The role of frequency resolution and temporal resolution
in the detection of frequency modulation
John P. Madden
Speechand Hearing Department,C/eve/andState University,1983 East 24th Street,C/eve/and,
Ohio 44115
(Received30 March 1993; acceptedfor publication26 August 1993)
The experimentinvestigatedsubjects'ability to detect short-durationchangesin frequency.In
an adaptive,2AFC task, three normal-heatingsubjectswere askedto distinguisha sinusoidal
signalthat increasedin frequencyin a seriesof discretestepsfrom a standardthat wasidentical
exceptthat its frequencyincreasedessentiallycontinuously.The signalswere 60 ms in duration
with' center frequenciesof 0.25, 0.5, 1, 2, 3, 4, and 6 kHz. The smallestfrequencyincrease
betweensteps(FI) at which the steppedsignalcould be distinguishedfrom the standardwas
determinedas a functionof the numberof stepsin the signal.As the numberof stepsincreased
and the stepdurationdecreased,the FI at first decreasedand then reacheda roughlyasymptotic
level.Eventually,however,at a certainnumberof steps,the FI increasedrapidly. The data were
analyzedusinga modelof auditorytemporalresolutionthat includeda bank of bandpassfilters,
a nonlinearity, a temporal integrator, and a decisiondevice.The analysisyielded ERDs that
rangedfrom 3.8 to 5.0 ms and did not changesystematicallywith frequency.Det.ectorefficiency
varied considerably,being greatestat 0.5 and 1 kHz, and decliningat higher and lower center
frequencies.
PACS numbers: 43.66.Mk, 43.66.Fe, 43.66.Ba [LLF]
INTRODUCTION
Naturally occurring acousticsignalssuch as speech
contain rapid amplitude and frequencymodulations.The
ability to follow thesemodulationsdepends,in part, on the
temporal resolutioncapacity of the auditory system,and
thus there have been many studiesof auditory temporal
resolution.Most of thesestudieshave involvedeither gap
detection (e.g., Plomp, 1964; Fitzgibbons, 1983; Shailer
and Moore, 1985; Formby and Forrest, 1991) or the temporal modulationtransferfunction (e.g., Viemeister,1979;
Bacon and Viemeister, 1985; Eddins, 1992). Also, Moore
and his colleagues(Moore et al., 1988; Plack and Moore,
1990) measuredthe shapeof the ear'stemporal"window"
by determiningthe thresholdof a brief sinusoidalsignal
precededand followedby noisebursts.The signalsusedin
these experimentschange rapidly in amplitude but are
spectrallystatic. In contrastto the large and growingliterature in this area, the number of studiesof temporal
resolutionusingfrequencymodulated(FM) signalsis very
small. Huffman sequences(Huffman, 1962) have been
used in a few experiments (e.g., Patterson and Green,
1970; Jesteadtet al., 1976), and studiesof the detection of
frequencymodulation in sinusoidshave implicationsfor
temporal acuity (see Kay, 1982, for a review). However,
theseapproacheshaveoftenbeenlimited by the presenceof
spectralartifactsthat can serveas confoundingcues.For
example, the detectability of FM sinusoidsimproves at
rateshigher than 100 Hz, apparentlydue to the resolution
of spectralsidebands(Kay, 1982). Thus, it has been difficult to measurethe auditory temporal resolutionof FM
signals,and it cannotbe assumedthat estimatesof tempo454
J. Acoust. Soc. Am. 95 (1), January 1994
ral resolutionderived from experimentswith signalsthat
changein amplitudealso hold for FM signals.
Feth and his co-workers (Feth et al., 1989; Madden
and Feth, 1992) recently developeda new meansof investigation the temporalprocessingof FM signals.Briefly, in
theseexperimentssubjectswere askedto discriminatebetweentwo FM sinusoidsignals.The standardsignalwas a
glide that made a transition from a lower frequencyto a
higher frequencyover a smooth, linear path. The target
signal,called the step signal,was identical to the standard
except that its trajectory followed a seriesof brief steps.
That is, the step signal remained at one frequencyfor a
brief time beforejumping to the next frequency.The longterm spectraof the standardand the step signalsare very
similar at moderate levels (see Madden and Feth, 1992 for
a spectralcomparison),and spectralartifactsappearnot to
have been a confoundingfactor in thesestudies.A schematic representationof thesesignalsis shownin Fig. 1.
As might be expected, as the number of steps was
increased (while holding overall duration constantand
thereforedecreasingthe duration of the individual steps)
discriminationbecamemore difficult, and listenerperformancedecreasedmonotonicallyto chance.It was inferred
that at the thresholdof discrimination,the internal representationof the step signal is "blurred" by the temporal
processing
systemto a point at which it is indistinguishable
from the standard glide. The results indicated that for a
signal with a center frequency of 1000 Hz, resolution
thresholdsoccurredat stepdurationsof about 5 to 10 ms,
dependingon the subject.The effectsof severalstimulus
parameterson the resolutionof the stepsignalwere noted
(Feth et al., 1989). No effect of overall stimuluslength
was found. Resolution thresholdsdid not changesignifi-
0001-4966/94/95(1)/454/9/$6.00
¸
1994 AcousticalSociety of America
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454
the sizeof the frequencyincrementbetweensteps(the FI).
For example,the F! at the thresholdof discriminationwas
determinedfor a two-stepsignal.That is, the smallestfrequencytransitionat which a two-stepsignalcould be distinguishedfrom a glidelikestandard (describedbelow) of
equal overall duration and transitionsize was determined.
This measurementwas repeatedfor signalswith increasingly greater numbersof stepsat various center frequencies.
I
I
I
I
TIME
FIG. 1. A schematicrepresentationof the step and glide signals.The
glidesignalis representedby the dashedline, the stepsignalby the solid
line.
It was predictedthat as the numberof stepsincreased
(and stepduration decreased,sincethe overall duration of
the signalwas held constant), at first the FI would remain
relatively constant,becausediscriminationwas being limited by frequencyresolution.Eventually, however,as the
number of stepscontinuedto increase,the FI at threshold
would beginto increaseas the limitationsimposedby temporal smoothingbeganto affect discrimination.
I. METHOD
cantly as a function of centerfrequencybetween0.25 and
2 kHz, but generally increasedat 4 kHz. The size of the
frequencytransition also affectedthe results,particularly
at 4 kHz, wherethe averagestepdurationat thresholdof a
signal with a 100-Hz transition (the smallestused) was
betweenthreeand four timesthat of a signalwith a 400-Hz
transition (the largest used). Step size at discrimination
thresholdincreasedfrom lessthan 10 ms for a signalwith
a 400-Hz transition to over 20 ms for a signal with a
100-Hz
transition.
A. Subjects
Three normal-hearingsubjectsparticipated.All had
thresholds
of 15 dB HL
or less at the audiometric
test
frequenciesfrom 250 to 8000 Hz.
B. Stimuli
The main featuresof the signalshavebeendescribedin
the introduction and in the previous studiesmentioned
(Feth et al., 1989;Madden and Feth, 1992). The stepsignals were like those used in Madden
and Feth in that the
In thesestudiesit was assumedthat temporalresolution played the dominant role in limiting discrimination
performance.However, becausethe frequencyincrements
betweenthe stepsdecreasedin magnitudeas stepduration
decreased,it is also possiblethat the resultsreflect limitations imposedby the frequencyresolutioncapabilitiesof
the auditorysystem.Although a rangeof transitionsizes
was used, the effect of frequencyresolutionwas not addressedspecificallyin these studies,and the results are
ambiguousin this respect.If step-glidediscriminationwas
limited entirelyby frequencyresolution,one would expect
a relatively linear decreasein discriminationperformance
with frequency,reflectingthe almostlinear increasein auditory filter bandwidth that occurs above 0.25 kHz
"corners" of the stepswere slightly rounded to minimize
artifactsfrom spectral"splatter." Instead of the glide used
in the two previousstudies,a 17-stepsignalwasusedas the
standard. A 17-step signal contains approximately twice
the number of stepscontainedin a signalof 1-kHz center
frequencyat discriminationthreshold (when the latter is
comparedto a glide). A 17-stepstandardwas usedinstead
of a pure glidebecausethe skirtsof the amplitudespectrum
of a step signalare slightly wider than thoseof the correspondingglide beginningabout 35 dB down from the signal peak. This wideningincreasesvery slowly as the number of steps is increased.Pilot studies have shown that
(Patterson and Moore, 1986), and this was not the casefor
standards at low stimulus levels (35 dB SL). However,
center frequenciesbetween 0.25 and 2 kHz. However, 'it
seemsprobablethat performanceat 4 kHz was affectedby
frequency resolution, since as overall transition size increased,discriminationperformanceincreasedas well. The
major purposeof the study was to clarify this situationby
investigatingthe respectiveroles of frequencyresolution
and temporal resolutionin the discriminationof FM signals of this type.
The experiment is superficially analogous to the
TMTF. In the caseof the TMTF, temporal resolutionis
measuredin termsof depthof amplitudemodulation(e.g.,
thesestudiesalso suggestedthat the spectralwidening of
the stepsignalbecomesperceptibleat higherstimuluslevels (e.g., 55 dB SL). Psychometricfunctionsbecamenonmonotonicat this level in somecases,with percentcorrect
first decreasingand then increasingas the numberof steps
increased.To eliminate any possiblecontamination from
this extraneouscue, the 17-stepstandardwas used.
The stimuli were generatedin real time usingan array
processor (TDT QAP1), played out through a 16-bit
D-to-A converter (TDT QDA2, samplingfrequency=20
kHz) low-passfiltered at 8000 Hz (TDT FSLT3), attenuated (TDT PA3), amplified, and sent to headphones
Viemeister, 1979). At modulation rates above about 2 Hz,
as the amplitude fluctuationsof the signal becomemore
rapid, modulation depth at threshold increases.In the
presentcase,temporal resolutionwas measuredin terms of
455
J. Acoust. Soc. Am., Vol. 95, No. 1, January 1994
there is no difference in the results obtained with the two
(Sennheiser HD450).
The stimulus duration was 60 ms overall, with a 5-ms
rise/fall time. The effectivelength of the stimuli therefore
J.P. Madden: FM detection
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455
was consideredto be 50 ms. Stimuli were generatedat
centerfrequenciesof 0.25, 0.5, 1, 2, 4, and 6 kHz. The size
of the stimulustransitionvariedadaptively.The maximum
overall transition
size was 500 Hz at the 0.25-kHz
center
frequency, 1000 Hz at 0.5 kHz, 2000 Hz at 1 kHz, and
4000 Hz at all other center frequencies.Transition sizes
were dictatedby the limits imposedby centerfrequencies
and by the overall bandwidth availableafter filtering. The
stimuli were presentedat a sensationlevel of 35 dB.
C. Procedure
A two-interval, forced-choice (2AFC) task, in which
the targetwasthe stepsignal,wasusedto determinethe FI
threshold.A three-down,one-up adaptiveprocedurewas
usedthat estimatedthe 79% correctpoint on the psychometric function (Levitt, 1971). That is, after three consec-
utive correctresponsesthe overall frequencytransitionof
the signalswas decreased,thus decreasingthe FI. After
one incorrect responsethe size of the transition was increased.Typically, the size of the increaseor decreasewas
halved after the first four reversals,and thesefour reversals
were discarded.The size of the changevaried, depending
on the centerfrequency.At low centerfrequencies,where
FIs were relatively small, a 10-Hz changein transitionsize
was usedafter the first four reversals.At high center frequencies,where FIs were larger, the changein sizeranged
up to 50 Hz. Further variation in theserules was necessary
in somecasesto accommodatethe rangeof difficultyof the
signals.For more difficult discriminations,involving signals with large numbersof steps,it was useful,to obtain
the most consistentresults,to discardas many as the first
eight reversals.This gave the subjectmore opportunityto
"home in on" the threshold
area. The arithmetic
mean of
the FIs at all reversals after the discarded ones were used
to calculatethe FI for a run. A singlestimulusrun consistedof 100 trials, with a pauseafter the first 50 trials.
At each center frequency,FI thresholdswere determined for step signalscontainingfrom two to as many as
elevensteps.The numberof stepsin a signalwasdefinedas
equal to the number of steady-stateportionsof the signal.
Both the step signal and the standard began and ended
with a steady-stateportion. In general,if a subjectconsistently reached the maximum possibletransition size at a
certain number of steps,signalswith higher numbers of
stepswere not run at that center frequency.
Subjectswere well practicedbeforedata collectionbegan, having servedin severalpilot studiesusingsignalsof
the same type. Data collection was continueduntil discrimination performancewas asymptotic.This meant at
least three runs per signal,each conductedon a different
day. If performancedid not improveon the third run, data
collection was ended for that signal. If the third run
showedimprovementover the second,a fourth run was
carriedout, and soon, until performancefailedto improve.
The data from the last two runs were averaged,and therefore each data point is derived from the results of 200
trials.
Stimulus presentationand responsecollection were
controlledby a PC. Stimulusand responseintervalswere
456
J. Acoust. Soc. Am., Vol. 95, No. 1, January 1994
signaledon a computermonitor. The subjectsenteredtheir
responseson a computer keyboard and received visual
feedbackafter every trial indicatingthe interval containing
the target signal.
II. RESULTS
The individualand averagedresultsare shownfor center frequenciesfrom 0.25 to 1 kHz in Fig. 2(a) and center
frequenciesfrom 2 to 6 kHz in Fig. 2(b). FI at discrimination thresholdis plotted as a function of the number of
stepsin the signal.The three lower centerfrequenciesare
plotted separatelyfrom the four higher centerfrequencies
for clarity. The scale of the y axis used for the higher
frequencies
would resultin a considerable
lossof resolution
if usedfor the lower frequencies.In the caseof the individual subjects,the upper end point of eachplot reflectsthe
maximum possibleFI at that centerfrequency,sincedata
collectionwas terminated at that number of steps.For a
particular center frequency,one subjectoften reachedthe
maximum FI at a smallernumber of stepsthan the other
subjects.For example,S3 reachedthe 6-kHz maximum at
five steps,whereasS2 reachedthe maximum at nine steps.
In the caseof suchsubjects,the FI at the final data point
was usedto calculatethe averageFI for larger numbersof
steps.
Each of the plots in the averageddata can be divided
into two portions.In the first portion,the FI firstdecreases
and then reachesa level that is roughly asymptotic.This
portion of the data can be interpretedas reflectingmainly
the limits imposedon discriminationby the subjects'frequencyresolutioncapacities.The initial decreasein the FI
might be accountedfor by Green and Swets'(1966) multiple look model,which predictsan increasein detectability
proportionalto the squareroot of the number of observations.On average,the FIs alongthis portionof the plot are
similar at 0.25, 5, and 1 kHz, and increase at center fre-
quenciesabove 1 kHz. The increaseabove 1 kHz is expected,becauseabsolutefrequencyresolutiondecreasesas
frequencyincreases.However, the fact that the 0.25-, 5-,
and 1-kHz plotsare nearly superimposed
on one anotheris
somewhatsurprising,in view of the fact that auditoryfilter
bandwidthincreasesalmostlinearlyin this frequencyrange
(Patterson and Moore, 1986). The data are much "nois-
ier" at 4 and 6 kHz, indicating that perhapsthe task is
somehowmore difficult at thesefrequencies.
The secondpart of each plot is marked by an abrupt
increasein the FI. This portion of the plot can be interpreted as reflectingmainly the subjects'temporal resolution capacities.At the point of upturn, temporalresolution
rapidly becomesthe limiting factor in the subjects'ability
to distinguishthe stepsignalfrom the standard.Temporal
smoothingincreasinglyobscuresthe discontinuitiesof the
step signal,and the subjecteventuallyis unableto distinguish it from the standard, even at very high FIs. The
upturn in the FI occurssooner(at smallerstepnumbers)
as centerfrequencyincreases,with the notableexceptionof
the resultsat 0.25 kHz. In the averageddata, at 0.5 and 1
kHz the upturn occursafter eightsteps,but at 4 and 6 kHz
J.P. Madden: FM detection
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456
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thresholds
measured
in termsoffrequency
increment
(FI) between
steps
andplottedasa function
ofthenumber
ofsteps
in the
signal.
Topermit
better
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457
J. Acoust.Soc.Am.,Vol. 95, No. 1, January1994
J.P. Madden:FM detection 457
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FIG. 3. The outputof the auditoryfilter, the temporalintegrator,and the decisiondeviceas a functionof time in response
to a five-stepsignalpassed
through a filter with a centerfrequencyof 940 Hz. Seethe text for further details.
it occursafter only four steps.Thesefrequencyeffectswill
be returned
to in the discussion section.
III. MODELING
THE
A. Components of the model
RESULTS
The shapeof the plots in Fig. 2 resemblesthe curves
found in decrement/increment detection studies, in which
the smallest detectable decrement
duration
is measured as
a function of decrementdepth (Forrest and Green, 1987;
Plack and Moore, 1991). Plack and Moore found that the
shortest detectable decrement
duration
decreased with in-
creasingdecrementdepth. However, as decrementduration became very small, a large increase in decrement
depth (from 5 to 20 dB) was associatedwith only a negligible decreasein decrementduration at threshold.That
is, once duration at threshold fell below about 5 ms, very
large increasesin decrementdepth correspondedto only
small decreases
in decrementduration. Theseresultsparallel the findingsof this study,in which a point is reached
at which further decreasesin step size at threshold are
accompaniedby relativelylarge incrementsin frequency.
These authors, as well as a number of others investi-
gatingtemporal acuity (e.g., Viemeister, 1979;Forrest and
Green, 1987; Shailer and Moore, 1987; Green and Forrest,
1988), have accounted reasonablywell for their results
using a model of temporal resolutionthat incorporatesa
bank of bandpassfilters, eachof which servesas the "front
end" of a channel consistingalso of a nonlinear device,a
temporal window, and a level-detectiondevice. To compare the resultsof this studywith previousstudies,the data
were analyzed with such a model. It was also of interest to
458
determinehow well a model of temporal processingderived from studiesof non-FM signalscould account for
data from FM signals.
J. Acoust. Soc. Am., Vol. 95, No. 1, January 1994
(1) The auditory filters are from Slaney's (1993) implementationof the Patterson-Holdsworthgammatonefilter bank (Patterson et al., 1992), which is based on a
fourth-ordergammatonefilter. The Patterson-Holdsworth
filter has an impulseresponseof the form
g[t] =a •-] cos[•rfct-t-qb]/e
2•røt,
( 1)
wheret is time, g[t] is the impulseresponse,a is amplitude,
n is the order of the filter (4), f½ is the centerfrequencyof
the filter, and b is a parameter that determinesthe bandwidth of the filter. b is equal to 1.019 times the equivalent
rectangular bandwidth (ERB) of the filter. The filter's
transfer function is designedto closelymatch the "roex"
filter often usedto accountfor auditory frequencyresolution (e.g., Pattersonand Moore, 1986). ERBs were determined usingthe formula
ERB = 24.7(4.37f/1000+
1),
where f is the center frequencyof the filter in Hz (Glasberg and Moore, 1990). The top panel of Fig. 3 showsthe
outputof a filter centeredat 940 Hz for a 5-stepsignalwith
a centerfrequencyof 1 kHz.
(2) The nonlinearity convertsthe filtered waveformto
a powerlikequantity by squaringthe instantaneous
amplitude of the filteredwaveforms(as, for example,in Moore,
1989).
J.P. Madden: FM detection
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458
(3) The temporalwindowor integratoris an intensityweightingfunctionthat slidescontinuouslyin time (Moore
TABLE I. Valuesof the model parametersderivedfrom the fitting procedure.ERDs are given in ms and A L is given in dB.
et al., 1988; Plack and Moore, 1990). Becauseof the lim-
Center frequency
ited dynamicrangeof the stimuli usedin this experiment,
the sidesof the window can be modeledby two roex functions of the form:
250
500
1000
2000
4000
6000
ERD
4.8
4.2
5.0
5.0
4.8
3.8
AL
2.0
1.2
1.0
1.0
1.8
2.0
IV(t) ----( 1d-2t/To)exp( -- 2t/To),
Iv(t) = ( 1d-2t/Ta)exp( -- 2t/Ta) ,
determine
the smallest FI at which the threshold
criterion
where t is time relative to the center of the window (t=0
was met. The smallest FI sometimes was obtained
ms), and T o and T a are parametersthat determinethe
sharpness
of the weightingfunctionbeforet=0 and after
t=0, respectively.Testing indicated that the addition of
functionsdescribingthe skirtsof the window had no effect
on the results.The equivalentrectangularduration (ERD)
of the windowis equalto Tod-Ta. Followingthe datafrom
filter at a centerfrequencybelow the startingfrequencyof
the signals.Becausethe magnitude of the filtered signal
decreasedas the center frequency of the filter decreased
below the signal starting frequency, the questionof the
perceptualsalienceof the output of suchfilters on the periphery of the signalhad to be addressed.Somewhatarbitrarily, it was decidedthat only filterswith outputsgreater
than 0.5 times that of the filters centeredat the signal
centerfrequency(and thereforewith the greatestpossible
output level) would be considered.Finally, and alsosomewhat arbitrarily, it was assumedthat the peakscalculated
by the decisiondevicehad to occurabovethe -20-dB level
to be evaluated. For most signals, peaks occurred only
Moore et al. (1988) and Plack and Moore (1990), the
ratio betweenTa and To was held constantat 0.6 as the
ERD was changed.The middle panel of Fig. 3 showsthe
output of the integratorfor the signaldescribedin ( 1). The
frequencychangesof the step signal are now evident as a
seriesof relatively abrupt changesin level, shapedby the
attenuationcharacteristicof that part of the auditoryfilter
that the signalcrossesand by the smoothingaction of the
temporal window.
(4) The decisiondevicecomparesthe output of the
temporal integrator for a step signal with that of the correspondingstandard.It doesso by calculatingthe ratio of
the instantaneouslevel of the step signal to that of the
standard. An example of the output of this operation is
shown in the bottom panel of Fig. 3. The differencesbetween the signalsare shown in dB as a function of time.
The frequencyincrementsof the stepsignalthus are transformed into peaksin the output of the decisiondevicethat
represent departuresfrom the smooth trajectory of the
standardsignal.The assumptionis that the step signalis
distinguished
from the standardby the presenceof one or
more peaksthat equalor exceeda criterionvalue (AL).
B. Predicting the results
The model was used to determine
the ERD
and A L
valuesthat bestpredictedthe FIs of the averageddata. For
each center frequency,ERD and AL valueswere varied
adaptively to minimize the sum of squareddeviationsof
the predictedFIs from the observedFIs. Startingpointsfor
the two parameterswere basedon data from Plack and
Moore's ( 1991) decrement-detection
study.Using a model
with the samebasic components,theseauthors reported
AL values(in their case,the dip in level associatedwith
the decrement)at thresholdin the 2.3- to 2.7-dBrangeand
ERDs in the 3- to 7-ms range.
Assumptionswere made concerningseveralother parametersof the model.The sizeof the predictedFI varied
considerablyas a functionof the relationshipbetweenthe
centerfrequencyof the signaland the centerfrequencyof
the auditory filter through which the signalwas passed.
Therefore,for eachcombinationof ERD and A L, the procedurecycledthrougha rangeof filter centerfrequencies
to
459
J. Acoust. Soc. Am., Vol. 95, No. 1, January 1994
'
with a
above this level.
The
ERDs
and detection
criteria
derived
from
the
model are listed in Table I, and the graphsin Fig. 4 show
the predictionsof the model in comparisonwith the actual
FI thresholdsat the various center frequencies.Overall,
the predictionsmatch the generaltrend of the data reasonably well. With the exceptionof 2 kHz, the model at least
approximatesthe point at which the sharpestincreasein FI
occurs.It is not clear why a better fit could not be achieved
at 2 kHz. The tendency to underestimatethe FIs at the
smallernumbersof stepsin the lower centerfrequenciesis
the only aspectof the predictionswhere the model systematically departsfrom the observedFI values.The FI predicted by the model doesnot changeat the smaller numbers of steps,or changesmuch lessthan the observedFI.
This may mean that the auditory systemneedsto "look" at
more than one or two peaks in the detector output to
achievemaximum efficiency,as was suggestedin the results section.
IV. DISCUSSION
The observedresultsshownin Figs. 2 and 3 indicate
an apparent decreasein temporal resolutionat 0.25 kHz
and above 1 kHz.
Numerous
studies also have noted de-
creasedtemporal resolutionat low frequencies(e.g., Fitzgibbons,1983;Plack and Moore, 1990), and severalexplanationshave been proposedfor this phenomenon.One is
that the relatively slow responseof the auditory filters at
low frequencies may limit temporal resolution (e.g.,
Shailer and Moore, 1983). The "tinging" of the auditory
filtersmay tend to smooththe temporaldetailsof the step
signal at the 0.25-kHz center frequency, but Plack and
Moore (1990) and Moore et al. (1993) found that the
auditory filter had little effect on temporal resolutionat
frequenciesof 100 and 300 Hz, thus castingdoubt on this
J.P. Madden: FM detection
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459
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OF STEPS
FIG. 4. Model predictions
of the FIs at the variousstepnumbersand centerfrequencies.
The opencirclesare the observed
FIs and the linesconnect
the predictedFIs. The linesreachexceedthe rangeof they axisat 1 and2 kHz. The modelwasunableto finda reasonable
setof parametervaluesthat
wouldgenerate
an FI at ten stepsat thesefrequencies.
Data pointsaboveeightstepsat 4 and6 kHz arenot includedsincetheFIs wereconstrained
by
the overall transition
limits.
hypothesis.Both studiesindicate insteadthat the ERD of
the temporalwindowincreasesmarkedlyat frequencies
in
this range.
A trend toward poorer temporal resolution in the
higherfrequencies
is not evidentin any previousstudiesof
which
the author
is aware.
Resolution
thresholds
for
gappedsinusoidshave been shownto be independentof
frequencybetween0.5 and 4 kHz (Formby and Forrest,
1991), and Eddinset al. (1992) provideevidencethat gap
detection
thresholds for narrow-band
noise in this fre-
quencyrangeare independentof frequencyas well, if sig460
J. Acoust.Soc. Am., Vol. 95, No. 1, January 1994
nal bandwidthis held constant.Data from anotherstudy
by Eddins (1993) indicates that the time constant of the
TMTF doesnot vary acrossfrequencyif signalbandwidth
is constant.Plack and Moore (1990) foundthat the equivalentrectangulardurationof the temporalwindowactually
decreasedas a function of frequencyfrom 900 to 8100 Hz.
As is evident from Table I, however, a different inter-
pretationof the data emergesfrom the modelinganalysis.
The ERDs givenin Table I are clusteredin a fairly narrow
range (3.8 to 5.0 ms) and exhibit no clear tendency to
changesystematicallywith frequency.This suggests
that
J.P. Madden: FM detection
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460
the changein performanceevidentin Fig. 2 is not due to
temporal resolutionper se, as reflectedin the width of the
temporal window. It should also be noted that the ERDs
are in the same range as those obtained by Plack and
Moore ( 1991) for decrement detection in wideband noise,
although they are somewhatsmaller than ERDs derived
from experimentsthat estimatethe shapeof the temporal
window (Moore et al., 1988; Plack and Moore, 1990).
Unlike the ERD values, the AL values in Table I ex-
hibit considerablevariation, being roughly one-half as
great at 0.5, 1, and 2 kHz as they are at the other center
frequencies.These are the frequencies,of course,at which
the best performanceis seenin Figs. 2 and 3 in the sense
that the smalleststepdurationsare reachedbeforegreater
FIs are needed for discrimination. The model analysis
thereforeindicatesthat the greaterability to resolveshortduration frequencychangesat thesecenter frequenciesis
due to greaterdetectorefficiency.Plack and Moore (1990)
reportedan effect of frequencyon detectorefficiencyin a
task involving the detectionof a tone burst betweentwo
noisebursts.In this case,however,the pattern was quite
different, as efficiency increasedalmost linearly between
300 and 8100 Hz.
Summarizingthe discussionto this point, it may be
said that the model can account for the data, but the ERD
and AL valuesthat bestpredictthe resultsare at oddswith
the findingsof previousstudies,mainly in that they indicate decreaseddetector efficiencyat high center frequencies. This suggeststhat the same temporal integration
mechanismis involved in the processingof both FM and
non-FM signalsbut that the detectionprocessdiffers.The
obviouscandidatefor the detector differenceis temporal
codingof the waveformthroughneuralsynchrony.In most
mammalianears,synchronyfadesabove2 kHz and is completely absentabove 5 kHz (Rose et al., 1967; Anderson
et al., 1971). This pattern parallelsthat found in the data
of this experiment.Both level of excitationand temporal
information would be availablein the lower frequencies,
but only level information would be presentin the higher
frequencies.It has been argued for some time that the
auditory systemcan make use of temporal coding in frequencydiscriminationtasks involving pulsedtones (e.g.,
Moore, 1973; Moore and Glasberg, 1986). Moore and
Glasberg(1989) contendthat phase-lockinginformationis
used at least to someextent in the detectionof frequency
modulation as well, although their results indicate that
temporalinformationis still presentat 4 kHz. The present
analysisalso suggeststhat the auditory systemmakesuse
of both temporal and level information in tracking these
FM signals.This analysisstill does not account for the
poorer detectorefficiencyat 0.25 kHz, however,sincetemporal information shouldbe availablethere as well.
Some potential confounding factors must be addressed.The subjectsalmostcertainlyexperiencedgreater
changesin SL when listeningto signalsat the higher center
frequenciesthan at the lower centerfrequencies.Sensation
levelswere basedon thresholdsdeterminedusingsignals
with an overall transition size of 400 Hz. At the higher
centerfrequencies,transitionsizeswereconsiderablylarger
461
J. Acoust. Soc. Am., Vol. 95, No. 1, January 1994
than this, extendinginto regionsof reducedsensitivity,and
were larger than the transitionsat the lower frequencies.
The results probably were not greatly affected by these
changes,however,sincepilot testingindicatedthat performance was relatively stable from about 30 to 50 dB SL.
Nevertheless,it is possiblethat the upper endsof the transitionswere not as audibleat the higher centerfrequencies
as at the lower ones.
There is someevidencethat frequencyresolutionworsensfor stimuli of short duration (e.g., Baconand Viemeister, 1985), and this alternativelycould explainthe upturn
in FI at short step durations. If this effect is frequency
dependent,it also could account for the pattern of the
results.This processfails to accountfor certain aspectsof
the data, however. Bacon and Viemeister demonstrated re-
ducedfrequencyresolutionin the detectionof a signalcentered
within
a 1-kHz
masker
of 50-ms
duration.
This
would seemto predict progressivelypoorer frequencyresolution at durations shorter than about 25 ms. Figure 2
indicates
that the FI
at 1000 Hz
does not increase until
step duration decreasesto 7.1 ms. In addition, another
experiment,not reported,measuredthe greatestnumber of
steps,or shorteststepduration,that could be detectedin a
signal for a given overall transition size. Using the same
step-standarddiscriminationtask, the numberof stepswas
varied adaptivelywhile the frequencytransition was held
constant. This procedure was repeated over a range of
transition sizes. To the extent that a worseningof frequencyresolutionwith decreasedstep duration limits performance,stepdetectionshouldhavecontinuedto improve
(larger numbersof stepsshouldhave beendetected) as the
transition size was increased,since the larger FIs would
compensatefor reduced frequency resolution. In fact, as
transition size was increased,performance increased,but
only up to a point, and then leveled off. For example,for
signalsat a center frequencyof 1500 Hz, the detection
threshold was about eight steps for transitions ranging
from 400 to 2000 Hz (FIs of 57 to 286 Hz). It should be
noted that eight stepsalso is about the averagepoint of
upturn for the 1000-Hz signal.The samepattern wasfound
at frequenciesabove 1 kHz.
V. SUMMARY
For a signalthat increasedin frequencyin a stepwise
fashion,the experimentmeasuredthe smallestincrement
in frequencybetweenstepsat which the signal could be
distinguishedfrom a standardsignalthat approximateda
glide. The resultsindicatedthat the subjects'performance
was best for signals at 0.5 and 1 kHz and declined for
signalsaboveand belowthosefrequencies.Analysisusinga
model incorporatingan auditory filter bank, a nonlinearity,
a temporal integratorand a detectiondeviceindicatedthat
these differencesin performanceresulted from increased
detector efficiencyin the midfrequencies.Detection criterion valuesapproximatedthosederivedin previoustemporal resolution experiments.The ERDs derived from the
model did not vary systematicallywith frequency,and valueswere similar to thoseobtainedin previousexperiments
with non-FM signals.
J.P. Madden: FM detection
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461
ACKNOWLEDGMENTS
This research was supported by a grant from the
NIDCD. I would like to thank Bill Jamesfor writing the
programs used in the study. I would also like to thank
Peter Fitzgibbonsand Chris Plack for their insightfuland
helpful comments.
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