117.2 [dB](in grey). Both signals have an LAeq,3min =
90 [dB].
Additionally, in complex sounds the temporal distribution of different frequency components
may not necessarily be the same. This means that some frequencies may exhibit impulsive
characteristics, while others are constant over time. By using broad-band time averaged
ratings, any information about band-limited temporal characteristics is lost.
Scientific evidence has shown that time and frequency characteristics of sound exposures
are determinant in the effects produced both in animal and human cochleas [e.g. 2, 3, 4].
Therefore, to improve the measurement of sound exposures for the assessment of hearing
damage, the entire measurement and analysis procedure should be revised (from the acous-
tical transducer to hazard rating). The aim of this paper is to discuss new strategies for the
assessment of time and frequency characteristics of sound exposures.
2 Sound exposure and the Equal Energy Hypothesis
Assessment of sound exposure according to the EEH is described in ISO 1999 [1] and S3.44
[5]. These standards define the equivalent continuous sound pressure level as:
Leq,T = 10 ·log10 1
TZT
0
pA(t)2
p2
0
dt,(1)
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which represents the energy of a broad-band time averaged signal. In Equation 1, Tis the
averaging time, pA(t)is the instantaneous A-weighted sound pressure, and p0is the reference
effective pressure (20 [µP a]). Noise ratings based on this calculation have the following time
and frequency characteristics.
2.1 Frequency weighting
For noise exposure assessment, the instantaneous sound pressure detected by a microphone
is frequency weighted using the A-weighting curve described in IEC 61672-1 [6]. The idea
of the frequency weighting is to give a greater emphasis to the frequency content that is
considered more harmful.
The A-weighting curve was devised to approximate the mirror of the 40-phon equal loudness
level curve (see ISO 226 [7]). The A-weighting assigns a weight to each frequency that is
related to the sensitivity of the ear at that frequency. These weights try to approximate the
response of the human hearing system giving greater importance to the frequency content
of greater sensitivity. Once the sound pressure is frequency weighted it is labeled with the
corresponding weighting index (i.e. pA(t)A-weighted sound pressure).
According to the current risk assessment methods, A-weighted sound pressure signals are
believed to compensate for the frequency sensitivity of the human auditory system. This
implies the following assumption: Sounds of equal loudness pose the same risk to the hearing
system. To our knowledge this hypothesis has not been thoroughly tested and there is no
obvious reason for loudness perception and risk of hearing damage to be same.
The main advantage of using A- (or C-weighting) for measurements of sound exposures is
that the resulting measurement will be band limited, no matter what measurement equipment
is used, provided that the weighting filters comply with the standardized responses. This facil-
itates comparisons of measurements obtained by different people, with different equipment.
It also facilitates inspection of compliance with limit values.
2.2 Time weighting
For the characterization of the temporal variations in magnitude of a sound pressure, the
effective value is used. This is because it has a close relationship to the intensity, power
and energy. The effective sound pressure is taken as the root mean squared value over a
specified averaging time. This corresponds to the term in parenthesis of Equation 1, without
the reference pressure p0.
Time averaged values give a good representation of stationary signals no matter what time
constant is used for the integration. For non-stationary sounds an averaging period must be
chosen so that the time variations of the signal are well represented. If a fast varying signal is
averaged during a long time the fast variations will average out. Figure 2 shows the result of
calculating the LAeq,T (Equation 1) for a 3 seconds segment of the impulsive sound presented
in Figure 1 (in grey) using different averaging times. The time history of the pressure has
been sampled at 48 [kHz].
In order to be able to detect the time characteristics of the signal the shortest integration time
is required. Long integration times (>1 [s]) will yield values that are closer to the total energy
of the signal and do not represent the instantaneous pressure values used for the calculation.
The implementation of these averaging methods in sound level meters limits the assessment
of maximum sound pressure values, rise time and decay time for impulsive sounds, important
parameters for risk evaluation.
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0 0.5 1 1.5 2 2.5 3
80
85
90
95
100
105
110
115
120
Time [seconds]
Sound Pressure Level [dB re. 20 µPa]
Sound Pressure Level [dB re. 20 µPa]
LAeq,1/fs; T = 20.833 µs
LAeq,I; T = 35 ms
LAeq,F; T = 125 ms
LAeq,S; T = 1 s
Figure 2: Examples of different averaging times in the calculation of
the sound pressure level of the same impulsive signal from Figure 1. In
light grey is the LAeq,1/fs calculated using each sample from the digital
signal (sampling frequency of 48 [kHz]). The bars graphs correspond
to the standardized time weightings: Impulse (LAeq,I ), Fast (LAeq,F ),
and Slow (LAeq,S ).
The standard averaging times stated in IEC 61672-1 [6] are: Fast (F) 125 [ms]and Slow (S)
1 [s]. Previously the standard suggested an Impulse (I) detector with an averaging time of
35 [ms](currently not recommended by the standard). These standardized time constants are
too long to represent the fast time variations of sound signals, especially impulsive sounds. An
averaging time of 125 [ms]corresponds to sampling a continuous time signal with a sampling
frequency of 8 [Hz], that is, 8 samples per second.
3 Human sound exposure
Intense sound exposures cause changes in the hearing system. The severity of the sound
exposure will determine the extent and type of damage to the hearing system. In general, it
is accepted that high intensity exposures (typical of impulsive noise) with peak values in ex-
cess of 140 [dB], can generate immediate irreversible mechanical damage to the cochlea, the
middle ear or the tympanic membrane. On the other hand, prolonged lower level exposures,
produce metabolic changes of the inner ear particularly to the hair cells and their supporting
structures. It is believed that the metabolic changes of the inner ear are the main responsible
mechanism of noise induced hearing loss from occupational noise exposure, where sounds
rarely exceed peak levels of 140 [dB]and are a mixture of continuous and impulsive compo-
nents of diverse frequency content.
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In order have a proper assessment of the potential risk posed by a given exposure, the fol-
lowing aspects must be considered:
•Physical characteristics of the sound signal: time course of pressure and frequency
content.
•The effect of the listener on the sound filed: changes in the sound pressure from the
free-field (or diffuse-field) to the sound pressure present at the ear-drum.
•The influence of non-linear components in the transmission of energy from the ear-drum
to the displacement of the basilar membrane.
3.1 Physical characteristics
The main requirement for an analysis of a sound wave is detailed time histories of the sound
pressure. This can be obtained by recording the exposure waveform as a digital signal. Digital
signals have an inherit time average equal to the sampling period. Any fluctuations of pressure
within a sampling period will be represented by a single value. A higher sampling frequency
will provide greater detail of the time history improving the estimation of peak values and
temporal characteristics of impulses (i.e. rise and decay time).
With respect to frequency resolution, research of auditory filters and equivalent rectangular
bandwidth (ERB) suggests that the frequency selectivity of the auditory system is a function
of the excitation frequency. Above 1 [kH z]the auditory filter bandwidths are approximately
10 to 17% of the center frequency [8]. This corresponds approximately to 1
6–octave bands.
For lower frequencies the auditory filter bandwidth increases to more that 1
3–octaves below
200 [Hz]. This does not give a clear picture as to what type of frequency analysis is bet-
ter suited for risk assessment from sound exposures. Nevertheless, the hearings’ upper fre-
quency range (above 1 [kHz]) has ERBs proportional to frequency, similar to fractional octave
filters, suggesting that a variable fractional-octave-band analysis (like the Bark scale used in
loudness calculations) could be suitable for the assessment of the frequency characteristics
of a sound exposure.
Another important frequency characteristic is the presence of tonal components. Changes in
DPOAEs after exposure to a continuous broad-band noise and a 2 [kHz]tone presented with
the same energy, resulted in similar maximum DPOAE-shift of approximately 5 [dB]immedi-
ately after the exposure, but in a different frequency range [manuscripts in preparation 9, 10].
In addition, the tonal exposure needed more time to recover than the continuous exposure.
The difference in the frequency specificity can be attributed to the different spectral content
of the stimuli. The difference in the recovery period can be interpreted in two ways: (1) the
longer recovery period of the tonal exposure could be due to differences in the presentation
method:–monaural vs. binaural– as reported by Hirsh [11]; or (2) if we assume that there
are no differences induced by the presentation method, the longer recovery period could be
a sign of a higher auditory fatigue. Therefore, tonal exposures might be more hazardous for
our hearing than continuous exposures with equal energy. One possible explanation is that
for tonal exposures the energy is concentrated in a narrow region of the basilar membrane,
which may pose a higher fatigue to the auditory system.
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3.2 Head related transfer-functions
The filtering properties of the human head, ears and torso are described by the Head Re-
lated Transfer Functions (HRTFs), which are dependent on direction of sound incidence and
the physical characteristics of the ear, head and torso. HRTFs are defined as a complex
pressure ratio that represent the change in the sound field introduced by the presence of a
listener [12]. For any particular sound incidence angle and head, there is a set of two HRTFs,
each describing the sound transmission to one of the ears.
ISO 11904-1 [13] has tabulated values for human free-field and diffuse-field frequency re-
sponses, which are the third-octave-band magnitude response of the free-field frontal inci-
dence HRTFs and diffuse-field HRTFs respectively. These values are given for three different
measurement positions inside the ear canal: ear-drum, open ear canal entrance and blocked
ear canal entrance. There is a considerable difference between a sound recorded with a
conventional (flat frequency response) measurement microphone and the signal present in
the ear canal of a listener exposed to the same sound field. This difference, described by the
HRTFs, is an important aspect of the sensitivity of the human hearing affecting the energy
arriving at the inner ear.
Another important aspect is the directional dependency of the HRTFs. Sounds arriving at the
listener from different angles will be weighted differently. The practical implications is that
the relative position and direction of the listener and sound source will change the frequency
content of the sound exposure.
3.3 Effective Quiet
Effective Quiet (EQ) levels can be defined as: The level that just fails to produce temporal
threshold shifts (TTS) that increase with time or retard its recovery [14, 15]. The experiments
by Ward et al. [15], reported EQ levels after exposures to octave bands of noise are: 77 [dB]
at 0.25 [kHz],76 [dB]at 0.5 [kHz],69 [dB]at 1 [kH z],68 [dB]at 2 [kH z]and 65 [dB]at 4 [kH z].
For a broad-band noise the EQ would correspond to an A-weighted level of 76 [dB]. These
studies provide useful data to determine safe exposure levels.
Exposure conditions with levels below the EQ levels should be considered innocuous. That
is, only the frequency components of a sound exposure that have levels above the EQ levels
will present a risk for the hearing. Zhu et al. [16] compared a series of noise metrics with
permanent threshold shifts (PTS) data from animal studies. One of the proposed metrics
that showed some of the greatest overall correlations with the observed PTS was a so-called
modified equivalent SPL, in which the instantaneous 1
3–octave pressure time history was set
to zero if it was below an arbitrary threshold value of 80 dB SPL, or set to the difference
between the measured pressure value and the threshold value. This suggests that correcting
the exposure levels to reflect the energy that exceeds EQ levels may give a closer prediction
of the effects of noise exposures.
4 Rating methods
It is well documented that EEH based ratings fail to predict hazard from high energy impulsive
noise. This has lead to a great deal of investigation into the statistical properties of the pres-
sure time history. On the other hand, analysis of the effects due to frequency content of the
exposure signals has not received such devoted attention. This is in part due to the simplicity
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of the A-weighting curve and that A-weighted energy levels and PTS are well correlated for a
great deal of exposure conditions.
Ratings based on broad-band time-averaged measures using the EEH fail to describe the
specific time and frequency variations of exposure signals. To improve exposure rating it is
necessary to be able to quantify the influence of temporal variations and frequency content
on the auditory system.
4.1 Description of the pressure time history
Starck and Pekkarinen [17] proposed the cumulative crest factor (CF) for classification of
noise environments into impulsive or non-impulsive. According to the method, a noise envi-
ronment is considered impulsive when the difference between the peak and RMS levels of
a sound pressure is equal to or greater than 15 dB. This criterion value corresponds to the
averaging time of the ear so that the loudness perception of impulsive sounds matches the
loudness of continuous sounds, and it is determined to be approximately 35 [ms][18].
The difference between peak and effective levels varies randomly in industrial noise. There-
fore, the method calculates the cumulative distribution function, which consists on calculations
of the CF at small intervals of time. In this way, the method determines the percentage of time
in the sample, the CF exceeds 15 [dB]. However, the method does not establish a fence value
regarding the percentage of time that the crest factor must exceed 15 [dB]for a noise to be
considered impulsive. Therefore, rather than indicating that the method allows classification
of noise environments into impulsive/non-impulsive, it would be more precise to state that
noise environments can be ranked in their impulsiveness.
Erdreich [19] proposed the kurtosis metric (β) as a statistical descriptor of impulsiveness. Ba-
sically, the kurtosis calculates the peakedness of a sound based on its pressure time history.
The advantage of the kurtosis over other the cumulative CF is that all peaks are accounted
for in the calculation and that the relative difference between peak and background level is
also incorporated; while the cumulative crest factor only computes the maximum peak level in
a given time frame. The kurtosis is calculated as the ratio of the fourth moment of the ampli-
tude distribution to the squared second moment of the distribution in the analysis window. A
pure continuous noise (Gaussian) will have a kurtosis value of β= 3; while purely impulsive
sounds (non-Gaussian) may reach values of β > 100.
Both cumulative CF and βcan be used as statistical tools to rank the hazard of different
exposures. A TTS experiment using exposures of equal A-weighted energy with different
frequency content showed marked differences in the resulting TTS patterns [20]. The three
two-octave band exposures were band-passed versions of the same signal, nevertheless they
showed differences in the CF and β. The differences in CF and βranked the exposures in
the same order than the TTS patters (highest CF and βhigher maximum TTS and longer
recovery).
4.2 Frequency characteristics
In order to quantify the energy that arrives at the external ear and the amount of energy
that is considered hazardous, the influence of the listener in the sound field, and safe sound
levels should be considered on a frequency band basis. The bandwidth for each band in
the analysis needs further investigation, but it would seem reasonable to have a variable
bandwidth, perhaps based on the ERB described in Section 3.1.
The amount of energy that reaches the ear can be described by the HRTFs for the specific
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exposure scenario (diffuse- or free-field, or even for specific directions of sound incidence).
From the energy present at the ear, the SPL of each relevant frequency band should be
compared and corrected to compensate for EQ levels. This could be done as suggested by
Zhu et al. [16] computing the difference in pressure between the exposure signal and the EQ
level, if the result is greater that zero it is used as the exposure level in that band, otherwise the
level in the band is set to zero. Another approach would be to normalize the EQ levels for all
bands to the level at the band centered at 1 [kHz]. This would produce a weighting function
that can be added to the band levels of the exposure signal. A first approximation of this
weighting function based on a diffuse-field HRTF and normalized values of the octave-band
EQ levels reported by [15], can be seen in Figure 3.
0.1 1 10
−30
−20
−10
0
10
Frequency [kHz]
Relative Gain [dB]
A−weighting
Diffuse−field corr.[ISO 11094]
Equivalent Quiet corr. [Ward et.al. 1976]
Diffuse−field + EQ corr.
Figure 3: Weighting functions for sound exposure risk assessment.
5 Conclusions
In order to have more reliable noise exposure assessment methods it is necessary to make a
simultaneous evaluation of the temporal and frequency characteristics of the sound exposure.
This is outlined in the following steps:
1. diffuse- or free-field corrections: filtering with HRTF from ISO 11904-1 [13]
2. impulsive weight: correction calculated from impulsiveness of each pressure time his-
tory in the frequency bands of interest using CF and/or β.
3. bandwidth weight: correction calculated for the influence of the exposure bandwidth
from tonal to octave band exposures in the frequency bands of interest.
4. EQ weight: correction of the innocuous energy in the exposure signal based on the
corrections calculated in 1 and 2.
It is important to have an accurate assessment of the energy that reaches the exposed ear,
this can be done using head related transfer functions (step 1). It is also necessary to quantify
the hazard potential of the energy reaching the ear (steps 2,3 and 4). A good approach would
be to investigate effective quiet levels for different exposure conditions. This approach is
appealing because the investigation of effective quiet levels can be safely done with human
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subjects. Additionally the use of oto-acoustic emissions to monitor the onset of changes of
the hearing, could provide new insight into the different underlying mechanism responsible
for metabolic changes of the inner ear. This would lead to a frequency weighting method that
would be based on the response of the hearing to exposure to sound (and not on loudness),
incorporating temporal and frequency characteristics of the exposure.
In order to implement the weights from points 2 and 3 of the list, it is necessary to investigate
the EQ levels as a function of impulsiveness and of bandwidth of the exposure signals. This
could lead to a weighting matrix for each frequency band where each element of the matrix
(EQij ) would indicate a safe exposure level for a signal having a given impulsiveness and
bandwidth. The proposed weighting matrix is shown in Table 1.
Center frequency fc
Impulsiveness (CF and/or β)
β= 3 ... β > 200
Bandwidth
1 [Hz]EQij
.
.
.
fc/√2 [Hz]
Table 1: Proposed EQ weighting matrix for expo-
sure bandwidth and impulsiveness. Matrices like this
should be obtained for center frequencies (fc) from
125 [Hz]to 8 [kH z]in octave-band steps.
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