Detection of combined frequency and amplitude modulation Brian C.J.
Moore
DepartmentofExperimentalPsychology, University of Cambridge,DowningStreet,CambridgeCB23EB, England Aleksander
Sek
Instituteof,4coustics, ,4damMickiewiczUniversity,60-769Poznan,Poland
(Received6 April 1992;acceptedfor publication6 August1992) This article is concernedwith the detectionof mixed modulation (MM), i.e., simultaneously occurringamplitudemodulation(AM) and frequencymodulation(FM). In experiment1, an adaptivetwo-alternativeforced-choicetaskwasusedto determinethresholdsfor detectingAM alone.Then, thresholdsfor detectingFM weredeterminedfor stimuliwhich had a fixed amountof AM in the signalinterval only. The amountof AM was alwayslessthan the thresholdfor detectingAM alone.The FM thresholdsdependedsignificantlyon the magnitudeof the coexistingAM. For low modulationrates (4, 16, and 64 Hz), the FM
thresholdsdid not dependsignificantlyon the relativephaseof modulationfor the FM and AM. For a high modulationrate (256 Hz) strongeffectsof modulatorphasewereobserved. Thesephaseeffectsare aspredictedby the modelproposedby Hartmann and Hnath [Acustica 50, 297-312 (1982) ], which assumesthat detectionof modulationat modulationfrequencies higherthan the criticalmodulationfrequencyis basedon detectionof the lowersidebandin the modulatedsignal'sspectrum.In the secondexperiment,psychometric functionswere measuredfor the detectionof AM aloneand FM alone,usingmodulationratesof 4 and 16 Hz. Resultsshowedthat, for eachtypeof modulation,d' is approximatelya linearfunctionof the squareof the modulationindex.Applicationof this findingto the resultsof experiment1 suggested that, at low modulationrates,FM and AM are not detectedby completely independentmechanisms. In the third experiment,psychometricfunctionswereagain measuredfor the detectionof AM aloneand FM alone,usinga 10-Hz modulationrate. Detectabilitywasthen measuredfor combinedAM and FM, with modulationdepthsselected sothat eachtypeof modulationwouldbeequally.detectable if presented alone.Significant effectsof relativemodulatorphasewerefoundwhendetectabilitywasrelativelyhigh. These effectswerenot correctlypredictedby eithera single-bandexcitation-patternmodelor a multiple-bandexcitation-pattern model.However,the detectabilityof the combinedAM and FM wasbetterthan wouldbe predictedif the two typesof modulationwerecodedcompletely independently. PACS numbers:43.66.Fe, 43.66.Ba, 43.66.Lj
INTRODUCTION
The Zwicker-Maiwald modelisessentiallya placemodel basedon the conceptof the psychoacoustic excitationpatThe perceptionand detectionof changesin the ampli- tern (Zwicker, 1956, 1970). The excitationpattern of a tude and frequencyof soundhasbeenextensivelydiscussed soundcanbe definedasthe outputof the auditoryfiltersasa function of center frequency,in responseto that sound in the psychoacoustic literature (Allanson and Newell, 1966; Coninx, 1978a; Feth, 1972; Hartmann and Hnath, (Moore andGlasberg,1983,1987). The modelassumes that 1982;Maiwald, 1967;Ozimek and Sek, 1987;Zwicker, 1952, changesin either amplitudeor frequencyare detectedby monitoringthe singlepoint on the excitationpattern that 1956). Thesestudieshaveledto twobasichypotheses on the changesmost;this is equivalentto monitoringa singleaudiperceptionof amplitudeand/or frequencychangesin an tory filter. Detectionof changesin amplitudeor frequency acousticsignal.One (Zwicker, 1956, 1962;Maiwald, 1967) occurswhen the changein the excitationpattern exceedsa postulates that a singlemechanismisresponsible for the percriterion amount, assumedby Zwicker (1956, 1970) to be ceptionof changesin amplitudeandfrequency.We will refer to this as the "single-mechanism" hypothesis.The other approximately1 dB. Some more recent models assume that information can (Feth, 1972,Coninx, 1978a)postulatesthe existenceof two be combinedover a certainregionof the excitationpattern independentmechanisms,one for amplitude changesand (equivalentto monitoringseveralauditory filters simultaonefor frequencychanges.We will referto this asthe "indeneously) (Florentine and Buus, 1981;Moore and Glasberg, pendent-mechanisms" hypothesis. 3119
J. Acoust.Soc. Am. 92 (6), December 1992
0001-4966/92/123119-13500.80
¸ 1992 AcousticalSociety of America
3119
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1989). For example,the modelproposedby Florentineand Buus ( 1981 ) assumesthat information from the entire exci-
tation pattern (i.e., from eachexcitedcriticalband or auditory filter) is combinedin an optimal way. However, within the frameworkof thesemodels,it is still possibleto envisage a singledetectionmechanismfor changesin amplitudeand frequency;both couldbe detectedby virtue of the changesin excitationlevel that they produce. One approachto evaluatingthesemodelsis to usesignals with simultaneousamplitude modulation (AM) and frequencymodulation (FM). This type of modulation is usuallycalledmixedmodulation(MM). Studiesof thistype have been carried out by Zwicker (1962), Allanson and Newell (1966), Feth (1972), Coninx (1978a,b), Hartmann
and Hnath (1982) and Ozimek and Sek (1987). According to the single-mechanism hypothesis,onewould expectthat the perceptionof amplitudechangeswould dependon coexisting frequencychangesand vice versa.Accordingto the independent-mechanisms hypothesis,onewouldexpectthat perceptionof amplitudechangeswould be independentof coexistingfrequencychangesand vice versa.Also, for the single-mechanism hypothesisthe relativephaseof the modulatorsfor AM and FM should play an important role, whereasfor the independent-mechanisms hypothesisrelative phaseshouldbe unimportant. Zwicker (1962) comparedthe sensations producedby AM, FM, and MM of an octave-widenoiseband.The upper sideof its excitationpattern was maskedby a second,fixed band of noise. The modulation
rate was either 3 or 10 Hz. He
found that the subjectivemodulation "strength" produced by FM couldbe either increasedor decreasedby the addition of AM, dependingon the relative modulationphaseof the
trum, sincethe highersidebandis completelymasked.This appliedto AM, FM, and MM signals,consistentwith a single-mechanism hypothesisfor high modulationfrequencies. Ozimek and Sek (1987) alsoinvestigatedthe detectability of MM, usingboth low andhighmodulatingfrequencies. For high modulation frequencies,they found, like Hartmann and Hnath (1982), that detection of modulation is based exclusivelyon the lower sideband of the modulated
signal.They alsofoundthat, at low modulationfrequencies, amountsof FM and AM that were separately"sub-threshold" could be detected. However, it is unclear whether this
reflectsthe ability of subjectsto combineinformationfrom independentsources,or whether it reflectsa summationof sensations, asassumedin the single-mechanism hypothesis. Ozimek and Sekonly usedin-phasemodulationfor the MM signal,so it is not known whether modulatorphaseaffects the results,aswouldbe expectedfrom the single-mechanism hypothesis. This overview of the literature indicates that, at least for low modulation rates, there is no clear consensusas to
whether the single-mechanism hypothesisor the independent-mechanisms hypothesisis correct.This article reports an attempt to evaluatethesemechanismsby studyingthe detectionof (MM). In the first experiment,thresholdswere initially determinedfor detectingAM aloneand FM alone, usinga two-alternativeforced-choice task.Then, thresholds for detectingFM were determinedfor stimuliwhich had a fixedamountof AM in the signalinterval only. The amount of AM wasalwayslessthan the thresholdfor detectingAM alone.The relativephaseof modulationfor the AM and FM was systematicallyvaried.
FM and AM. He concluded that, for noise bands, the sensa-
I. TEMPORAL
tions produced by amplitude change and by frequency changeare basedon the samemechanism. The perceptionof MM signalswith clearlyaudiblemodulation depthswasalsoinvestigatedby Coninx (1978b). In addition, he measuredthresholdsfor detectingcombined differences in frequencyand amplitude(Coninx, 1978a). In somecases,the modulatedsinusoidswere presentedwith a noiseband intendedto maskthe uppersideof the excitation pattern. In most cases,he found that the resultswere not affectedby the relativephaseof the modulatorsfor AM and FM, whichhe interpretedasindicatingessentiallyindependent mechanismsfor the detectionand perceptionof FM and AM. Where phaseeffectswere found, he interpreted thesein termsof the influenceof amplitudeon pitch or frequencyon loudness(Czajkowskaet al., 1988).
MIXED
Hartmann and Hnath (1982) extended the model advanced by Goldstein (1967) to account for differencesin
modulationperceptionat low andhigh modulationfrequencies.For a sinusoidalcarrier and low modulationfrequencies,the perceptis of a puretonethat is changingin pitchor loudness.For high modulation frequencies,for which the spectrumof the modulatedsignalcoversa frequencyrange greater than one critical band, the perceptis of a steady soundthat may have an impure tone quality.Their results suggestedthat modulation detectionat high modulation ratesis basedexclusivelyon the lower sidebandof the spec3120
J. Acoust. Soc. Am., Vol. 92, No. 6, December 1992
AND SPECTRAL
MODULATION
STRUCTURE
OF A
SIGNAL
In this section,we givea brief descriptionof the temporal and spectralstructureof the MM stimuli usedin our experiments. FollowingOzimekandSek (1987), the instantaneousamplitudeof a MM signalcanbe written
A(t) = Ao[ 1 + m cos(co,• t -{-•) ]
X cos[COo t -{-/3sin(corot -{-O)],
(1)
wheret is time,Ao is the envelopeamplitudeof the unmodulated signal,m and/3are the modulationindicesfor AM and FM, respectively,COrn is the modulationfrequency,COo is the carrier frequency,and ß and O are terms representingthe phaseof the modulation.The phasedifferencebetweenthe modulatingsignals,A4, is ß- O. When A4 = 0, a maximum in frequencycoincideswith a maximumin amplitude. In our experiments,we usedvaluesfor A4 of 0, •r/2, •r, and 3•r/2. Following the argumentspresentedby Ozimek and Sek (1987), it may be shownthat the spectrumof a MM signalconsistsprimarily of three componentsof which the middle one correspondsto the carrier, while the two sidebandsare the resultof the modulationprocess.The relative amplitudesand phasesof the sidebandsdependon the value of A4. Figure 1(a)-(d) illustratesthe temporaland spectral structureof MM signalsfor A4 = 0, •r/2, •r, and 3•r/2, reB.C.J. Moore and A. Sek: Detection of mixed modulation
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A(t): Aocos•ot+ (Ao/2)(m-/t)cos(•o-•m)f+(Ao/2)(m+ •)cos(•o+•m)t
A(t): AoCOS•ot+ (Ao/2)(-m-•)cos(•o-•m)t +(Ao/2)(-m+• )cos(• o+•m)t
TIME
TIME
•o-•m
•o-•rn •o •o't'•rn
•O
FREQUENCY
SIDEBANDS:
(a)
•o't'•rn
FREQUENCY
SIDEBANDS:
Al=(Ao/2)(m-•)
Au:(Ao/2)(m+/•)
Al=(Ao?2)(-m-/•)
(c)
Au=(Ao/2)(-m+/•)
b½=3•/2 A(t)= A•,cOs•ot+
A(t)= Aocos•ot+ (Ao/2)(-rnsin(•o-•m)t-/tcos(•o-•m)t)+ (Ao/2)(msin(•o +•m)'f+•cøS(•o+•m)'f)
(Ao/2)(msin(•o-•m•t-/tcos(•o-•m)f)+
(Ao/2)(-rnsin(•o +•m)t+,Scøs(•o +•m)t)
i,i
TIME
TIME
•o--•m •
•o-•m FREQUENCY
SIDEBANDS:
(b)
Al=(Ao/2)•(m2+j •2) Au=(Ao/2)•(rn2+j ?)
i'•
FREQUENCY
SIDEBANDS:
(d)
Al=(Ao/2)•(rn2+• 2) Au=(Ao/2)•(m2+j ?)
FIG. 1.The timepattern(top) andspectralstructure(bottom) of mixedmodulationsignals.Eachpanelshowsa differentrelativephaseof the modulators for AM and FM: (a) A•b= 0; (b) A•b= •r/2; (c) A•b=• (d) A•b= 3•r/2.
spectively.Each panelshows:an expression for the instantaneousamplitudeof the MM signalin terms of its three largest Fourier components;a portion of the waveform for m -- 0.5 and•/-- 20 (valuesof theseparameterswereselected sothat amplitudeand frequencychangescouldeasilybe
seen);the spectrumof the MM signal;and expressions for 3121
J. Acoust. Soc. Am., Vol. 92, No. 6, December 1992
the amplitudevaluesof the sidebands.When A• -- 0 [Fig. 1(a) ], the amplitudesof the sidebandsare proportionalto the sum (upper sideband)and difference(lower sideband) of the modulationindicesm and •/. When A• -- •r/2 [Fig. 1(b) ], the sidebandshaveequalamplitudesproportionalto the vectorsumof the two modulationindices.When A• = •r B.C.J. Moore and A. Sek: Detection of mixed modulation
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[ Fig. 1(c) ], the amplitudesof the sidebandsare proportional to the difference(upper sideband) and sum (lower sideband) of the modulationindicesm and/3.When A& = 3rr/2 [Fig. 1(d)], the amplitudespectrumis the sameas when A& = rr/2; the sidebands haveequalamplitudesproportional to the vector sum of the two modulation indices. However,
the phase spectrum is different for A&=rc/2 Ad•- 3rr/2.
II. EXPERIMENT
MIXED
1' THRESHOLDS MODULATION
and
FOR DETECTING
A. Method 1. Stimuli
The carrier signalwasalwaysa sinusoidwith frequency fo = COo/2rr = 1000Hz andlevel70 dB SPL. The modulator was a sinusoidwith frequencyfm= com/2rr= 4, 16, 64, or 256 Hz. The valuesforfro were selectedso as to coverthree different perceptualranges. For fm= 4 and 16 Hz, the changesin amplitudeand frequencycan be heard as such. For fr• = 64 Hz, the fluctuationsare too fast to follow, and the sound has a certain "roughness" (Terhardt, 1974; Kemp, 1982). Forfro = 256 Hz, the soundqualitybecomes smoother, and individual sidebands may be perceived (Hartmann and Hnath, 1982; Ozimek and Sek, 1987). The signalswere digitally generatedusinga Masscomp
5400computersystemvia a 16-bitdigital-to-analogconverter (DAC, model DA04H) at a samplingfrequencyof 10 kHz. The output of the DAC was low-passfiltered (Fern EF 16, 100dB/oct) with a cutofffrequencyof 4 kHz, passed through a manual attenuatorand deliveredto one earpiece of a Sennheiser HD
414 headset.
tracksthe point on the psychometricfunctioncorresponding to 79.4% correct (Levitt, 1971 ). The modulation index was
changedby a factorof 1.5until four reversalshad occurred, and by a factor of 1.26 for the rest of the run. For each thresholdmeasurement,12 turnpoints were obtained;the thresholdwascalculatedasthe geometricmeanvalueof the modulation index at the last eight turnpoints.Thresholds presentedare the averageof at leastfive (usuallymorethan five) single thresholddeterminations.When the standard deviation of the mean value was more than 15% of the mean, at least one additional threshold estimate was obtained, and
all estimateswere averaged. Subjectsweretestedin a double-walledsound-attenuating chamber.Their task wasto indicate (by pushingan appropriatebutton) whetherthe firstor the secondstimulusin a pair was modulatedin amplitudeor frequency.Correctanswerfeedbackwasprovidedby lightson the response box. 3. Subjects
Three subjectswith normal hearing at all audiometic frequencieswere used.One was author AS. The other two subjectswere paid for their services.Two subjects(AS and RO) were experiencedin similar tasks,while one, KR, had no previousexperience.All subjectsweretraineduntil their performanceappearedto be stable. B. Results
Thresholdsfor detectingAM alone and FM alone are shownin Fig. 2. The resultsare very similaracrosssubjects and are consistentwith thoseobtainedby Zwicker (1952), Goldstein (1967), Schorer (1986), and Ozimek and Sek
(1987). When AM and FM soundshaveequalmodulation
On each trial, two successivestimuli were presented, one modulated and the other unmodulated.
The order of the
two stimuli in eachpair wasrandom.Each stimulushad an overalldurationof 1000ms,includingraised-cosine rise/fall t
times of 50 ms. The time interval between the stimuli was
i
i
i
i
iiii. = =
.
500 ms.
.
.
Initially, thresholdsfor detectingAM alone and FM alone were determinedfor eachmodulationfrequency.The thresholdmodulationindex for AM will be denotedby mth and that for FM by/3th. Next, thresholdswere measuredfor detectingFM, when that FM was combinedwith "subthreshold"amountsof AM at the samemodulationfrequency. In this stageof the experiment,the stimulusin the signal interval was both amplitude and frequency modulated, while the other stimulus was unmodulated.
Within
.
a•
0.1
x
a block o
of trials, the amount of AM (m) was held constant, and the amount of FM (/3) was varied to determine threshold. Val-
uesof m usedwere0.2ruth,0.4ruth,0.6ruth,0.Broth,and ruth. Four valuesof A&, the phaseshift betweenthe modulators for AM and FM, were used,namely 0, rr/2, rr, and 3rr/2.
7- 0.01 -
AM
-
0
An adaptive two-alternative forced-choice (2AFC) procedurewasused.The modulationindex (either m or/3) was increasedafter one incorrect responseand decreased after three successivecorrect responses.This procedure 3122
J. Acobst.Soc. Am., Vol. 92, No. 6, December1992
RO AS KR
ß
o ..
0.001
2. Procedure
FM
I
I
I I IIIll
,
,
, , ,,,ll
10
Modulation
•
,
, , ,,,,
1O0
Rate
1000
Hz
FIG. 2. The modulationindex requiredfor thresholdfor AM (open symbols) and FM (closedsymbols)plottedas a functionof modulationfrequency.Each symbolrepresents resultsfor a differentsubject.
B.C.J. Moore and A. Sek: Detectionof mixedmodulation
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indices (rn --/3), and when the indices are small, the AM
and FM soundshavethe sameamplitudespectrumbut differentphasespectrœFor the two highermodulationrates, the phasespectrumevidentlyplaysno role,since,at threshold, the modulation index is the samefor AM and FM. However, for the two lowestmodulation rates,the thresholdsare
clearly lower for AM than for FM, indicatinga monaural phaseeffect.The criticalmodulationfrequencyis between 16 and 64 Hz, consistentwith the data of Schorer (1986),
who founda critical modulationfrequencyslightlylessthan 64 Hz for a 1-kHz carrier at 50 dB SPL.
The thresholdsfor detectingFM in the presenceof fixed "sub-threshold"amountsof AM are shown in Fig. 3 for modulationfrequencies up to 64 Hz. The abscissa showsthe fixedamountof AM asa proportionof the "threshold"value (as shownin Fig. 2 ) for eachsubject,andthe ordinateshows the amountof FM requiredfor thresholdwith the MM stimulus,plottedas a percentageof the thresholdfor FM alone. The parameteris the phaseshiftbetweenthe AM and FM, A•b.Eachcolumnshowsresultsfor onemodulationfrequency, while eachrow showsresultsfor one subject. The results for the cases where the fixed amount of AM
wasequalto the thresholdfor AM alone( 100% on the abscissa) need to be treated with caution. In theory, the AM alone shouldhave beensufficientto give the 79.4% correct
responses neededfor "threshold."However,becausethe valueof/3waschangedby a certainfactorin the adaptiveprocedure, and was never allowed to becomezero or negative,a positivevalueof/3 wasalwaysobtainedfor "threshold"in
the MM case.The "thresholds"in thesecaseswerenot properly determinedby the adaptiveprocedureand werehighly variable;that is why the pointsin the figurecorrespondingto thesethresholdsare not connectedby the linesthrough the
otherpoints.This problemmayalsohavehadsomeeffecton the thresholdsestimatedwhenthe amountof AM wasa high proportionof its thresholdvalue. For fixed amounts of AM
less than the threshold for
AM alone(pointsjoinedby linesin Fig. 3), the amountof FM requiredfor thresholddecreased asthe fixedamountof AM increased.This effect was rather large at the lowest modulationfrequency(4 Hz, left column), and decreased somewhatas the modulationfrequencyincreasedto 16 Hz (middle column) and 64 Hz (right column). However, therewasno cleareffectof the relativemodulatorphase,A•. The thresholds for fixed amounts of AM
less than the
thresholdfor AM aloneweresubjectedto an analysisof variance (ANOVA) with factorssubjects,modulationrate, AM depth,andrelativemodulatorphase.The varianceassociated with the four-way interactionwasusedas an estimateof the residualvariance.The main effectsof subjects,modulation rate, and AM depth were all highly significant (p < 0.001). Thresholdswerelower for the lower modulation ratesandthe highervaluesof AM depth.However,the effect of relative modulator phase was not significant; F(3,36) = 1.23,p = 0.308. Sincethe resultswere very similar acrosssubjectsand acrossthe valuesof A•, they wereaveragedacrosssubjects andphasevaluesto givea clearerindicationof the effectsof the fixed amount of AM and of modulation rate. The results
areshownin Fig. 4. The dashedlineshowsthepredictions of a model that will be describedlater. These averaged data showan orderly decreasein the amountof FM requiredfor fmod=4Hz
fmod =16Hz
fmod=64Hz
120
100 80
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predictions
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Depth of AM as ß AM threshold FIG. 3. Thresholdsfor detectingFM in the presence of a fixedamountof AM, for modulationfrequenciesof 4, 16, and 64 Hz. Thresholdsare expressedas a percentageof the thresholdmeasuredfor the detectionFM alone.The amountof AM is expressed asa percentage of the thresholdfor detectingAM alone.Eachsymbolshowsresultsfor a differentvalueof A•b, the phaseshiftbetweenthe modulatorsfor AM and FM. 3123
_
o
_c
2o o
4O
J. Acoust. Soc. Am., Vol. 92, No. 6, December 1992
I 0
I 20
I 40
I 60
I 80
I loo
Depfh of AM as •o AM ,hreshold FIG. 4. As Fig. 3, but showingresultsaveragedacrosssubjects andmodulator phases. Eachsymbolshowsresultsfor a differentmodulationfrequency. The dashedline showspredictionsof a modelassuming independent mechanisms for the detection
of AM
and FM.
B.C.J. Moore and A. Sek: Detectionof mixed modulation
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thresholdasthe fixedamount of AM is increased.They also confirm that the decrease tends to be smaller as the modulation rate increases.
Figure 5 showsresultsfor eachsubjectusinga modulation frequencyof 256 Hz. Here, therewerevery largeeffects of relativemodulatorphase,A•b.For A•b= 0, i.e., whenthe maximain amplitudeand frequencywere coincident,an increasein AM depth (m) causedan increasein the FM index (•) requiredfor threshold.In other words,the coexisting AM made the FM harder to detect.An oppositeeffectwas observedfor A• -- •r; an increasein m causeda significant decrease the value of /• required for threshold. For A4 = •r/2 or 3•r/2, the valuesof/• requiredfor threshold decreasedslightlywith increasingm. At this modulationrate, the sidebandsin the spectrum would probablybe resolvedin the auditory system.Thus a descriptionof the modulatedsignalin termsof its temporal structure(i.e., as changesin frequencyand amplitudeover time) is not appropriatein this case.The resultsshownin Fig. 5 can be predictedon the basisof the spectralstructure of the modulatedsignaland the frequencyselectivityof the auditory system.These predictionsare presentedin Sec. VI
B.
ing at 16 Hz. Initially, we tried usinga 2AFC taskwith the modulationindex fixedfor a block of 55 trials, treatingthe first five trials as practice.However, we found that performance at low modulation depths was often erratic, and worsethan wouldbeexpectedfrom the thresholdsmeasured usingthe adaptiveprocedureof experiment1. It appeared that subjectshad difficultyin "knowing what to listenfor" when the modulationdepth was fixed at a low value (for a similar effect in simple signal detection, see Taylor and Forbes, 1983).
To overcomethis problem,we modifiedthe procedure so that five different modulation depthswere usedin each blockof 55 trials.The highestmodulationdepthwaschosen to be rather easily detectable(typically giving 93%-99% correct responses),and the first five trials within a block
werepracticetrialsat thismodulationdepth,to helpthe subjectto "homein" on the appropriatedetectioncues.The remaining50 trials were test trials. In the first five of these, the modulation depth started at the highestvalue and decreasedprogressively to the lowest.This wasthen repeated for the next five, and soon. Thus the subjectwaspresented with an "easy" stimulusevery five trials, as a reminder of what to listenfor. The five valuesof modulationdepthwere chosenon the basisof pilot data so as to give valuesof d' between about 0.25 and 2.8 (values of % correct between
III. EXPERIMENT
2
In this experiment,we determinedpsychometricfunctions for the detection of AM alone and FM alone. The basic
aim was to establishhow the detectability index d' varied with modulationdepth. The resultsare usedlater in this paperto predictthresholdsfor the MM datapresentedabove on the basisof the single-mechanism hypothesisand the independent-mechanisms hypothesis. A. Method
The stimuli had the samefrequency,leveland time pattern asin experiment1. Modulation frequenciesof 4 and 16 Hz wereused.The subjectswerethe sameasfor experiment 1. Unfortunately, subjectAS was not able to completetest-
about 57 and 98). Twenty blocksof trials were run for each modulation frequencyand type of modulation (AM or FM), soeachpoint on eachpsychometri'c functionis based on 200 judgments. B. Results
The percentcorrectvalueswere convertedto valuesof d' (Green and Swets, 1974; Hacker and Ratcliff, 1979). In a few cases,three or fewer errors were made in the 200 trials
for a givencondition.It is not possibleto make an accurate estimateof d' in such cases,so they were excludedfrom furtheranalysis.Hence,the data presentedarebasedonlyon stimulifor which the percentcorrectwas98% or less.Analysisof the resultssuggested that d' wasapproximatelya linear functionof the modulationindex squared,for both AM and FM. Hence, valuesof d' are plotted as a function of
1000m 2or• 2in Figs.6 and7. Left-handpanelsshowresults AS
R0
180P
for AM detectionand right-handpanelsshowresultsfor FM detection.The diagonalline in each panel showsthe bestfitting straightline, constrainedto passthroughthe origin. As canbe seen,theselinesgenerallyfit the data ratherwell;
KR
+
+
all deviations from the fitted lines are within the limits of
experimentalerror. Theseresultsare consistentwith those reportedby Sheftand Yost (1989) for the detectionof AM usinga sinusoidalcarrier,andby Irwin (1989) for thedetection of 10-Hz AM of Gaussiannoise;their data alsosuggest that d' is a linear function of m 2.
IV. EVALUATION
0
¸ 0
20
40
60
80
100
0
20
40
60
80
100
MECHANISMS 0
20
40
60
80
100
Depth of AM as •[ AM fhr'eshold
FIG. 5. As Fig. 3, but showingresultsfor a modulationfrequencyof 256 Hz. 3124
J. Acoust. Soc. Am., Vol. 92, No. 6, December 1992
OF THE INDEPENDENT-
HYPOTHESIS
In this section,we considerpredictionsbasedon the independent-mechanisms hypothesis,withoutassumingany specificdetectionmechanisms for AM or FM. Let •th correB.C.J. Moore and A. Sek: Detection of mixed modulation
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fmod =16 Hz
fmod=4Hz AM
FM
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d'=133,m2
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ß
i
,
ß
i
ß
i
,
i
,
i
i
,
i
,
2
i
,
3
i
,
4
i
,
5
i
6
,
7
0.00
0.05
0.09
0.14
,
m2.1000
•2
2.2
d' =2.89*/52
0'61/ d':640*m 2 0.0 I• 0
FIG. 7. As Fig. 6, but for a modulationfrequencyof 16 Hz.
KR
1.7
.
, I
,
i 2
,
i 3
,
• 4
m2. !000
Consider a situation like that used in experiment 1, wherethe AM modulationindexis fixedat someproportion, P(
Moore
DepartmentofExperimentalPsychology, University of Cambridge,DowningStreet,CambridgeCB23EB, England Aleksander
Sek
Instituteof,4coustics, ,4damMickiewiczUniversity,60-769Poznan,Poland
(Received6 April 1992;acceptedfor publication6 August1992) This article is concernedwith the detectionof mixed modulation (MM), i.e., simultaneously occurringamplitudemodulation(AM) and frequencymodulation(FM). In experiment1, an adaptivetwo-alternativeforced-choicetaskwasusedto determinethresholdsfor detectingAM alone.Then, thresholdsfor detectingFM weredeterminedfor stimuliwhich had a fixed amountof AM in the signalinterval only. The amountof AM was alwayslessthan the thresholdfor detectingAM alone.The FM thresholdsdependedsignificantlyon the magnitudeof the coexistingAM. For low modulationrates (4, 16, and 64 Hz), the FM
thresholdsdid not dependsignificantlyon the relativephaseof modulationfor the FM and AM. For a high modulationrate (256 Hz) strongeffectsof modulatorphasewereobserved. Thesephaseeffectsare aspredictedby the modelproposedby Hartmann and Hnath [Acustica 50, 297-312 (1982) ], which assumesthat detectionof modulationat modulationfrequencies higherthan the criticalmodulationfrequencyis basedon detectionof the lowersidebandin the modulatedsignal'sspectrum.In the secondexperiment,psychometric functionswere measuredfor the detectionof AM aloneand FM alone,usingmodulationratesof 4 and 16 Hz. Resultsshowedthat, for eachtypeof modulation,d' is approximatelya linearfunctionof the squareof the modulationindex.Applicationof this findingto the resultsof experiment1 suggested that, at low modulationrates,FM and AM are not detectedby completely independentmechanisms. In the third experiment,psychometricfunctionswereagain measuredfor the detectionof AM aloneand FM alone,usinga 10-Hz modulationrate. Detectabilitywasthen measuredfor combinedAM and FM, with modulationdepthsselected sothat eachtypeof modulationwouldbeequally.detectable if presented alone.Significant effectsof relativemodulatorphasewerefoundwhendetectabilitywasrelativelyhigh. These effectswerenot correctlypredictedby eithera single-bandexcitation-patternmodelor a multiple-bandexcitation-pattern model.However,the detectabilityof the combinedAM and FM wasbetterthan wouldbe predictedif the two typesof modulationwerecodedcompletely independently. PACS numbers:43.66.Fe, 43.66.Ba, 43.66.Lj
INTRODUCTION
The Zwicker-Maiwald modelisessentiallya placemodel basedon the conceptof the psychoacoustic excitationpatThe perceptionand detectionof changesin the ampli- tern (Zwicker, 1956, 1970). The excitationpattern of a tude and frequencyof soundhasbeenextensivelydiscussed soundcanbe definedasthe outputof the auditoryfiltersasa function of center frequency,in responseto that sound in the psychoacoustic literature (Allanson and Newell, 1966; Coninx, 1978a; Feth, 1972; Hartmann and Hnath, (Moore andGlasberg,1983,1987). The modelassumes that 1982;Maiwald, 1967;Ozimek and Sek, 1987;Zwicker, 1952, changesin either amplitudeor frequencyare detectedby monitoringthe singlepoint on the excitationpattern that 1956). Thesestudieshaveledto twobasichypotheses on the changesmost;this is equivalentto monitoringa singleaudiperceptionof amplitudeand/or frequencychangesin an tory filter. Detectionof changesin amplitudeor frequency acousticsignal.One (Zwicker, 1956, 1962;Maiwald, 1967) occurswhen the changein the excitationpattern exceedsa postulates that a singlemechanismisresponsible for the percriterion amount, assumedby Zwicker (1956, 1970) to be ceptionof changesin amplitudeandfrequency.We will refer to this as the "single-mechanism" hypothesis.The other approximately1 dB. Some more recent models assume that information can (Feth, 1972,Coninx, 1978a)postulatesthe existenceof two be combinedover a certainregionof the excitationpattern independentmechanisms,one for amplitude changesand (equivalentto monitoringseveralauditory filters simultaonefor frequencychanges.We will referto this asthe "indeneously) (Florentine and Buus, 1981;Moore and Glasberg, pendent-mechanisms" hypothesis. 3119
J. Acoust.Soc. Am. 92 (6), December 1992
0001-4966/92/123119-13500.80
¸ 1992 AcousticalSociety of America
3119
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1989). For example,the modelproposedby Florentineand Buus ( 1981 ) assumesthat information from the entire exci-
tation pattern (i.e., from eachexcitedcriticalband or auditory filter) is combinedin an optimal way. However, within the frameworkof thesemodels,it is still possibleto envisage a singledetectionmechanismfor changesin amplitudeand frequency;both couldbe detectedby virtue of the changesin excitationlevel that they produce. One approachto evaluatingthesemodelsis to usesignals with simultaneousamplitude modulation (AM) and frequencymodulation (FM). This type of modulation is usuallycalledmixedmodulation(MM). Studiesof thistype have been carried out by Zwicker (1962), Allanson and Newell (1966), Feth (1972), Coninx (1978a,b), Hartmann
and Hnath (1982) and Ozimek and Sek (1987). According to the single-mechanism hypothesis,onewould expectthat the perceptionof amplitudechangeswould dependon coexisting frequencychangesand vice versa.Accordingto the independent-mechanisms hypothesis,onewouldexpectthat perceptionof amplitudechangeswould be independentof coexistingfrequencychangesand vice versa.Also, for the single-mechanism hypothesisthe relativephaseof the modulatorsfor AM and FM should play an important role, whereasfor the independent-mechanisms hypothesisrelative phaseshouldbe unimportant. Zwicker (1962) comparedthe sensations producedby AM, FM, and MM of an octave-widenoiseband.The upper sideof its excitationpattern was maskedby a second,fixed band of noise. The modulation
rate was either 3 or 10 Hz. He
found that the subjectivemodulation "strength" produced by FM couldbe either increasedor decreasedby the addition of AM, dependingon the relative modulationphaseof the
trum, sincethe highersidebandis completelymasked.This appliedto AM, FM, and MM signals,consistentwith a single-mechanism hypothesisfor high modulationfrequencies. Ozimek and Sek (1987) alsoinvestigatedthe detectability of MM, usingboth low andhighmodulatingfrequencies. For high modulation frequencies,they found, like Hartmann and Hnath (1982), that detection of modulation is based exclusivelyon the lower sideband of the modulated
signal.They alsofoundthat, at low modulationfrequencies, amountsof FM and AM that were separately"sub-threshold" could be detected. However, it is unclear whether this
reflectsthe ability of subjectsto combineinformationfrom independentsources,or whether it reflectsa summationof sensations, asassumedin the single-mechanism hypothesis. Ozimek and Sekonly usedin-phasemodulationfor the MM signal,so it is not known whether modulatorphaseaffects the results,aswouldbe expectedfrom the single-mechanism hypothesis. This overview of the literature indicates that, at least for low modulation rates, there is no clear consensusas to
whether the single-mechanism hypothesisor the independent-mechanisms hypothesisis correct.This article reports an attempt to evaluatethesemechanismsby studyingthe detectionof (MM). In the first experiment,thresholdswere initially determinedfor detectingAM aloneand FM alone, usinga two-alternativeforced-choice task.Then, thresholds for detectingFM were determinedfor stimuliwhich had a fixedamountof AM in the signalinterval only. The amount of AM wasalwayslessthan the thresholdfor detectingAM alone.The relativephaseof modulationfor the AM and FM was systematicallyvaried.
FM and AM. He concluded that, for noise bands, the sensa-
I. TEMPORAL
tions produced by amplitude change and by frequency changeare basedon the samemechanism. The perceptionof MM signalswith clearlyaudiblemodulation depthswasalsoinvestigatedby Coninx (1978b). In addition, he measuredthresholdsfor detectingcombined differences in frequencyand amplitude(Coninx, 1978a). In somecases,the modulatedsinusoidswere presentedwith a noiseband intendedto maskthe uppersideof the excitation pattern. In most cases,he found that the resultswere not affectedby the relativephaseof the modulatorsfor AM and FM, whichhe interpretedasindicatingessentiallyindependent mechanismsfor the detectionand perceptionof FM and AM. Where phaseeffectswere found, he interpreted thesein termsof the influenceof amplitudeon pitch or frequencyon loudness(Czajkowskaet al., 1988).
MIXED
Hartmann and Hnath (1982) extended the model advanced by Goldstein (1967) to account for differencesin
modulationperceptionat low andhigh modulationfrequencies.For a sinusoidalcarrier and low modulationfrequencies,the perceptis of a puretonethat is changingin pitchor loudness.For high modulation frequencies,for which the spectrumof the modulatedsignalcoversa frequencyrange greater than one critical band, the perceptis of a steady soundthat may have an impure tone quality.Their results suggestedthat modulation detectionat high modulation ratesis basedexclusivelyon the lower sidebandof the spec3120
J. Acoust. Soc. Am., Vol. 92, No. 6, December 1992
AND SPECTRAL
MODULATION
STRUCTURE
OF A
SIGNAL
In this section,we givea brief descriptionof the temporal and spectralstructureof the MM stimuli usedin our experiments. FollowingOzimekandSek (1987), the instantaneousamplitudeof a MM signalcanbe written
A(t) = Ao[ 1 + m cos(co,• t -{-•) ]
X cos[COo t -{-/3sin(corot -{-O)],
(1)
wheret is time,Ao is the envelopeamplitudeof the unmodulated signal,m and/3are the modulationindicesfor AM and FM, respectively,COrn is the modulationfrequency,COo is the carrier frequency,and ß and O are terms representingthe phaseof the modulation.The phasedifferencebetweenthe modulatingsignals,A4, is ß- O. When A4 = 0, a maximum in frequencycoincideswith a maximumin amplitude. In our experiments,we usedvaluesfor A4 of 0, •r/2, •r, and 3•r/2. Following the argumentspresentedby Ozimek and Sek (1987), it may be shownthat the spectrumof a MM signalconsistsprimarily of three componentsof which the middle one correspondsto the carrier, while the two sidebandsare the resultof the modulationprocess.The relative amplitudesand phasesof the sidebandsdependon the value of A4. Figure 1(a)-(d) illustratesthe temporaland spectral structureof MM signalsfor A4 = 0, •r/2, •r, and 3•r/2, reB.C.J. Moore and A. Sek: Detection of mixed modulation
3120
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A(t): Aocos•ot+ (Ao/2)(m-/t)cos(•o-•m)f+(Ao/2)(m+ •)cos(•o+•m)t
A(t): AoCOS•ot+ (Ao/2)(-m-•)cos(•o-•m)t +(Ao/2)(-m+• )cos(• o+•m)t
TIME
TIME
•o-•m
•o-•rn •o •o't'•rn
•O
FREQUENCY
SIDEBANDS:
(a)
•o't'•rn
FREQUENCY
SIDEBANDS:
Al=(Ao/2)(m-•)
Au:(Ao/2)(m+/•)
Al=(Ao?2)(-m-/•)
(c)
Au=(Ao/2)(-m+/•)
b½=3•/2 A(t)= A•,cOs•ot+
A(t)= Aocos•ot+ (Ao/2)(-rnsin(•o-•m)t-/tcos(•o-•m)t)+ (Ao/2)(msin(•o +•m)'f+•cøS(•o+•m)'f)
(Ao/2)(msin(•o-•m•t-/tcos(•o-•m)f)+
(Ao/2)(-rnsin(•o +•m)t+,Scøs(•o +•m)t)
i,i
TIME
TIME
•o--•m •
•o-•m FREQUENCY
SIDEBANDS:
(b)
Al=(Ao/2)•(m2+j •2) Au=(Ao/2)•(rn2+j ?)
i'•
FREQUENCY
SIDEBANDS:
(d)
Al=(Ao/2)•(rn2+• 2) Au=(Ao/2)•(m2+j ?)
FIG. 1.The timepattern(top) andspectralstructure(bottom) of mixedmodulationsignals.Eachpanelshowsa differentrelativephaseof the modulators for AM and FM: (a) A•b= 0; (b) A•b= •r/2; (c) A•b=• (d) A•b= 3•r/2.
spectively.Each panelshows:an expression for the instantaneousamplitudeof the MM signalin terms of its three largest Fourier components;a portion of the waveform for m -- 0.5 and•/-- 20 (valuesof theseparameterswereselected sothat amplitudeand frequencychangescouldeasilybe
seen);the spectrumof the MM signal;and expressions for 3121
J. Acoust. Soc. Am., Vol. 92, No. 6, December 1992
the amplitudevaluesof the sidebands.When A• -- 0 [Fig. 1(a) ], the amplitudesof the sidebandsare proportionalto the sum (upper sideband)and difference(lower sideband) of the modulationindicesm and •/. When A• -- •r/2 [Fig. 1(b) ], the sidebandshaveequalamplitudesproportionalto the vectorsumof the two modulationindices.When A• = •r B.C.J. Moore and A. Sek: Detection of mixed modulation
3121
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[ Fig. 1(c) ], the amplitudesof the sidebandsare proportional to the difference(upper sideband) and sum (lower sideband) of the modulationindicesm and/3.When A& = 3rr/2 [Fig. 1(d)], the amplitudespectrumis the sameas when A& = rr/2; the sidebands haveequalamplitudesproportional to the vector sum of the two modulation indices. However,
the phase spectrum is different for A&=rc/2 Ad•- 3rr/2.
II. EXPERIMENT
MIXED
1' THRESHOLDS MODULATION
and
FOR DETECTING
A. Method 1. Stimuli
The carrier signalwasalwaysa sinusoidwith frequency fo = COo/2rr = 1000Hz andlevel70 dB SPL. The modulator was a sinusoidwith frequencyfm= com/2rr= 4, 16, 64, or 256 Hz. The valuesforfro were selectedso as to coverthree different perceptualranges. For fm= 4 and 16 Hz, the changesin amplitudeand frequencycan be heard as such. For fr• = 64 Hz, the fluctuationsare too fast to follow, and the sound has a certain "roughness" (Terhardt, 1974; Kemp, 1982). Forfro = 256 Hz, the soundqualitybecomes smoother, and individual sidebands may be perceived (Hartmann and Hnath, 1982; Ozimek and Sek, 1987). The signalswere digitally generatedusinga Masscomp
5400computersystemvia a 16-bitdigital-to-analogconverter (DAC, model DA04H) at a samplingfrequencyof 10 kHz. The output of the DAC was low-passfiltered (Fern EF 16, 100dB/oct) with a cutofffrequencyof 4 kHz, passed through a manual attenuatorand deliveredto one earpiece of a Sennheiser HD
414 headset.
tracksthe point on the psychometricfunctioncorresponding to 79.4% correct (Levitt, 1971 ). The modulation index was
changedby a factorof 1.5until four reversalshad occurred, and by a factor of 1.26 for the rest of the run. For each thresholdmeasurement,12 turnpoints were obtained;the thresholdwascalculatedasthe geometricmeanvalueof the modulation index at the last eight turnpoints.Thresholds presentedare the averageof at leastfive (usuallymorethan five) single thresholddeterminations.When the standard deviation of the mean value was more than 15% of the mean, at least one additional threshold estimate was obtained, and
all estimateswere averaged. Subjectsweretestedin a double-walledsound-attenuating chamber.Their task wasto indicate (by pushingan appropriatebutton) whetherthe firstor the secondstimulusin a pair was modulatedin amplitudeor frequency.Correctanswerfeedbackwasprovidedby lightson the response box. 3. Subjects
Three subjectswith normal hearing at all audiometic frequencieswere used.One was author AS. The other two subjectswere paid for their services.Two subjects(AS and RO) were experiencedin similar tasks,while one, KR, had no previousexperience.All subjectsweretraineduntil their performanceappearedto be stable. B. Results
Thresholdsfor detectingAM alone and FM alone are shownin Fig. 2. The resultsare very similaracrosssubjects and are consistentwith thoseobtainedby Zwicker (1952), Goldstein (1967), Schorer (1986), and Ozimek and Sek
(1987). When AM and FM soundshaveequalmodulation
On each trial, two successivestimuli were presented, one modulated and the other unmodulated.
The order of the
two stimuli in eachpair wasrandom.Each stimulushad an overalldurationof 1000ms,includingraised-cosine rise/fall t
times of 50 ms. The time interval between the stimuli was
i
i
i
i
iiii. = =
.
500 ms.
.
.
Initially, thresholdsfor detectingAM alone and FM alone were determinedfor eachmodulationfrequency.The thresholdmodulationindex for AM will be denotedby mth and that for FM by/3th. Next, thresholdswere measuredfor detectingFM, when that FM was combinedwith "subthreshold"amountsof AM at the samemodulationfrequency. In this stageof the experiment,the stimulusin the signal interval was both amplitude and frequency modulated, while the other stimulus was unmodulated.
Within
.
a•
0.1
x
a block o
of trials, the amount of AM (m) was held constant, and the amount of FM (/3) was varied to determine threshold. Val-
uesof m usedwere0.2ruth,0.4ruth,0.6ruth,0.Broth,and ruth. Four valuesof A&, the phaseshift betweenthe modulators for AM and FM, were used,namely 0, rr/2, rr, and 3rr/2.
7- 0.01 -
AM
-
0
An adaptive two-alternative forced-choice (2AFC) procedurewasused.The modulationindex (either m or/3) was increasedafter one incorrect responseand decreased after three successivecorrect responses.This procedure 3122
J. Acobst.Soc. Am., Vol. 92, No. 6, December1992
RO AS KR
ß
o ..
0.001
2. Procedure
FM
I
I
I I IIIll
,
,
, , ,,,ll
10
Modulation
•
,
, , ,,,,
1O0
Rate
1000
Hz
FIG. 2. The modulationindex requiredfor thresholdfor AM (open symbols) and FM (closedsymbols)plottedas a functionof modulationfrequency.Each symbolrepresents resultsfor a differentsubject.
B.C.J. Moore and A. Sek: Detectionof mixedmodulation
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indices (rn --/3), and when the indices are small, the AM
and FM soundshavethe sameamplitudespectrumbut differentphasespectrœFor the two highermodulationrates, the phasespectrumevidentlyplaysno role,since,at threshold, the modulation index is the samefor AM and FM. However, for the two lowestmodulation rates,the thresholdsare
clearly lower for AM than for FM, indicatinga monaural phaseeffect.The criticalmodulationfrequencyis between 16 and 64 Hz, consistentwith the data of Schorer (1986),
who founda critical modulationfrequencyslightlylessthan 64 Hz for a 1-kHz carrier at 50 dB SPL.
The thresholdsfor detectingFM in the presenceof fixed "sub-threshold"amountsof AM are shown in Fig. 3 for modulationfrequencies up to 64 Hz. The abscissa showsthe fixedamountof AM asa proportionof the "threshold"value (as shownin Fig. 2 ) for eachsubject,andthe ordinateshows the amountof FM requiredfor thresholdwith the MM stimulus,plottedas a percentageof the thresholdfor FM alone. The parameteris the phaseshiftbetweenthe AM and FM, A•b.Eachcolumnshowsresultsfor onemodulationfrequency, while eachrow showsresultsfor one subject. The results for the cases where the fixed amount of AM
wasequalto the thresholdfor AM alone( 100% on the abscissa) need to be treated with caution. In theory, the AM alone shouldhave beensufficientto give the 79.4% correct
responses neededfor "threshold."However,becausethe valueof/3waschangedby a certainfactorin the adaptiveprocedure, and was never allowed to becomezero or negative,a positivevalueof/3 wasalwaysobtainedfor "threshold"in
the MM case.The "thresholds"in thesecaseswerenot properly determinedby the adaptiveprocedureand werehighly variable;that is why the pointsin the figurecorrespondingto thesethresholdsare not connectedby the linesthrough the
otherpoints.This problemmayalsohavehadsomeeffecton the thresholdsestimatedwhenthe amountof AM wasa high proportionof its thresholdvalue. For fixed amounts of AM
less than the threshold for
AM alone(pointsjoinedby linesin Fig. 3), the amountof FM requiredfor thresholddecreased asthe fixedamountof AM increased.This effect was rather large at the lowest modulationfrequency(4 Hz, left column), and decreased somewhatas the modulationfrequencyincreasedto 16 Hz (middle column) and 64 Hz (right column). However, therewasno cleareffectof the relativemodulatorphase,A•. The thresholds for fixed amounts of AM
less than the
thresholdfor AM aloneweresubjectedto an analysisof variance (ANOVA) with factorssubjects,modulationrate, AM depth,andrelativemodulatorphase.The varianceassociated with the four-way interactionwasusedas an estimateof the residualvariance.The main effectsof subjects,modulation rate, and AM depth were all highly significant (p < 0.001). Thresholdswerelower for the lower modulation ratesandthe highervaluesof AM depth.However,the effect of relative modulator phase was not significant; F(3,36) = 1.23,p = 0.308. Sincethe resultswere very similar acrosssubjectsand acrossthe valuesof A•, they wereaveragedacrosssubjects andphasevaluesto givea clearerindicationof the effectsof the fixed amount of AM and of modulation rate. The results
areshownin Fig. 4. The dashedlineshowsthepredictions of a model that will be describedlater. These averaged data showan orderly decreasein the amountof FM requiredfor fmod=4Hz
fmod =16Hz
fmod=64Hz
120
100 80
_.phase shift v o
60
AS
40
õ--
0
•/2
--
20
v--
0
n
..
A
3n/2
I
I
I
I
I
I
120
12
•-
100
1oo 8O
6O
8O
KR
40
20
__
o
6O
__
12o
__
1oo •
80
60
&
"
O
RO
40
[]
fmod = 4 Hz
O
fmod =16 Hz
A
fmod=64Hz
i
i i
2o _
i
i
•
i
__
i i
0
i
i
i
i
i
20 40 60 80 100
i
0
i
•
predictions
i
20 40 60 80 100
0
i i i
20 40 60 80 100
Depth of AM as ß AM threshold FIG. 3. Thresholdsfor detectingFM in the presence of a fixedamountof AM, for modulationfrequenciesof 4, 16, and 64 Hz. Thresholdsare expressedas a percentageof the thresholdmeasuredfor the detectionFM alone.The amountof AM is expressed asa percentage of the thresholdfor detectingAM alone.Eachsymbolshowsresultsfor a differentvalueof A•b, the phaseshiftbetweenthe modulatorsfor AM and FM. 3123
_
o
_c
2o o
4O
J. Acoust. Soc. Am., Vol. 92, No. 6, December 1992
I 0
I 20
I 40
I 60
I 80
I loo
Depfh of AM as •o AM ,hreshold FIG. 4. As Fig. 3, but showingresultsaveragedacrosssubjects andmodulator phases. Eachsymbolshowsresultsfor a differentmodulationfrequency. The dashedline showspredictionsof a modelassuming independent mechanisms for the detection
of AM
and FM.
B.C.J. Moore and A. Sek: Detectionof mixed modulation
3123
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thresholdasthe fixedamount of AM is increased.They also confirm that the decrease tends to be smaller as the modulation rate increases.
Figure 5 showsresultsfor eachsubjectusinga modulation frequencyof 256 Hz. Here, therewerevery largeeffects of relativemodulatorphase,A•b.For A•b= 0, i.e., whenthe maximain amplitudeand frequencywere coincident,an increasein AM depth (m) causedan increasein the FM index (•) requiredfor threshold.In other words,the coexisting AM made the FM harder to detect.An oppositeeffectwas observedfor A• -- •r; an increasein m causeda significant decrease the value of /• required for threshold. For A4 = •r/2 or 3•r/2, the valuesof/• requiredfor threshold decreasedslightlywith increasingm. At this modulationrate, the sidebandsin the spectrum would probablybe resolvedin the auditory system.Thus a descriptionof the modulatedsignalin termsof its temporal structure(i.e., as changesin frequencyand amplitudeover time) is not appropriatein this case.The resultsshownin Fig. 5 can be predictedon the basisof the spectralstructure of the modulatedsignaland the frequencyselectivityof the auditory system.These predictionsare presentedin Sec. VI
B.
ing at 16 Hz. Initially, we tried usinga 2AFC taskwith the modulationindex fixedfor a block of 55 trials, treatingthe first five trials as practice.However, we found that performance at low modulation depths was often erratic, and worsethan wouldbeexpectedfrom the thresholdsmeasured usingthe adaptiveprocedureof experiment1. It appeared that subjectshad difficultyin "knowing what to listenfor" when the modulationdepth was fixed at a low value (for a similar effect in simple signal detection, see Taylor and Forbes, 1983).
To overcomethis problem,we modifiedthe procedure so that five different modulation depthswere usedin each blockof 55 trials.The highestmodulationdepthwaschosen to be rather easily detectable(typically giving 93%-99% correct responses),and the first five trials within a block
werepracticetrialsat thismodulationdepth,to helpthe subjectto "homein" on the appropriatedetectioncues.The remaining50 trials were test trials. In the first five of these, the modulation depth started at the highestvalue and decreasedprogressively to the lowest.This wasthen repeated for the next five, and soon. Thus the subjectwaspresented with an "easy" stimulusevery five trials, as a reminder of what to listenfor. The five valuesof modulationdepthwere chosenon the basisof pilot data so as to give valuesof d' between about 0.25 and 2.8 (values of % correct between
III. EXPERIMENT
2
In this experiment,we determinedpsychometricfunctions for the detection of AM alone and FM alone. The basic
aim was to establishhow the detectability index d' varied with modulationdepth. The resultsare usedlater in this paperto predictthresholdsfor the MM datapresentedabove on the basisof the single-mechanism hypothesisand the independent-mechanisms hypothesis. A. Method
The stimuli had the samefrequency,leveland time pattern asin experiment1. Modulation frequenciesof 4 and 16 Hz wereused.The subjectswerethe sameasfor experiment 1. Unfortunately, subjectAS was not able to completetest-
about 57 and 98). Twenty blocksof trials were run for each modulation frequencyand type of modulation (AM or FM), soeachpoint on eachpsychometri'c functionis based on 200 judgments. B. Results
The percentcorrectvalueswere convertedto valuesof d' (Green and Swets, 1974; Hacker and Ratcliff, 1979). In a few cases,three or fewer errors were made in the 200 trials
for a givencondition.It is not possibleto make an accurate estimateof d' in such cases,so they were excludedfrom furtheranalysis.Hence,the data presentedarebasedonlyon stimulifor which the percentcorrectwas98% or less.Analysisof the resultssuggested that d' wasapproximatelya linear functionof the modulationindex squared,for both AM and FM. Hence, valuesof d' are plotted as a function of
1000m 2or• 2in Figs.6 and7. Left-handpanelsshowresults AS
R0
180P
for AM detectionand right-handpanelsshowresultsfor FM detection.The diagonalline in each panel showsthe bestfitting straightline, constrainedto passthroughthe origin. As canbe seen,theselinesgenerallyfit the data ratherwell;
KR
+
+
all deviations from the fitted lines are within the limits of
experimentalerror. Theseresultsare consistentwith those reportedby Sheftand Yost (1989) for the detectionof AM usinga sinusoidalcarrier,andby Irwin (1989) for thedetection of 10-Hz AM of Gaussiannoise;their data alsosuggest that d' is a linear function of m 2.
IV. EVALUATION
0
¸ 0
20
40
60
80
100
0
20
40
60
80
100
MECHANISMS 0
20
40
60
80
100
Depth of AM as •[ AM fhr'eshold
FIG. 5. As Fig. 3, but showingresultsfor a modulationfrequencyof 256 Hz. 3124
J. Acoust. Soc. Am., Vol. 92, No. 6, December 1992
OF THE INDEPENDENT-
HYPOTHESIS
In this section,we considerpredictionsbasedon the independent-mechanisms hypothesis,withoutassumingany specificdetectionmechanisms for AM or FM. Let •th correB.C.J. Moore and A. Sek: Detection of mixed modulation
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fmod =16 Hz
fmod=4Hz AM
FM
FM ß
i
ß
i
ß
I
ß
i
,
2.8
ß
!
,
!
ß
E 2.2
2.2
d'=133,m2
1.7
1.7
R0
AS l.l
d' =2.75./52
o.s [] d'=420.m 2
.6,82
0.6
0.0
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.
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at 2.8
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2.2
2.2
d'
J
1.7
[]
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1.7
RO 1,1
=724.m2
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o
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.
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0.00
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,
m2.1000
•2
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d' =2.89*/52
0'61/ d':640*m 2 0.0 I• 0
FIG. 7. As Fig. 6, but for a modulationfrequencyof 16 Hz.
KR
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.
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i 2
,
i 3
,
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m2. !000
Consider a situation like that used in experiment 1, wherethe AM modulationindexis fixedat someproportion, P(
