Modeling auditory processing of amplitude modulation. I. Detection and masking with narrow-band carriers

Abstract

This paper presents a quantitative model for describing data from modulation-detection and modulation-masking experiments, which extends the model of the "effective" signal processing of the auditory system described in Dau et al. [J. Acoust. Soc. Am. 99, 3615-3622 (1996)]. The new element in the present model is a modulation filterbank, which exhibits two domains with different scaling. In the range 0-10 Hz, the modulation filters have a constant bandwidth of 5 Hz. Between 10 Hz and 1000 Hz a logarithmic scaling with a constant Q value of 2 was assumed. To preclude spectral effects in temporal processing, measurements and corresponding simulations were performed with stochastic narrow-band noise carriers at a high center frequency (5 kHz). For conditions in which the modulation rate (fmod) was smaller than half the bandwidth of the carrier (delta f), the model accounts for the low-pass characteristic in the threshold functions [e.g., Viemeister, J. Acoust. Soc. Am. 66, 1364-1380 (1979)]. In conditions with fmod > delta f/2, the model can account for the high-pass characteristic in the threshold function. In a further experiment, a classical masking paradigm for investigating frequency selectivity was adopted and translated to the modulation-frequency domain. Masked thresholds for sinusoidal test modulation in the presence of a competing modulation masker were measured and simulated as a function of the test modulation rate. In all cases, the model describes the experimental data to within a few dB. It is proposed that the typical low-pass characteristic of the temporal modulation transfer function observed with wide-band noise carriers is not due to "sluggishness" in the auditory system, but can instead be understood in terms of the interaction between modulation filters and the inherent fluctuations in the carrier.

Full text

Modeling auditory processing of amplitude modulation. I.
Detection and masking with narrow-band carriers
a)
Torsten Dau
b)
and Birger Kollmeier
Carl von Ossietzky Universita
¨
t Oldenburg, Graduiertenkolleg Psychoakustik, AG Medizinische Physik,
D-26111 Oldenburg, Germany
Armin Kohlrausch
IPO Center for Research on User-System Interaction, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
~Received 28 June 1996; accepted for publication 4 August 1997!
This paper presents a quantitative model for describing data from modulation-detection and
modulation-masking experiments, which extends the model of the ‘‘effective’’ signal processing of
the auditory system described in Dau et al. @J. Acoust. Soc. Am. 99, 3615–3622 ~1996!#. The new
element in the present model is a modulation filterbank, which exhibits two domains with different
scaling. In the range 0–10 Hz, the modulation filters have a constant bandwidth of 5 Hz. Between
10 Hz and 1000 Hz a logarithmic scaling with a constant Q value of 2 was assumed. To preclude
spectral effects in temporal processing, measurements and corresponding simulations were
performed with stochastic narrow-band noise carriers at a high center frequency ~5 kHz!. For
conditions in which the modulation rate (f
mod
) was smaller than half the bandwidth of the carrier
(D f), the model accounts for the low-pass characteristic in the threshold functions @e.g., Viemeister,
J. Acoust. Soc. Am. 66, 1364–1380 ~1979!#. In conditions with f
mod
. D f/2, the model can account
for the high-pass characteristic in the threshold function. In a further experiment, a classical masking
paradigm for investigating frequency selectivity was adopted and translated to the
modulation-frequency domain. Masked thresholds for sinusoidal test modulation in the presence of
a competing modulation masker were measured and simulated as a function of the test modulation
rate. In all cases, the model describes the experimental data to within a few dB. It is proposed that
the typical low-pass characteristic of the temporal modulation transfer function observed with
wide-band noise carriers is not due to ‘‘sluggishness’’ in the auditory system, but can instead be
understood in terms of the interaction between modulation filters and the inherent fluctuations in the
carrier. © 1997 Acoustical Society of America. @S0001-4966~97!05611-7#
PACS numbers: 43.66.Ba, 43.66.Dc, 43.66.Mk @JWH#
INTRODUCTION
Temporal resolution in the auditory system, or the abil-
ity to resolve dynamic acoustic cues, is very important for
the processing of complex sounds. A general psycho-
acoustical approach to describing temporal resolution is to
measure the threshold for detecting changes in the amplitude
of a sound as a function of the rate of the changes. The
function which relates threshold to modulation rate is called
the temporal modulation transfer function ~TMTF!~Viemeis-
ter, 1979!. The TMTF might provide important information
about the processing of temporal envelopes. Since the modu-
lation of a sound modifies its spectrum, wide-band noise is
often used as a carrier signal in order to prevent subjects
from using changes in the overall spectrum as a detection
cue; modulation of white noise does not change its long-term
spectrum ~e.g., Burns and Viemeister, 1981!. The subject’s
sensitivity for detecting sinusoidal amplitude modulation of a
broadband noise carrier is high for low modulation rates and
decreases at high modulation rates. It is therefore often ar-
gued that the auditory system is ‘‘sluggish’’ in following fast
temporal envelope fluctuations. Since this sensitivity to
modulation resembles the transfer function of a simple low-
pass filter, the attenuation characteristic is often interpreted
as the low-pass characteristic of the auditory system. This
view is reflected in the structure of a widely accepted model
for describing the TMTF ~Viemeister, 1979!.
It is often argued that the auditory filters play a role in
limiting temporal resolution ~e.g., Moore and Glasberg,
1986!, especially at frequencies below 1 kHz where the
bandwidths of the auditory filters are relatively narrow, lead-
ing to longer impulse responses or ‘‘ringing’’ of the filters.
However, the response of auditory filters at high center fre-
quencies is too fast to be a limiting factor in most tasks of
temporal resolution ~Ronken, 1970; Green, 1973!. Thus there
must be a process at a more central level of the auditory
system than the peripheral auditory filters which limits tem-
poral resolution and causes the ‘‘sluggishness’’ in following
fast modulations of the stimulus envelope.
Results from several studies concerning modulation
masking, however, are not consistent with the idea of only
one broad filter, as reflected in the TMTF. Houtgast ~1989!
designed experiments to estimate the degree of frequency
selectivity in the perception of simultaneously presented am-
a!
Part of this research was presented at the 129th meeting of the Acoustical
Society of America @T. Dau, B. Kollmeier and A. Kohlrausch, ‘‘Modeling
modulation perception: modulation low-pass filter or modulation filter-
bank?,’’ J. Acoust. Soc. Am. 97, 3273 ~A!~1995!#.
b!
Corresponding author. Electronic mail: torsten@medi.physik.uni-
oldenburg.de
2892 2892J. Acoust. Soc. Am. 102 (5), Pt. 1, November 1997 0001-4966/97/102(5)/2892/14/$10.00 © 1997 Acoustical Society of America

plitude modulation, using broadband noise as a carrier. Us-
ing narrow bands of noise as the masker modulation, the
modulation-detection threshold function showed a peak at
the masker modulation frequency. This indicates that mask-
ing is most effective when the test modulation frequency
falls within the masker-modulation band. In the same vein,
Bacon and Grantham ~1989! found peaked masking patterns
using sinusoidal masker modulation instead of a noise band.
Fassel ~1994! found similar masking patterns using sinusoids
at high frequencies as carriers and sinusoidal masker modu-
lation.
For spectral tone-on-tone masking, effects of frequency
selectivity are well established and are associated with the
existence of independent frequency channels. When trans-
lated to the modulation-frequency domain, the data of Hout-
gast and of Bacon and Grantham suggest the existence of
modulation-frequency specific channels at a more central
stage in the auditory system than the peripheral auditory fil-
ters. Yost et al. ~1989! also suggested amplitude modulation
channels to explain their data on modulation-detection inter-
ference and to account for the formation of auditory ‘‘ob-
jects’’ based on common modulation. Similarly, Martens
~1982! proposed that the auditory system realizes some kind
of short-term spectral analysis of the temporal waveform of
the signal’s envelope.
Modulation-frequency specificity has also been observed
in different physiological studies of neural responses to am-
plitude modulated tones ~Creutzfeldt et al., 1980; Langner
and Schreiner, 1988; Schreiner and Urbas, 1988; Langner,
1992!. Langner and Schreiner ~1988! stated that the auditory
system contains several levels of systematic topographical
organization with respect to the response characteristics that
convey temporal modulation aspects of the input signal. A
general reduction in the temporal activity patterns of neural
elements along the auditory pathway was described as the
most basic temporal organizational feature. That is, the tem-
poral resolution of the auditory nerve ~Palmer, 1982! appears
to be higher than at any other processing level. The highest
best modulation frequencies ~BMF! found in the inferior col-
liculus ~IC!—which is about 1000 Hz—are still comparable
with the temporal resolution of auditory nerve fibers
~Schreiner and Langner, 1984; Langner and Schreiner,
1988!. However, the majority of units in the IC are tuned to
modulation frequencies well below the upper frequency limit
given by the auditory nerve. All estimates of temporal reso-
lution in the IC were found to be higher than estimates in the
auditory cortex ~which are in the range of BMF50–20 Hz in
cats!. Thus the auditory cortex seems to be limited in its
ability to follow fast temporal changes in the input envelope.
On the other hand, the cortex seems to be capable of pro-
cessing slow modulations like rhythmlike envelope fluctua-
tions ~Creutzfeldt et al., 1980!. A further organizational level
of the temporal processing is reflected by differences found
in various subdivisions of auditory nuclei. For example,
Langner and Schreiner ~1988! found a highly systematically
organized map of best modulation frequencies within the IC
of the cat. Overall, Langner and Schreiner ~1988! concluded
that temporal aspects of a stimulus, such as envelope varia-
tions, represent a major organizational principle of the audi-
tory system, that complements the well-established spectral
~tonotopic! and binaural organization.
The present psycho-acoustical study further analyzes the
processing of amplitude modulation in the auditory system.
The goal is to gather more information about modulation-
frequency selectivity and to set up corresponding simulations
with an extended version of a model of the ‘‘effective’’ sig-
nal processing in the auditory system, which was initially
developed to describe temporal masking effects ~Dau et al.,
1996a, b!. As already pointed out, in most classical studies of
temporal processing, a broadband noise carrier has been ap-
plied to determine the TMTF. Unfortunately, the use of
broadband noise carriers does not provide direct information
about spectral effects in temporal processing: Broadband
noise excites a wide region of the basilar membrane, leaving
unanswered the question of what spectral region or regions
are being used to detect the modulation. For this reason,
measurements and corresponding simulations with stochastic
narrow-band noises as carriers at a high center frequency
were performed, as was done earlier by Fleischer ~1982a,
1983!. At high center frequencies, the bandwidth of the au-
ditory filters is relatively large so that there is a larger range
of modulation rates over which the sidebands resulting from
the modulation are not resolved. Instead, the modulation is
perceived as a temporal attribute, like fluctuations in loud-
ness ~for low modulation rates! or as roughness ~for higher
modulation rates!. The bandwidth of the modulated signal
was chosen to be smaller than the bandwidth of the stimu-
lated peripheral filter. This implies that all spectral compo-
nents are processed together and that temporal effects are
dominant over spectral effects.
I. DESCRIPTION OF THE MODEL
In Dau et al. ~1996a!, a model was proposed to describe
the effective signal processing in the auditory system. This
model allows the prediction of masked thresholds in a vari-
ety of simultaneous and nonsimultaneous conditions ~Dau
et al., 1996b!. It combines several stages of preprocessing
with a decision device that has the properties of an optimal
detector. Since then, the model has also been used to predict
speech perception tasks, such as automatic speech recogni-
tion and speech quality evaluation ~cf. Holube and Koll-
meier, 1996; Kollmeier et al., 1996!. Figure 1 shows the ex-
tended model that is proposed to describe experimental data
on modulation perception. Instead of the implementation of
the basilar-membrane model developed by Strube ~1985!,as
used in Dau et al. ~1996a!, the gammatone filterbank model
of Patterson et al. ~1987! is used to simulate the bandpass
characteristics of the basilar membrane. The gammatone fil-
terbank has the advantages that its algorithm is much more
efficient than the Strube model and that the bandwidths more
closely match estimates of auditory-filter bandwidths. The
signal at the output of a single filter of the gammatone filter-
bank is half-wave rectified and low-pass filtered at 1 kHz, as
in the model described in Dau et al. ~1996a!.
The subsequent nonlinear adaptation stage is a slightly
modified version ~Mu
¨
nkner, 1993! of the adaptation stage
~Pu
¨
schel, 1988! implemented within the masking model of
Dau et al. ~1996a!. In this modified version the amplitude of
2893 2893J. Acoust. Soc. Am., Vol. 102, No. 5, Pt. 1, November 1997 Dau
et al.
: Detection and masking with narrow-band carriers

the onset response was limited to a value of maximally 10
times the value of the steady state response of the stage ~for
details see Mu
¨
nkner, 1993!.
1
With regard to the transforma-
tion of envelope variations of the signal, the adaptation stage
transforms rapid input variations ~as compared with the time
constants of the low-pass filters! linearly. If these changes
are slow enough then, because of the time constants of the
model, the gain is also changed. Each element within the
adaptation model combines a static compressive nonlinearity
with a higher sensitivity for fast temporal variations ~for de-
tails, see Dau et al., 1996a!.
The following stage in the model, as shown in Fig. 1,
contains the most substantial changes compared to the model
described in Dau et al. ~1996a!. Instead of the low-pass filter
with a cutoff frequency of 8 Hz, a linear filterbank is as-
sumed to further analyze the amplitude changes of the enve-
lope. This stage will be called the modulation filterbank
throughout this paper. A first implementation of such a
modulation filterbank was presented in Fassel and Pu
¨
schel
~1993! and Mu
¨
nker and Pu
¨
schel ~1993!. The implementation
of this stage is in contrast to the signal processing within
other models in the literature ~e.g., Viemeister, 1979; Forrest
and Green, 1987!.
It is postulated within the present model that the modu-
lation filterbank exhibits two domains with different scaling.
Figure 2 shows the transfer functions of the modulation fil-
ters. In the range 0–10 Hz a constant bandwidth of 5 Hz is
assumed. The lowest modulation filter represents a low-pass
filter with a cutoff frequency of 2.5 Hz. From 10 Hz up to
1000 Hz a logarithmic scaling with a constant Q value of 2 is
assumed.
2
The spacing in the modulation-frequency domain
resembles the spacing of critical bands in the audio-
frequency domain. Within the model only the ~Hilbert!
envelope of the modulation filter outputs for center frequen-
cies above 10 Hz is further examined, introducing a nonlin-
earity in the processing of amplitude modulation.
3
For filters
with a lower center frequency it is not reasonable to extract
the Hilbert envelope from the signal, because the distinction
between carrier and envelope becomes ambiguous due to the
large relative bandwidth of these filters. Furthermore, the
successful description of masking data by the original model
version in Dau et al. ~1996b! suggests that use is made of
information about modulation phase at low modulation rates.
In this model the signal envelope was analyzed by the simple
8-Hz low-pass filter and this filtering preserves all informa-
tion about the modulation phase for low modulation frequen-
cies. The present model thus tries to find a ‘‘link’’ between
the description of phenomena of modulation detection and
those of the more common signal detection.
The output of the ‘‘preprocessing’’ stages can now be
interpreted as a three-dimensional, time-varying activity pat-
tern. Limitations of resolution are again simulated by adding
internal noise with a constant variance to each modulation
filter output.
4
The internal noises at the outputs of the differ-
ent modulation channels are assumed to be independent of
each other. For stochastic input signals, the outputs of the
modulation channels are not ~fully! uncorrelated because of
the overlap of the modulation filters. The transformed signal
after the addition of noise is called the internal representation
of the signal. The decision device is realized as an optimal
detector in the same way as described in Dau et al. ~1996a,
b!. There, the decision device of the model was first de-
scribed for masking conditions using sinusoidal test signals
presented in a frozen-noise masker. In each interval of a
simulated 3-interval forced-choice ~3IFC! adaptive para-
digm, the difference between the current representation and
the ‘‘stored’’ internal representation of the deterministic
FIG. 1. Block diagram of the psycho-acoustical model for describing
modulation-detection data with an optimal detector as decision device. The
signals are preprocessed, subjected to adaptation, filtered by a modulation
filterbank and finally added to internal noise; this processing transforms the
signals into their internal representations.
FIG. 2. Transfer functions of the modulation filters. In the range 0–10 Hz
the functions have a constant bandwidth of 5 Hz. Between 10 and 1000 Hz
a logarithmic scaling with a constant Q value of 2 is applied. Only the range
from 0 to 200 Hz is plotted.
2894 2894J. Acoust. Soc. Am., Vol. 102, No. 5, Pt. 1, November 1997 Dau
et al.
: Detection and masking with narrow-band carriers

masker was calculated, leading to two intervals containing
only internal noise and one interval containing the nonlin-
early transformed signal plus internal noise. To apply the
model to random noise, a different sample of the masker was
presented in each interval; the ‘‘reference’’ representation
was modeled by calculating the mean internal representation
of several masker samples ~cf. Dau et al., 1996b!. This av-
eraged reference was computed once before the adaptive pro-
cedure was started. During the adaptive procedure, the three
difference representations ~in a trial! were affected by the
statistical properties of the external noise in addition to the
internal noise. Such an algorithm is also used for the present
study dealing with stochastic noise as the carrier ~and refer-
ence! and a sinusoidal modulation ~as the test signal!. The
template is generated in the present study as the normalized
difference between an averaged suprathreshold internal rep-
resentation of several modulated carrier samples and the av-
eraged internal representation of the reference alone ~cf. Dau
et al., 1996b!. The decision criterion within the optimal de-
cision stage ~see Green and Swets, 1966! is given by the
difference between the largest cross-correlation coefficient of
the two carrier-alone representations with the template and
the correlation value between the representation in the signal
interval and the template. When this difference is smaller
than the limit of resolution determined by the internal noise,
the test modulation is not detected ~for details, see Dau et al.,
1996b!.
5
II. METHOD
A. Procedure and subjects
Modulation detection thresholds were measured and
simulated using an adaptive 3IFC procedure. The carrier was
presented in three consecutive intervals separated by silent
intervals of 300 ms. In one randomly chosen interval the
carrier was sinusoidally amplitude modulated. In the other
intervals it was unmodulated. The subject’s task was to
specify the interval containing the modulation. During a
threshold run, the modulation depth in dB (20 log m), was
adjusted using a 2-down 1-up rule ~Levitt, 1971! which pro-
vides an estimate of the modulation depth necessary for
70.7% correct responses. The step size was 4 dB at the start
of a run and was divided by 2 after every two reversals of the
modulation depth until the step size reached a minimum of 1
dB, at which time it was fixed. Using this 1-dB step size, 10
reversals were obtained and the median value of the modu-
lation depths at these 10 reversals was used as the threshold
value. The subjects received visual feedback after each re-
sponse. The procedure was repeated four times for each sig-
nal configuration and subject. All figures show the median
and interquartile ranges based on four single measurements.
All five subjects had experience in psycho-acoustic measure-
ments and had clinically normal hearing. They were between
23 and 29 years old and participated voluntarily in the study.
B. Apparatus and stimuli
All acoustic stimuli were digitally generated at a sam-
pling frequency of 30 kHz. The stimuli were transformed to
analog signals with the aid of a two-channel 16-bit D/A con-
verter, attenuated, low-pass filtered at 10 kHz, and diotically
presented via headphones ~HDA 200! in a sound-attenuating
booth. Signal generation and presentation were controlled by
a SUN Workstation using a signal-processing software pack-
age developed at the Drittes Physikalisches Institut in Go
¨
t-
tingen.
Several modulation-detection and modulation-masking
experiments were performed. In most measurements narrow-
band Gaussian noise centered at 5 kHz was used as the car-
rier. In the masking experiment a sinusoidal carrier at 5 kHz
was used. The carrier level was 65 dB SPL in both cases.
The specific choice of the parameters for the windowing of
the stimuli will be described later in the paper when the
corresponding experiments are discussed. In the experiments
using a noise carrier, an independent sample of noise was
presented in each interval. With one exception described be-
low, the noise stimuli were digitally filtered before modula-
tion by setting the magnitude of the Fourier coefficients to
zero outside the desired passband.
An amplitude-modulated noise has sidebands that ex-
tend 6 f
m
Hz from the edges of the passband of the unmodu-
lated noise, where f
m
indicates the modulation frequency. In
principle it is possible that the detection of modulation is
based on spectral changes in the modulated waveform. The
usability of these spectral cues depends on frequency region,
owing to the relation of frequency difference limens and cen-
ter frequency ~Wier et al., 1977; Eddins, 1993!. One way to
avoid these spectral cues is to apply the modulation to wide-
band noise before bandpass filtering. In the present study this
was done for the largest applied carrier bandwidth, 314 Hz,
by setting the magnitude of the Fourier coefficients to zero
outside the desired passband. This is the same procedure that
was applied by Eddins ~1993!. Thus in this case, the band-
width of the stimuli is the same regardless of the presence or
absence of modulation. By filtering after amplitude modula-
tion, the sidebands introduced by modulation are effectively
reduced. The filtering after modulation causes a partially fill-
ing in the valleys of the temporal waveform ~e.g., Eddins,
1993!. However, this technique ensures that spectral cues
were not available and the task was purely temporal in na-
ture. In contrast, for the carrier bandwidths of 3 and 31 Hz,
no filtering after modulation was applied.
When generating amplitude-modulated narrow-band
stimuli, the average power of the modulated signal is in-
creased by 11 m
2
/2 compared with the unmodulated signal.
For large modulation depths, detection might therefore be
based on changes in overall intensity rather than on the pres-
ence or absence of modulation. To eliminate level cues, the
digital waveforms were adjusted to have equal power in each
interval of the forced-choice trial.
In most cases sinusoidal test modulation with zero onset
phase was applied. In one experiment a complex modulator
was used, consisting of five adjacent components of a har-
monic tone complex. In each case the carrier and the applied
modulators were windowed with a length depending on the
particular experiment.
2895 2895J. Acoust. Soc. Am., Vol. 102, No. 5, Pt. 1, November 1997 Dau
et al.
: Detection and masking with narrow-band carriers

III. RESULTS
A. Amplitude-modulation thresholds of narrow-band
noise as a function of the carrier bandwidth
In this experiment, TMTFs were measured and simu-
lated for narrow-band noise carriers of bandwidths 3, 31, and
314 Hz, centered at 5 kHz in each condition ~cf. Fleischer,
1982a, 1983!. Fleischer’s experiments were replicated in this
study and compared with corresponding simulations carried
out with the present model. In contrast to Fleischer, an adap-
tive threshold procedure was used and the carrier level was
somewhat lower ~65 dB SPL!. For the three noise band-
widths, the corresponding spectrum levels were about 60, 50,
and 40 dB SPL. The carrier and the applied sinusoidal modu-
lation had a duration of 1 s. Both were windowed with
200-ms cosine-squared ramps. Figure 3 shows the present
experimental results for amplitude modulation detection em-
ploying a carrier bandwidth of 3 Hz at a center frequency of
5 kHz. The figure shows the data of three subjects ~open
symbols! together with the model predictions ~closed sym-
bols!. For comparison, data obtained by one subject using a
sinusoidal carrier at 5 kHz are shown as asterisks. For the
sinusoidal carrier, the same stimulus parameters were used as
for the noise carrier conditions. The ordinate indicates modu-
lation depth at threshold, and the abscissa represents the
modulation frequency. A comparatively high detection
threshold is observed at a modulation rate of 3 Hz. This is
due to the inherent statistical fluctuations of the narrow-band
3-Hz-wide carrier. These inherent fluctuations of the carrier
envelope mask the additional periodic 3-Hz test modulation.
With increasing modulation frequency, thresholds decrease
and converge with those obtained using a sinusoidal carrier
at a modulation frequency of 20 Hz. The threshold remains
flat up to a modulation frequency of 100 Hz. This finding
indicates that the auditory system does not seem too slow or
sluggish to follow fast fluctuations in this range. There is
very good agreement between the measurements and simu-
lations. The flat threshold function up to 100 Hz contrasts
with the conclusions derived from modulation detection data
for broadband noise carriers ~e.g., Viemeister, 1979! and also
contrasts with data in Zwicker ~1952! obtained with a sinu-
soidal carrier. Zwicker found an increase in threshold be-
tween 4 and 64 Hz of about 9 dB at a carrier frequency of 4
kHz. However, the present data are in good agreement with
more recent data by Fleischer ~1982a, 1983!, Fassel ~1994!,
Fassel and Kohlrausch ~1995!, Dau ~1996!, and Fassel et al.
~1997!, who measured TMTFs with sinusoidal carriers at 5
and 10 kHz.
Flat thresholds up to a modulation frequency of 128 Hz
were also observed by Strickland and Viemeister ~1997! in
an experiment where subjects had to discriminate between
AM and quasi-frequency modulation ~QFM! applied to a
sinusoidal carrier of 4 kHz. Based on additional data on
QFM detection, these authors argued that the flatness in their
TMTF between 64 and 128 Hz may have been caused by the
increasing role of spectral cues and thus did not reflect true
temporal processing. Since the assumptions about available
cues are of relevance for the interpretation of our data, we
will return to the arguments put forward by Strickland and
Viemeister in the discussion ~Sec. V! of the present paper.
Figure 4 shows thresholds using a narrow-band carrier
with a bandwidth of 31 Hz. Again, the modulation depth, m,
at threshold was measured and simulated as a function of the
test-modulation frequency. The open symbols represent the
measured data of three subjects and the filled symbols indi-
cate the simulated thresholds. The threshold at a very low
modulation rate ~3Hz!is several dB lower than in the case of
the 3-Hz-wide carrier. This decrease is due to the decreasing
spectral energy density in the modulation spectrum with in-
creasing bandwidth of the carrier ~see the Appendix!.In
terms of the model, less ‘‘noise energy’’ falls into the low-
frequency modulation filter which is tuned to the test-
modulation frequency. For modulation frequencies larger
than half the bandwidth of the noise (f
mod
. D f/2) thresholds
begin to decrease, both in the measurements and in the simu-
lations, so that a high-pass characteristic in the threshold
function becomes apparent. However, thresholds decrease
more slowly with increasing modulation frequency than the
FIG. 3. Modulation-detection thresholds of sinusoidal amplitude modulation
as a function of the modulation frequency. The carrier was a 3-Hz-wide
running noise at a center frequency of 5 kHz. Carrier and modulation dura-
tion: 1 s. Level: 65 dB SPL. Subjects: JV ~h!;AS~L!;TD~s!; optimal
detector ~d!. In addition, the modulation detection thresholds of one subject
~TD! for a 5-kHz sinusoidal carrier are indicated by ~!!.
FIG. 4. Modulation-detection thresholds of sinusoidal amplitude modulation
as a function of the modulation frequency. The carrier was a 31-Hz-wide
running noise at a center frequency of 5 kHz. Carrier and modulation dura-
tion: 1 s. Level: 65 dB SPL. Subjects: AS ~L!;TD~s!;JV~h!; optimal
detector ~d!.
2896 2896J. Acoust. Soc. Am., Vol. 102, No. 5, Pt. 1, November 1997 Dau
et al.
: Detection and masking with narrow-band carriers

spectrum of the inherent envelope fluctuations itself ~e.g.,
Lawson and Uhlenbeck, 1950!. The idealized modulation
spectrum of a rectangular shaped bandpass noise has a trian-
gular shape which stretches from 0 to D f Hz ~see the Ap-
pendix and Lawson and Uhlenbeck, 1950!. If the auditory
system would be sharply tuned in frequency selectivity for
modulation, thresholds would decrease with increasing
modulation frequency more or less in parallel with the spec-
tral shape of the modulation spectrum of the carrier ~assum-
ing a constant signal-to-noise ratio at the output!. Appar-
ently, this is not the case. Hence, even at high modulation
rates of 100 and 150 Hz, thresholds have not yet converged
with those for the 3-Hz-wide carrier nor with those for the
sinusoidal carrier, but are about 5 dB higher. This implies
that the relatively slow inherent fluctuations of the 31-Hz-
wide carrier make it difficult to detect the higher-frequency
test modulation. This phenomenon was also observed by
Fleischer ~1982a! who referred to it as ‘‘cross-talk’’ of the
inherent fluctuations of the noise on the added modulation.
This effect decreases with increasing rate of the test modu-
lation.
This experiment reveals much about the auditory sys-
tem’s selectivity for modulation frequency. In the model it
was necessary to use wide modulation filters (Q5 2) at high
modulation frequencies so that some energy from the low-
frequency fluctuations of the ‘‘masker’’ leaks through a
modulation filter that is tuned to a high modulation fre-
quency ~like 150 Hz!. This leakage decreases the signal-to-
noise ratio and therefore leads to a higher detection threshold
at f
mod
5150 Hz than would be the case for a more sharply
tuned filter. Again, there is good agreement between the
form of the simulated and measured data.
Figure 5 shows results for the carrier bandwidth of 314
Hz. Thresholds are higher for a modulation rate of 3 Hz than
for a rate of 5 Hz. This is probably caused by the use of a
gated carrier. Such an effect has been observed in several
psycho-acoustical studies ~e.g., Viemeister, 1979; Sheft and
Yost, 1990!. Based on their results it can be assumed that the
threshold at 3 Hz would decrease if a continuous carrier had
been used instead of a gated one. For modulation frequencies
above 7 Hz, thresholds increase by about 3 dB per doubling
of the modulation frequency. This threshold pattern agrees
well with comparable experimental data of Eddins ~1993! for
a carrier bandwidth of 400 Hz. The form of the TMTF is
similar to the pattern found in ‘‘classical’’ measurements of
the TMTF using a broadband noise as a carrier, but it has a
much lower cutoff frequency ~Viemeister, 1979!. Overall,
the threshold curve is very different from those obtained with
smaller carrier bandwidths since the detectability of the test
modulation decreases with increasing modulation frequency.
Consistent with the data, the simulations also show increas-
ing thresholds with increasing modulation frequency.
For a carrier bandwidth of 314 Hz, the spectrum of the
intrinsic fluctuations is relatively flat over the whole range of
the test-modulation frequencies. The additional test compo-
nent falls in the passband of mainly one modulation filter.
Assuming a constant decision criterion at threshold, the loga-
rithmic scaling of the modulation filters with center frequen-
cies above 10 Hz leads to an approximately 3-dB increase of
modulation depth, m, at threshold per doubling of modula-
tion frequency. In other words, to get the same signal-to-
noise ratio at threshold, a greater modulation depth is re-
quired with increasing modulation frequency. Thus the
apparent modulation low-pass behavior in the model data in
Fig. 5 is not explained by assuming a general low-pass char-
acteristic in the auditory system, but is caused by the con-
stant relative width ~or logarithmic scaling! of the modula-
tion filters.
Figure 6 gives an illustration of how the signals are in-
ternally represented in the model. It shows how the template
is derived from the internal representation of suprathreshold
test modulation and that of the unmodulated carrier alone.
The upper panel shows the three-dimensional internal repre-
sentation of a 3-Hz-wide carrier alone ~centered at 5 kHz!.It
represents the internal activity as a function of time and cen-
ter frequency of the modulation filters. The ordinate is scaled
in model units ~MU!. The modulation center frequencies
range from 0 to 1000 Hz. Since the total energy within the
modulation spectrum of the signal is concentrated at very
low modulation rates, only the lowest modulation filters are
excited by the input signal. This is indicated by the hatched
lines in the figure. At the beginning of the carrier, all modu-
lation filters show a short period of high excitation. This
response reflects the step response of the filters to the enve-
lope onset. The middle panel of Fig. 6 shows the internal
representation of the carrier, this time sinusoidally modu-
lated with a test-modulation rate of 20 Hz at a highly detect-
able modulation depth. The test modulation mainly activates
the modulation filter tuned to 20 Hz but also stimulates ad-
jacent modulation filters, because of the relatively low
modulation-frequency selectivity assumed in the model.
Again, the inherent fluctuations of the carrier itself primarily
activate the region at low modulation frequencies. However,
because of the large spectral separation between the test
modulation and the inherent fluctuations of the carrier, there
is no interaction between the two components; that is, no
competing ‘‘noise’’ energy leaks into the transfer range of
the test-modulation filter. The lower panel in Fig. 6 gives the
FIG. 5. Modulation-detection thresholds of sinusoidal amplitude modulation
as a function of the modulation frequency. The carrier was a 314-Hz-wide
running noise at a center frequency of 5 kHz. Carrier and modulation dura-
tion: 1 s. Level: 65 dB SPL. Subjects: JV ~h!;TD~s!;AS~L!; optimal
detector ~d!.
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template which is derived by subtracting the upper panel
from the middle one and normalizing the result. As a conse-
quence of the marked separation in modulation frequency,
the internal representation of the template contains a repre-
sentation of the temporal course of the test modulation with-
out interference from the carrier modulation.
B. Amplitude modulation thresholds of third-octave-
wide noisebands as a function of the center
frequency
In the previous section it was observed that the detection
threshold for amplitude modulation depends on the spectral
density of the inherent fluctuations of the carrier, when the
total energy of the modulated signal is constant. This is ex-
amined further in the following experiment using a third-
octave-wave noiseband as the carrier. The detection thresh-
old for 25-Hz modulation was measured and simulated as a
function of the center frequency of the band. Stimulus pa-
rameters were the same as in the experiments of the previous
section. In the model, only the output of the peripheral filter
centered on the bandpass noise was analyzed. It was further
assumed that the scaling of the modulation filters does not
change with the peripheral frequency region. Figure 7 shows
the modulation depth at threshold as a function of the center
FIG. 6. Generation of the template representation ~at the bottom! of a 20-Hz test modulation which was impressed on a 3-Hz-wide running noise carrier
centered at 5 kHz. The template is the normalized difference between the mean representation of the carrier plus the suprathreshold modulation ~in the middle!
and the mean representation of the carrier alone ~at the top!. The ordinate is scaled in model units ~MU!.
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frequency of the third-octave-wide noiseband. Modulation
thresholds decrease with increasing center frequency. The
increasing absolute bandwidth results in a decreasing density
of inherent low-frequency envelope fluctuations, if the total
energy of the modulated stimulus is kept constant. As a con-
sequence, less energy from the random envelope fluctuations
of the carrier falls within the passband of the modulation
filter tuned to the test-modulation frequency. This leads to
decreasing thresholds with increasing center frequency in the
model. Apart from the systematic 2- to 3-dB difference in the
absolute sensitivity, there is good agreement between the
simulated and the measured data.
C. Modulation masking: a harmonic tone-complex
masker
In a further experiment concerning modulation-
frequency selectivity, a masking paradigm for investigating
frequency selectivity in the audio-frequency domain was
adopted. It served as a test for spectral analysis in the modu-
lation domain, as opposed to a periodicity analysis. The car-
rier was a 5-kHz sinusoid. A narrow-band tone complex was
used as masker modulation. This complex consisted of the
third through seventh components of a harmonic tone com-
plex with a fundamental frequency of 30 Hz, with frequen-
cies of 90, 120, 150, 180, and 210 Hz. The amplitude of each
component was 0.16, a value sufficiently low to avoid over-
modulation when the test modulation was combined with the
tone-complex modulation. In each interval, the starting phase
of each spectral component was randomly chosen from a
uniform distribution in the range 0–360°. With this choice,
the modulating tone complex had a noiselike, but periodic,
waveform. A sinusoidal test modulation was imposed on the
same carrier. The test modulation was chosen from the range
20–120 Hz. Thus the bandwidth of the modulated signal
remained within the bandwidth of the auditory filter centered
at 5 kHz. Figure 8 shows schematically the spectral distribu-
tion of the masker and test components in the modulation
spectrum. The modulated stimuli were presented at a level of
65 dB SPL, and had a duration of 400 ms. Test and masker
modulation were present for the whole duration of the carrier
and were gated with 20-ms cosine-squared ramps.
The amount of modulation masking as a function of the
test-modulation frequency is shown in Fig. 9. The unmasked
modulation thresholds, i.e., the thresholds for sinusoidal test
modulation without any interfering masker modulation, were
used as a reference to evaluate the effect of the modulated
masker. These reference thresholds were similar across sub-
jects and were similar to those described in the first experi-
ment of this paper ~see Fig. 3!, remaining more or less flat up
to a modulation frequency of 120 Hz. The ‘‘masking pat-
tern’’ was derived by subtracting the unmasked threshold
from the masked threshold at each test-modulation fre-
quency. As can be seen from Fig. 9, the amount of masking
increases with increasing test-modulation frequency. The dif-
ference between the highest and the lowest threshold was
more than 10 dB. Note that there is no peak at 30 Hz, the
‘‘missing fundamental.’’ This indicates that the masking ef-
fect is not determined by the period of the masker modula-
tion. Also, no pronounced peak in threshold is observed for
FIG. 7. Modulation-detection thresholds for a 25-Hz modulation as a func-
tion of the center frequency of a third-octave-wide noise carrier. Carrier and
modulation duration: 1 s. Level: 65 dB SPL. Subjects: Data from Fleischer
~1981!~h!;TD~s!;JV~,!, optimal detector ~d!.
FIG. 8. Logarithmic spectrum of the Hilbert envelope of the stimuli pre-
sented in the signal interval of the modulation masking experiment. The
signal interval contains the five components of the masking tone complex
and the signal component. The subject’s task was to detect the signal com-
ponent.
FIG. 9. Amount of modulation masking as a function of the modulation
frequency. Carrier: 5-kHz sinusoid, modulation masker: 3rd–7th compo-
nents of a harmonic tone complex with fundamental f
0
5 30 Hz. Level: 65
dB SPL. Subjects: TD ~s!;JV~L!; optimal detector ~d!.
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modulation frequencies of 90 and 120 Hz, corresponding to
the lowest harmonic components of the masker complex.
This indicates that no sharp tuning in modulation frequencies
occurs at these comparatively high modulation frequencies.
An increasing masking effect with increasing test modulation
frequency is also seen in the simulations ~filled symbols in
Fig. 9!. If masking effects in the modulation-frequency do-
main were determined by the periodicity of the stimuli one
would expect an increased threshold at the fundamental fre-
quency of the tone complex and at higher harmonics. If,
however, the masked threshold of the test signal were mainly
determined by the auditory system’s frequency selectivity for
modulation, one could conclude that the system performs a
modulation analysis which is comparable and analogous to
the ‘‘critical-band’’ filtering on the basilar membrane. The
experimental data clearly suggest the latter case. The simu-
lations show good agreement with the experimental data.
However, there is a systematic difference of 2–4 dB between
the measured and simulated masking patterns. The masked
threshold is directly related to the amount of masker energy
falling within the passband of the modulation filter tuned to
the actual test modulation. For the lowest test modulation
rate ~20 Hz! there is only a very small masking effect in the
model since the modulation filters in the low modulation-
frequency region are assumed to be relatively sharply tuned
~see Fig. 2!. With increasing test-modulation frequency,
more and more components of the masker contribute to
masking. Also, in the simulations the difference between the
highest and the lowest masked threshold amounts to nearly
10 dB. These results further support the notion of
modulation-frequency selectivity, although this selectivity
seems to be relatively broadly tuned.
IV. COMPARISON WITH PREDICTIONS OF
VIEMEISTER’S MODEL FOR MODULATION
DETECTION
The modulation filterbank concept differs considerably
in its structure from the ‘‘classical’’ modulation low-pass
filter approach ~e.g., Viemeister, 1979!. In this section, pre-
dictions of the modulation low-pass filter approach are inves-
tigated and compared with the performance of the modula-
tion filterbank model.
The structure of Viemeister’s model incorporates a pre-
detection bandpass filter ~with a bandwidth of D f
5 2000 Hz! which is followed by a nonlinearity ~half-wave
rectification! and a low-pass filter. Viemeister fitted the cut-
off frequency of the low-pass filter to the TMTF data ob-
tained with a broadband noise carrier. The resulting cutoff
frequency was 64 Hz. As a decision variable he suggested
the ac-coupled root-mean-square ~rms! value of the output of
the low-pass filter which was calculated over the duration of
the observation interval. The thresholds were defined as the
modulation depth necessary to produce a certain average in-
crement ~in dB! in the rms value, compared to that for an
unmodulated noise.
Figure 10 shows simulated TMTFs for noise carriers of
3-, 31-, 314-, 2000-, and 6000-Hz bandwidth on the basis of
Viemeister’s model. The narrow-band stimuli were the same
as in Figs. 3–5. All curves show a low-pass characteristic
with a similar cutoff frequency. This characteristic reflects
the influence of the low-pass filter stage. With decreasing
carrier bandwidth, the simulated TMTFs shift toward higher
thresholds. For the output of Viemeister’s model, this in-
crease will be seen for carrier bandwidths that are less than
the bandwidth of the predetection filter and greater than the
cutoff frequency of the low-pass filter. For these conditions,
the ac-coupled rms value of the unmodulated noise carrier at
the output of the modulation low-pass stage increases with
decreasing carrier bandwidth.
At very low modulation frequencies, the increase in
threshold agrees qualitatively with the experimental data. At
higher modulation frequencies, however, the model predicts
a totally different threshold pattern than that observed ex-
perimentally.
While the pattern of the experimental data varies sys-
tematically with increasing carrier bandwidth, the model al-
ways predicts a low-pass characteristic in the threshold func-
tion independent of the carrier bandwidth. Note that the
model proposed here provides a better description of the ex-
perimental data ~cf. see Sec. III A, Figs. 3–5!.
Figure 11 shows model predictions of amplitude modu-
FIG. 10. Simulations on the basis of Viemeister’s model. Predicted modu-
lation detection thresholds are shown for five different bandwidths of the
noise carrier. Center frequency of the carrier: 5 kHz. Carrier bandwidth: l:
3 Hz; m:31Hz;j: 314 Hz; .: 2000 Hz; d: 6000 Hz.
FIG. 11. Simulated modulation detection thresholds for 25-Hz amplitude
modulation as a function of the center frequency of the third-octave-wide
noise carrier. Viemeister model: ~j!; modulation filterbank model ~d!.
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lation detection thresholds of third-octave-noise bands as a
function of the center frequency. The stimuli were the same
as in Sec. III B. The filled squares represent thresholds on the
basis of the Viemeister model. Thresholds decrease mono-
tonically with increasing center frequency. This is again
caused by the decreasing ac-coupled rms value of the un-
modulated noise with increasing center frequency ~and in-
creasing linear bandwidth! at the output of the modulation
low-pass stage, in the same way as described above. The
filled circles in the figure show the simulated data obtained
with the modulation filterbank model ~replotted from Fig. 7!.
There is virtually no difference between the predictions of
the two models. The predicted threshold functions account
well for the data ~see Fig. 7!.
Finally, model predictions were calculated for the
modulation-masking experiment with the harmonic tone
complex as the masker. The stimuli were the same as in Sec.
III C. The model of Viemeister predicts about 5-dB masking
for all test-modulation frequencies. This frequency-
independent masking is caused by the specific model struc-
ture: Because there is only one modulation-frequency spe-
cific channel ~the output of the low-pass filter! the effect of
the masker modulation is the same for all test modulation
frequencies at least in combination with the decision algo-
rithm proposed by Viemeister ~1979!. Hence the experimen-
tally observed increase in modulation masking with decreas-
ing spectral distance between modulation masker and test
modulation cannot be described properly with Viemeister’s
model.
While this paper was being written, a recent article by
Strickland and Viemeister ~1996! showed that by replacing
the rms criterion with a max/min statistic, a single-channel
envelope detector can capture some aspects of modulation
masking data, so that the effect of masker modulation is not
the same at all test modulation rates. However, their model
predictions showed a much too sharp ‘‘tuning’’ to modula-
tion frequency compared to the relatively broadly tuned
masking patterns found in the data ~Houtgast, 1989; Bacon
and Grantham, 1989!. In order to better understand the prop-
erties of such statistics, we repeated the simulations shown in
Fig. 10 using a max/min decision device. Basically, the
change in detector criterion from rms to max/min does not
change the main aspects of the previously discussed curves:
Independent of carrier bandwidth, all TMTFs have the same
shape and increase with increasing modulation frequency.
For a reduction of the carrier bandwidth between 2000 and
about 30 Hz, the TMTFs are shifted toward higher threshold
values. In addition, as already mentioned by Forrest and
Green ~1987!, the max/min statistic is less stable than the
rms statistic.
In summary, the analysis of various models proposed in
the literature and the simulations from the present study pro-
vide a strong indication for a modulation-frequency specific
analysis in the auditory system. The modulation filterbank
model, which is able to reproduce at least the trend in the
data, is one possible realization for this analysis.
V. DISCUSSION
The main goal of this study was to develop a model
which describes the effective processing of envelope fluctua-
tions in the auditory system. Experiments concerning modu-
lation detection and modulation masking were performed
which suggest that the auditory system realizes some kind of
spectral decomposition of the temporal envelope of the sig-
nals. There seem to be channels in the auditory system which
are tuned to modulation frequency, much like there are chan-
nels ~critical bands or auditory filters! tuned to spectral fre-
quency.
With regard to the experiments performed and the struc-
ture of the model that is inferred from these data, the follow-
ing points should be discussed: ~a! the assumption that the
use of spectral cues, effects of peripheral filtering, and off-
frequency listening can be neglected for the conditions tested
in this paper; ~b! the concept of a modulation filterbank as
opposed to a modulation low-pass filter in each critical band;
and ~c! the envelope statistics of the different noise maskers
employed and their influence on the thresholds obtained
here.
A. Role of spectral cues, peripheral filtering, and off-
frequency listening
The experiments in this study have been designed so as
to minimize effects of spectral cues and peripheral filtering.
The carrier frequency was very high and therefore the band-
width of the modulated signals was always smaller than the
bandwidth of the stimulated peripheral filter. We also argued
that at a carrier frequency of 5 kHz, temporal cues are domi-
nant over spectral cues in modulation detection for modula-
tion frequencies up to at least 100 Hz, a view we find sup-
ported by measurements with sinusoidal carriers ~see Sec.
III A, and Fleischer, 1982a, 1983; Fassel and Kohlrausch,
1995, 1996; Dau, 1996; Fassel et al., 1997!.
A somewhat different view about the flatness of TMTFs
for tonal carriers at 4 kHz was put forward in a recent paper
by Strickland and Viemeister ~1997!. Based on data for dis-
crimination between AM and QFM, and on data for detect-
ing QFM, they argued that the thresholds for AM vs QFM at
a modulation frequency of 128 Hz were not just caused by
temporal cues ~as we assume!, but that other, probably spec-
tral cues, were also involved. It is further implied that this
may also be the reason for the flatness in tonal TMTFs at 3
and 5 kHz in Fassel and Kohlrausch ~1996! and Dau ~1996!,
which would undermine one of the assumptions used in our
interpretation. In the following we argue why we find this
implication not convincing.
According to Strickland and Viemeister, the sensitivity
to temporal cues alone would lead to an increase in thresh-
olds for AM vs QFM discrimination above 64-Hz modula-
tion frequency. Only due to the availability of additional
cues, thresholds appear to be flat up to 128 Hz. The usability
of these additional cues is derived from experiments measur-
ing QFM detection. At a 4-kHz carrier frequency and 128-Hz
modulation frequency, QFM detection thresholds are about 8
dB higher than the thresholds for discriminating AM from
QFM. These differences in level make it, in our view, very
difficult to see room for a reasonable contribution of nontem-
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poral cues, unless it was shown that the psychometric func-
tion for QFM detection was sufficiently shallow.
If we compare AM detection thresholds at a wider range
of carrier frequencies, the interpretation by Strickland and
Viemeister leads to the following view. Data by Zwicker
~1952! show that QFM detection thresholds as a function of
modulation frequency decrease earlier for lower than for
higher carrier frequencies and that the shift in shape is about
1 oct in modulation frequency per 1 oct in carrier frequency
~cf. Figs. 10 and 11 in Zwicker, 1952!. If we make the par-
simonous assumption that the contribution of nontemporal
cues to AM vs QFM discrimination follows the same basic
rules across carrier frequencies, the modulation frequency at
which nontemporal cues start to contribute should be lower
than 128 Hz for carrier frequencies below 5 kHz and higher
than 128 Hz for carriers above 5 kHz. Our own results on
AM detection for sinusoidal carriers do not show such be-
havior ~Fassel and Kohlrausch, 1995; Dau, 1996; Fassel
et al., 1997!. For all carrier frequencies between 3 and 10
kHz, AM detection thresholds remain flat up to the same
modulation frequency of about 100 to 130 Hz.
Another problem in interpreting AM detection thresh-
olds is that observers may increase the relative modulation
depth in the AM stimulus by positioning their ‘‘internal ob-
servation filter’’ away from the carrier frequency in such a
way as to better equate the amplitude of the carrier and one
of the sidebands ~e.g., Goldstein, 1967!. The increase in rela-
tive modulation depth resulting from listening off frequency
would improve performance. We think that for 5-kHz carri-
ers and modulation frequencies in the range 0–100 Hz, it is
unlikely that this type of off-frequency listening would be
advantageous, and that subjects most likely monitor the in-
ternal filter at the carrier frequency.
First of all, the ~relative! frequency difference between
carrier and one of the sidebands is no larger than 2%, which
corresponds to about 0.15 ERB or 0.1 Bark. In order to in-
crease the modulation depth m at the output of an off-
frequency filter by 2 dB, this filter would need to have a
slope of 6 dB per 100 Hz ~assuming a constant slope over the
spectrum of the AM stimulus!. This corresponds at 5 kHz to
slopes of about 33 dB/ERB or 56 dB/Bark, values clearly
higher than typical estimates of auditory filter slopes.
In addition, if this effect contributes to AM detection, it
should be even stronger in single-sideband detection. If only
one sideband and the carrier are available, optimal placing of
a filter away from the carrier will increase the degree of
modulation even more than is possible for modulation detec-
tion, where the ~relative! increase of one sideband is accom-
panied by a decrease of the other sideband. Both for 5-kHz
~Dau, 1996! and 10-kHz carriers ~Fassel et al., 1997!,we
found basically flat thresholds for detecting the lower or the
upper sideband up to about 100 Hz. Even more important is
the observation that sideband detection thresholds for larger
spectral distances first increased, before they finally de-
creased. We take this as an indication that monitoring an
off-frequency filter cannot significantly influence TMTFs at
5 kHz for modulation frequencies up to at least 100 Hz.
Alternatively, off-frequency listening could influence
modulation detection for narrow-band carriers by the in-
creased internal modulation depth in the region of upward
spread of excitation. Such a mechanism has been proposed in
the past as one of the sources for the level dependence of
AM detection thresholds for sinusoidal carriers ~e.g.,
Zwicker, 1956; Maiwald, 1967b!. According to Strickland
and Viemeister ~1997!, it also affects thresholds for low
modulation frequencies in the case of bandlimited noise car-
riers. This conclusion was based on the fact that by adding
unmodulated notched noise designed to mask the region of
upward spread of a bandlimited noise carrier, modulation-
detection thresholds increased by up to 7 dB. Based on this
result, it was argued that measuring modulation thresholds
without a notched noise would not reveal true temporal pro-
cessing within the auditory filter centered on the carrier.
Interestingly, the usability of nonlinear upward spread in
modulation detection for noise carriers has been addressed
theoretically and by model simulations earlier by Maiwald
~1967b! and we will recall the relevant points here. In the
region of upward spread, both the inherent fluctuations of the
noise carrier and the applied AM will be enhanced in a simi-
lar way. As long as the intrinsic fluctuations of the carrier are
the limiting factor for modulation detection, the upward
spread region does not allow a better detectability than the
on-frequency region. This contrasts to the situation for sinu-
soidal carriers, where only the applied modulation, but not
the limiting ~internal! noise are enhanced in the region of
upward spread.
Second, if nonlinear upward spread indeed plays such a
significant role as stated by Strickland and Viemeister
~1997!, modulation thresholds for bandlimited noise carriers
should strongly increase with decreasing carrier level, since
the availability of nonlinear upward spread is strongly re-
duced at low and medium carrier levels. Data by Maiwald
~1967b! for a 127-Hz-wide noise carrier at 1 kHz show that
detection thresholds for 4-Hz modulation vary by no more
than 2 dB for a level variation of 60 dB. In contrast, the same
level variation for a sinusoidal carrier reveals a 15-dB effect.
This suggests that the results of Strickland and Viemeister
were not primarily due to the masking of the upward spread
of excitation.
Following from these considerations we conclude that
for the conditions investigated in the present study, monitor-
ing off-frequency filters does not contribute significantly to
modulation detection and we can indeed attribute the thresh-
olds to being based on temporal, rather than on spectral cues.
Of course, in modulation-detection conditions with car-
rier bandwidths larger than a critical band, the influence of
peripheral filtering on the processing of modulation frequen-
cies can no longer be neglected. For such conditions, an ex-
tension of the ‘‘single-channel’’ model is required that al-
lows integration of signal information across frequency.
Such an extension of the single-channel model to a multi-
channel model, that is able to simulate effects of spectral
integration in amplitude-modulation detection and masking,
is described in the accompanying paper ~Dau et al., 1997!.
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B. Modulation filterbank versus modulation low-pass
filter
The modulation filterbank concept proposed here is dif-
ferent both from the previous version of the current model
~cf. Dau et al., 1996a, b! and from models proposed in the
literature ~e.g., Viemeister, 1979!. Both of these models em-
ployed some kind of a modulation low-pass filter. The pre-
vious version of the current model was developed to describe
simultaneous and forward masking data and included a low-
pass filter with a cutoff frequency of 8 Hz. Such low-pass
filtering, however, would fail to describe experiments con-
cerning modulation masking and would also fail to describe
basic experiments concerning modulation detection with
narrow-band carriers at high center frequencies ~cf. Sec.
III A!. The present model allows the prediction of modula-
tion data and, at the same time, preserves the capabilities of
the earlier model for describing simultaneous and nonsimul-
taneous masking data. This is because the linear modulation
low-pass filtering ~with a cutoff frequency at very slow
modulations! is retained in the current model and is com-
bined with the analysis of faster modulations by a modula-
tion filterbank. The idea behind the modulation low-pass fil-
ter approach described in the literature ~cf. Viemeister, 1979!
is that a ‘‘minimum integration time’’ is typically derived
from the cutoff frequency of the low-pass characteristic in
the threshold function as a parameter that describes the au-
ditory system’s temporal resolution ~for a review, see Vie-
meister and Plack, 1993!. Such a model is capable of pre-
dicting a variety of different experiments, for example, the
TMTF for broadband noise carriers ~cf. Fig. 5! and modula-
tion thresholds in third-octave band noise at different center
frequencies ~cf. Fig. 11!. However, a model employing only
a low-pass filter fails to describe the modulation detection
data for a narrow-band noise carrier ~cf. Fleischer, 1982a,
1983!. Furthermore, such a model fails to describe the mask-
ing data using the tone-complex modulation masker. Hence,
the model proposed here considerably expands the class of
experiments that can be modeled correctly while still main-
taining some of the properties and predictions of the model
proposed by Viemeister ~1979!.
C. Intrinsic fluctuations of the noise carrier
In the past, only a few studies have attempted to involve
the inherent statistical properties of the noise carriers in ex-
plaining and modeling TMTFs ~e.g., Zwicker, 1953; Mai-
wald, 1967a, b; Fleischer, 1981, 1982b!. For example, Fleis-
cher ~1981, 1982a, b! investigated TMTFs using narrow-
band noise as the carrier. He developed a model for
describing the interaction between inherent fluctuations
within a noise carrier and the detectability of added modula-
tion. The ‘‘modulation spectrum’’ was weighted by a certain
factor which essentially represented a low-pass characteris-
tic. For modulation frequencies lower than half the band-
width of the noise carrier, this model yields good agreement
with experimental results for modulation detection and
modulation difference limens ~Fleischer, 1981, 1982a,
1982b!. For modulation frequencies larger than half the
bandwidth of the noise carrier, this model would always pre-
dict a low-pass characteristic in the threshold function with-
out regard to the applied carrier bandwidth—in the same way
as shown in Sec. IV for the Viemeister model. Therefore, to
account for the data, Fleischer extended the model by assum-
ing ‘‘cross-talk’’ between the inherent fluctuations of the
noise and the added modulation. He postulated a decay at a
rate of 16 dB per decade of the modulation frequency to
account for the high-pass characteristic in the data. In order
to find a description for the inherent modulation of the noise,
Fleischer ~1981! regarded narrow-band noise with a band-
width D f as a pure tone which was amplitude modulated by
a continuum of equal-amplitude modulation frequencies be-
tween zero and half the bandwidth of the noise. But this
assumption is not correct. It would imply that the modulation
spectrum of noise has a flat rather than a triangular shape, as
shown by Lawson and Uhlenbeck ~1950!~see the Appendix!.
Even though the exact shape of the modulation spectrum
assumed by Fleischer ~1981! was not correct and the subse-
quent explanation of the data was based on a different con-
cept than the one described here, Fleischer’s concept of
cross-talk between inherent envelope fluctuations of the car-
rier noise and the test modulation is compatible with the
bandpass analysis proposed here. Within the modulation fil-
terbank model, the low-pass characteristic of the threshold
function for conditions with f
mod
, D f/2 does not result from
a specific weighing function used to model the ‘‘sluggish-
ness’’ of the auditory system. Instead, it is a consequence of
the intrinsic envelope fluctuations of noise bands and their
spectral distribution on the one hand, and of the logarithmic
scaling of the postulated modulation filters on the other hand.
A critical test for this interpretation would be to obtain
TMTFs for noise carriers with an envelope spectrum differ-
ent from that of Gaussian noise, for example, low-noise
noise ~Hartmann and Pumplin, 1988; Kohlrausch et al.,
1997!.
The current model can also account for the data using
very narrow-band stimuli as the carrier, describing a high-
pass or bandpass characteristic in the threshold function.
VI. CONCLUSIONS
~1! The experiments on modulation detection and modu-
lation masking described here agree well with experiments
from the literature. They provide a strong indication for an
analysis of envelopes in terms of a separation into different
modulation frequencies.
~2! The model of the effective signal processing in the
auditory system proposed here is capable of quantitatively
modeling most aspects of the experiments described. It em-
ploys a modulation filterbank for envelope analysis that ex-
hibits a constant absolute bandwidth for low frequencies and
a constant relative bandwidth for modulation frequencies
above 10 Hz. Within the context of this model, the low-pass
characteristic of the broadband TMTF is due to the inherent
fluctuations of the carrier and constant relative bandwidth of
the modulation filters, and not to a low-pass characteristic
within the auditory system per se.
~3! While the predictions of the model proposed here
agree with some predictions of the modulation low-pass
model by Viemeister ~1979! and an earlier version of the
2903 2903J. Acoust. Soc. Am., Vol. 102, No. 5, Pt. 1, November 1997 Dau
et al.
: Detection and masking with narrow-band carriers

current model ~Dau et al., 1996a, b!, the model also holds for
experiments such as modulation detection for narrow-band
noise carriers, where the modulation low-pass approach
clearly fails.
ACKNOWLEDGMENTS
We would like to thank all our colleagues of the Gra-
duiertenkolleg Psychoakustik at the University of Oldenburg
for fruitful discussions on the content of this paper. We also
thank Brian Moore, Jesko Verhey, Andrew Oxenham, Stefan
Mu
¨
nkner, and Ralf Fassel for their comments and sugges-
tions concerning this study and for their critical reading of
earlier versions of this paper. Two anonymous reviewers also
provided very constructive criticism.
APPENDIX: ENVELOPE SPECTRA OF GAUSSIAN
NOISES
The time-averaged power of the envelope is twice the
average power of the waveform. Hence, it is independent of
the noise bandwidth, as long as the total waveform power is
fixed ~cf. Hartmann and Pumplin, 1988!. Therefore, for ex-
ample, two Gaussian waveforms with the same power but
with different bandwidths, have the same envelope power.
An interesting question is related to the spectral distri-
bution of the envelope power. Lawson and Uhlenbeck ~1950!
calculated the spectrum of the envelope via Fourier trans-
form of the autocorrelation function of the envelope. Assum-
ing a rectangular shape of the power spectrum of the noise,
they showed that the modulation spectrum N5 N(f
mod
), i.e.,
the power spectrum of the ~linear! envelope of the noise, is
given approximately by the formula:
N
D f,
r
~
f
mod
!
'
p
D f
r
d
~
f
mod
!
1
pr
4Df
~
Df2 f
mod
!
, ~A1!
where D f is the noise bandwidth,
r
is the power spectral
density, and f
mod
indicates modulation frequency. Besides
the dc peak represented by the
d
function, an approximately
triangular continuous spectrum results. In the case of the
squared envelope, the modulation spectrum has exactly a tri-
angular shape besides the dc peak. This corresponds to the
Wiener–Chintchin theorem which states that the Fourier
transform of the squared signal equals the autocorrelation of
the spectrum of the signal.
The following aspects are of particular relevance for
modulation-detection experiments using a narrow-band noise
as carrier: For a constant overall level of a noise band, the
total power of intrinsic noise fluctuations, i.e., the total area
under the triangle, remains constant. What changes is the
spectral region over which the envelope spectrum stretches.
Hence, with increasing noise bandwidth, the modulation
spectrum becomes broader and flatter.
1
This modification was motivated by physiological studies on adaptation in
auditory nerve fibres where a comparable ratio of onset and steady state
response was found ~e.g., Smith and Zwislocki, 1975; Westerman and
Smith, 1984!. It was further assumed that the too strong overshoot at the
output of the adaptation model in its original version ~see Dau et al., 1996a,
b! would have a detrimental effect on psychoacoustical threshold predic-
tions. However, the limitation of the onset response by Mu
¨
nkner ~1993!
was found to not have a significant influence on the results in the present
study.
2
The transfer functions of the resonance filters can be derived from the
following recursive function: y
i
5 e
2
p
BD
• e
2 i2
p
f
0
D
• y
i2 1
1 (12e
2
p
BD
)
•x
i
, where B is the filter bandwidth, f
0
is the center frequency of the
resonance filter, and D is the inverse sample rate. The output y
i
at time i
depends on the input x
i
at time i and on the last output value y
i2 1
.
3
The adaptation loops transform fast envelope fluctuations nearly linearly.
However, in the framework of the present model, without any further non-
linearity at a level where the signal envelope has already been extracted, it
would not be possible to simulate a sufficient amount of masking in con-
ditions with random modulation maskers. Particularly, in such masking
experiments, the scaling of the modulation filters would not have an effect
and masked thresholds would not depend on signal modulation frequency
which is in contrast with experimental data ~see also the accompanying
paper by Dau et al., 1997!. A physiological motivation for the calculation
of the envelope of the modulation filter output may be given by the finding
of Langner and Schreiner ~1988! that a much greater percentage of neurons
in the central nucleus of the inferior colliculus of the cat show sensitivity
for modulation rate than for modulation phase, indicating that at this stage
of processing a modulation-rate place coding is performed and modulation
phase information is reduced. Such a coding has already been incorporated
by Hewitt and Meddis ~1994! in a computer model of amplitude-
modulation sensitivity of single units in the IC.
4
Because of the relatively broad tuning of the modulation filters, some en-
ergy of a ~stationary! signal also leaks into the transfer range of the over-
lapping modulation filters tuned to ‘‘higher’’ modulation frequencies. Thus
the internal representation contains signal information in parallel at the
output of several modulation filters, whereas in the original model version
~Dau et al., 1996a, b! only the lowest modulation channel ~low-pass! con-
tributed to the decision. Therefore, in the corresponding calibration experi-
ment, a somewhat higher variance of the internal noise at the output of each
modulation filter is required to satisfy the 1-dB criterion compared to the
variance adjusted with the modulation low-pass approach described in Dau
et al. ~1996a, b!.
5
The optimal detector realized in the model clearly is an application of the
original concept of the optimal detector developed in signal detection
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exactly—the signal itself ~and not the signal with noise! is used for the
correlation with the received signal. It should be noted, as already men-
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is typically not presented in isolation, and that, second, the presence of the
‘‘masker’’ influences the internal representation of the signal in a nonlinear
way. It appears to be an appropriate strategy to extract the internal repre-
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comparable with the situation at the beginning of an actual experiment—
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level of the internal representation of the stimuli. All information about the
signal that is available at this stage of processing, is used in an ‘‘optimal’’
way. That is, information is combined optimally, although, for example,
modulation phase is lost at a certain stage of preprocessing.
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