Detection of frequency modulation (FM) in the presence of a second FM tone

A series of three experiments was undertaken to investigate detection of sinusoidal frequency modulation (FM) in the presence of FM at a separate frequency. The first experiment measured detection of modulation for an FM tone with a modulation frequency (fm) of 6 Hz as a function of carrier frequency (fc) under three conditions: (1) in quiet, (2) in the presence of a 2500-Hz pure tone, and (3) in the presence of a 2500-Hz FM tone with fm = 6 Hz, modulating in phase with the signal. Detection of FM in the presence of the second FM tone was worse than for either the signal presented in quiet or in the presence of the unmodulated tone. Threshold varied as an inverse function of frequency separation between the signal and the masker. In the second experiment, FM detection for a signal with fc = 1900 Hz and fm = 6 Hz was measured as a function of the modulation frequency (fm = 2-18 Hz) of the 2500-Hz masker tone. FM detection improved significantly with increasing difference between the modulation frequencies of the signal and the masker. The final experiment measured detection of FM for a signal (fc = 1900 Hz, fm = 6 Hz) in the presence of a second FM tone (fc = 2500 Hz, fm = 6 Hz) as a function of the relative phase of the 6-Hz modulators. Detection of FM improved monotonically as a function of increasing phase difference between the two modulators. The results are discussed in terms of modulation detection interference and perceptual grouping.     

A comparison of steady-state evoked potentials to modulated tones in awake and sleeping humans.

Steady-state evoked potential responses were measured to binaural amplitude-modulated (AM) and combined amplitude- and frequency-modulated (AM/FM) tones. For awake subjects, AM/FM tones produced larger amplitude responses than did AM tones. Awake and sleeping responses to 30-dB HL AM/FM tones were compared. Response amplitudes were lower during sleep and the extent to which they differed from awake amplitudes was dependent on both carrier and modulation frequencies. Background EEG noise at the stimulus modulation frequency was also reduced during sleep and varied with modulation frequency. A detection efficiency function was used to indicate the modulation frequencies likely to be most suitable for electrical estimation of behavioral threshold. In awake subjects, for all carrier frequencies tested, detection efficiency was highest at a modulation frequency of 45 Hz. In sleeping subjects, the modulation frequency regions of highest efficiency varied with carrier frequency. For carrier frequencies of 250 Hz, 500 Hz, and 1 kHz, the highest efficiencies were found in two modulation frequency regions centered on 45 and 90 Hz. For 2 and 4 kHz, the highest efficiencies were at modulation frequencies above 70 Hz. Sleep stage affected both response amplitude and background EEG noise in a manner that depended on modulation frequency. The results of this study suggest that, for sleeping subjects, modulation frequencies above 70 Hz may be best when using steady-state potentials for hearing threshold estimation.     

Potentials evoked by the sinusoidal modulation of the amplitude or frequency of a tone

Steady state responses to the sinusoidal modulation of the amplitude or frequency of a tone were recorded from the human scalp. For both amplitude modulation (AM) and frequency modulation (FM), the responses were most consistent at modulation frequencies between 30 and 50 Hz. However, reliable responses could also be recorded at lower frequencies, particularly at 2-5 Hz for AM and at 3-7 Hz for FM. With increasing modulation depth at 40 Hz, both the AM and FM response increased in amplitude, but the AM response tended to saturate at large modulation depths. Neither response showed any significant change in phase with changes in modulation depth. Both responses increased in amplitude and decreased in phase delay with increasing intensity of the carrier tone, the FM response showing some saturation of amplitude at high intensities. Both responses could be recorded at modulation depths close to the subjective threshold for detecting the modulation and at intensities close to the subjective threshold for hearing the stimulus. The responses were variable but did not consistently adapt over periods of 10 min. The 40-Hz AM and FM responses appear to originate in the same generator, this generator being activated by separate auditory systems that detect changes in either amplitude or frequency.     

Detection of modulation of a 4-kHz carrier

To better understand the processing of complex high-frequency sounds, modulation-detection thresholds were measured for sinusoidal frequency modulation (SFM), quasi-frequency modulation (QFM), sinusoidal amplitude modulation (SAM), and random-phase FM (RPFM). At the lowest modulation frequency (5 Hz) modulation thresholds expressed as AM depth were similar for RPFM, SAM and QFM suggesting the predominance of envelope cues. At the higher modulation frequencies (20 and 40 Hz) thresholds expressed as total frequency excursions were similar for SFM and QFM suggesting a common mechanism, one perhaps based on single-channel FM-to-AM conversion or on a multi-channel place mechanism. The fact that the nominal envelopes of SFM and QFM are different (SFM has a flat envelope), seems to preclude processing based on the envelope of the external stimulus. Also, given the 4-kHz carrier and the similarity to previously published results obtained with a 1-kHz carrier, processing based on temporally-coded fine structure for all four types of modulation appears unlikely.     

An analysis of quasi-frequency-modulated noise and random-sideband noise as comparisons for amplitude-modulated noise

Experiments were performed to determine under what conditions quasi-frequency-modulated (QFM) noise and random-sideband noise are suitable comparisons for AM noise in measuring a temporal modulation transfer function (TMTF). Thresholds were measured for discrimination of QFM from random-sideband noise and AM from QFM noise as a function of sideband separation. In the first experiment, the upper spectral edge of the noise stimuli was at 2400 Hz and the bandwidth was 1600 Hz. For sideband separations up to 256 Hz, at threshold sideband levels for discriminating AM from QFM noise, QFM was indiscriminable from random-sideband noise. For the largest sideband separation used (512 Hz), listeners may have used within-stimulus envelope correlation in the QFM noise to discriminate it from the random-sideband noise. Results when stimulus bandwidth was varied suggest that listeners were able to use this cue when the carrier was wider than a critical band, and the sideband separation approached the carrier bandwidth. Within-stimulus envelope correlation was also present in AM noise, and thus QFM noise was a suitable comparison because it made this cue unusable and forced listeners to use across-stimulus envelope differences. When the carrier bandwidth was less than a critical band or was wideband, QFM noise and random-sideband noise were equally suitable comparisons for AM noise. When discrimination thresholds for QFM and random-sideband noise were converted to modulation depth and modulation frequency, they were nearly identical to those for discrimination of AM from QFM noise, suggesting that listeners were using amplitude modulation cues in both cases.     

Detectability of a pulsed tone in the presence of a masker with time-varying interaural correlation.

Detectability of a filtered probe tone (250, 500, or 1000 Hz) was measured in the presence of a narrow-band Gaussian masker centered at the signal frequency. The signal was interaurally phase-reversed (Spi), and the masker's interaural correlation varied sinusoidally between +1.00 (NO) and -1.00 (Npi) at a varaible rate (fm = 0--4 Hz). The signal was presented at various points on the masker's modulation cycle. For 0-Hz modulation (fixed interaural correlation) signal threshold decreased monotonically as the masker's interaural correlation was changed from -1.00 to +1.00 (by a total of about 20, 16, and 8 dB, respectively, for 250-, 500-, and 1000-Hz signals). For fm greater than 0 the function relating signal threshold to the masker's interaural correlation at the moment of signal presentation became progressively flatter with increasing fm for all signal frequencies. For fm = 4 Hz the function was flat; there was no measurable effect of masker interaural correlation on signal detectability. Estimates of minimum binaural integration time based on these data ranged from 44--243 ms, supporting previous studies which have noted the binaural system's relative insensitivity to dynamic stimulation. Additionally, the estimated time constants were approximately twice as large at 250 Hz as at 500 Hz, indicating observers could follow binaural fluctuations better at 500 Hz. The time-constant estimates at 1000 Hz were not suggiciently reliable to permit comparisons with the lower-frequency data.     

The effect of modulation coherence on signal threshold in frequency-modulated noise bands

A series of four experiments was undertaken to ascertain whether signal threshold in frequency-modulated noise bands is dependent upon the coherence of modulation. The specific goal was to determine whether a masking release could be obtained with frequency modulation (FM), analogous to the comodulation masking release (CMR) phenomenon observed with amplitude modulation (AM). It was hypothesized that an across-frequency grouping process might give rise to such an effect. In experiments 1-3, maskers were composed of three noise bands centered on 1600, 2000, and 2400 Hz; these were either comodulated or noncomodulated with respect to both FM and AM. In experiment 1, the modulation was sinusoidal, and the signal was a 2000-Hz pure tone; in experiment 2, the modulation was random, and the signal was an FM noise band centered on 2000 Hz. The results obtained showed that, given sufficient width of modulation, thresholds were lower in a coherent FM masker than in an incoherent FM masker, regardless of the pattern of AM or signal type. However, thresholds in multiband maskers were usually elevated relative to that in a single-band masker centered on the signal. Experiment 3 demonstrated that coherent FM could be discriminated from incoherent FM. Experiment 4 gave similar patterns of results to the respective conditions of experiments 2 and 3, but for an inharmonic masker with bands centered on 1580, 2000, and 2532 Hz. While within-channel processes could not be entirely excluded from contributing to the present results, the experimental conditions were designed to be minimally conducive to such processes.     

Time course of adaptation and recovery of channels selectively sensitive to frequency and amplitude modulation

In a series of experiments we investigated the time course of adaptation and recovery of channels in the human auditory system selectively sensitive to frequency and amplitude modulation (FM and AM). We determined the rate of loss of sensitivity to modulation using sinusoidal frequency or amplitude modulation (SFM or SAM) of a 50 dB SL, 500-Hz pure tone carrier over a 30-min period. Adaptation stimuli were modulated at ten times the preadaptation modulation detection threshold, as determined immediately before the 30-min adaptation session. Modulation rates investigated were 2, 4, 8, 16, and 32 Hz. Long exposure to SFM always elevated thresholds for detection of SFM more than this exposure elevated thresholds for detection of SAM. Similarly, adapting to SAM always elevated SAM detection thresholds more than SFM thresholds. Loss of sensitivity during adaptation was relatively slow; asymptotic loss of modulation sensitivity took 20 to 30 min. The recovery of modulation sensitivity after cessation of the modulation component of the adapting stimulus was determined in a second experiment. Recovery was found to be rapid; most of the recovery occurred within the first 60 sec. Our evidence suggests that there exist two types of modulation-sensitive channels in the human auditory system--one selectively sensitive to amplitude modulation and the other to frequency modulation. They appear to have similar time courses for adaptation and for recovery.     

Modulation rate discrimination for unresolved components: temporal cues related to fine structure and envelope

The present study investigated the hypothesis that the cues for modulation rate discrimination for unresolved spectral components differ as a function of the spectral region occupied by the stimuli. Specifically, it was hypothesized that when components occupy relatively low spectral regions, phase locking both to the fine structure and to the envelope are useful cues. However, as the spectral region occupied by the components increases, phase locking to the fine structure becomes less robust, whereas phase locking to the envelope remains as a potentially strong cue. Observers were asked to detect a decrease in modulation rate for carrier frequencies between 1500 and 6000 Hz. Both amplitude-modulated (AM) and quasifrequency-modulated (QFM) tones were used in order to produce stimuli having strong and weak envelope cues, respectively. Although there were marked individual differences, the results showed an interaction between modulation type and spectral region, with AM and QFM performance being relatively similar at low spectral region, but with QFM showing a steeper reduction in performance as the spectral region of the carrier frequency increased. Overall, the data are consistent with an interpretation that pitch perception for unresolved components depends upon both fine structure and envelope cues, and that the relative importance of these cues depends upon the spectral region occupied by the stimuli.     

Subcomponent cues in binaural unmasking

The addition of a signal in the N0Sπ binaural configuration gives rise to fluctuations in interaural phase and amplitude. Sensitivity to these individual cues was measured by applying sinusoidal amplitude modulation (AM) or quasi-frequency modulation (QFM) to a band of noise. Discrimination between interaurally in-phase and out-of-phase modulation was measured using an adaptive task for narrow bands of noise at center frequencies from 250 to 1500 Hz, for modulation rates of 2-40 Hz, and with or without flanking bands of diotic noise. Discrimination thresholds increased steeply for QFM with increasing center frequency, but increased only modestly for AM, and mainly for modulation rates below 10 Hz. Flanking bands of noise increased thresholds for AM, but had no consistent effect for QFM. The results suggest that two underlying mechanisms may support binaural unmasking: one most sensitive to interaural amplitude modulations that is susceptible to across-frequency interference, and a second, most sensitive to interaural phase modulations that is immune to such effects.     

Detection of combined frequency and amplitude modulation.

This article is concerned with the detection of mixed modulation (MM), i.e., simultaneously occurring amplitude modulation (AM) and frequency modulation (FM). In experiment 1, an adaptive two-alternative forced-choice task was used to determine thresholds for detecting AM alone. Then, thresholds for detecting FM were determined for stimuli which had a fixed amount of AM in the signal interval only. The amount of AM was always less than the threshold for detecting AM alone. The FM thresholds depended significantly on the magnitude of the coexisting AM. For low modulation rates (4, 16, and 64 Hz), the FM thresholds did not depend significantly on the relative phase of modulation for the FM and AM. For a high modulation rate (256 Hz) strong effects of modulator phase were observed. These phase effects are as predicted by the model proposed by Hartmann and Hnath [Acustica 50, 297-312 (1982)], which assumes that detection of modulation at modulation frequencies higher than the critical modulation frequency is based on detection of the lower sideband in the modulated signal's spectrum. In the second experiment, psychometric functions were measured for the detection of AM alone and FM alone, using modulation rates of 4 and 16 Hz. Results showed that, for each type of modulation, d' is approximately a linear function of the square of the modulation index. Application of this finding to the results of experiment 1 suggested that, at low modulation rates, FM and AM are not detected by completely independent mechanisms. In the third experiment, psychometric functions were again measured for the detection of AM alone and FM alone, using a 10-Hz modulation rate. Detectability was then measured for combined AM and FM, with modulation depths selected so that each type of modulation would be equally detectable if presented alone. Significant effects of relative modulator phase were found when detectability was relatively high. These effects were not correctly predicted by either a single-band excitation-pattern model or a multiple-band excitation-pattern model. However, the detectability of the combined AM and FM was better than would be predicted if the two types of modulation were coded completely independently.     

Critical modulation frequency based on detection of AM versus FM tones

The ratios between the modulation index (eta) for just noticeable FM of a sinusoidally modulated pure tone and the degree of modulation (m) for just noticeable AM at the same carrier and the same modulation frequency were measured at carrier frequencies of 0.125, 0.25, 0.5, 1, 2, 4, and 8 kHz. Signal levels were 20 dB SL and 50 dB SPL or 80 dB SPL. At low modulation frequencies, for example, 8 Hz, AM and FM elicit very different auditory sensations (i.e., a fluctuation in loudness or pitch, respectively). In this case, eta and m show different values for just noticeable modulation. Since both stimuli have almost equal amplitude spectra if eta equals m (m less than 0.3), the difference in detection thresholds reflects differences in the phase relation between carrier and sidebands in AM and FM. With increasing modulation frequency, the eta-m ratio decreases and reaches unity at a modulation frequency called the "critical modulation frequency" (CMF). At modulation frequencies above the CMF, the same modulation thresholds are obtained for AM and FM. Therefore, it can be concluded that the difference in phase between the two types of stimuli is not perceived in this range. At center frequencies below 1 kHz, where phase errors caused by headphones and ear canal presumably are small, the CMF is useful in estimating critical bandwidth.     

Response dynamics of goldfish saccular fibers: effects of stimulus frequency and intensity on fibers with different tuning, sensitivity, and spontaneous activity

The effects of stimulus frequency and intensity on response patterns (PST histograms) to tone burst stimulation were examined in differently tuned saccular fibers of the goldfish. In addition, the sensitivity of these fibers to amplitude-modulated (AM) signals of different carrier frequencies was measured. The response patterns evoked by unmodulated signals were a complex function of tuning, spontaneous activity and sensitivity of the fiber, and the frequency and intensity of the signal. Frequency-dependent response patterns were found in low-frequency fibers with best frequencies (BF) below 200 Hz. Responses in these fibers ranged from tonic to phasic in nonspontaneous fibers and included more complex patterns in spontaneously active fibers, such as suppression of evoked activity below spontaneous levels. Midfrequency fibers (BF = 500-600 Hz) showed responses similar to those in low-frequency fibers, but with less dependence on frequency. In contrast, both high-frequency (BF = 800-1000 Hz) and wideband, untuned fibers showed frequency-invariant patterns of adaptation. High-frequency fibers were equally sensitive to AM signals at all frequencies tested. The sensitivity of low-frequency fibers to AM, however, increased as a function of carrier frequency and corresponded to the degree of adaptation in response to unmodulated tones. In general, the AM sensitivity of a fiber could be predicted more by its pattern of response to unmodulated signals than by its tuning characteristics.     

Within- versus cross-channel mechanisms in detection of envelope phase disparity

These experiments were designed to examine the mechanism of detection of phase disparity in the envelopes of two sinusoidally amplitude-modulated (AM) sinusoids. Specifically, they were performed to determine whether detection of envelope phase disparity was consistent with processing within a single channel in which the AM tones were simply added. In the first condition, with an 8-Hz modulation frequency, phase-disparity thresholds increased sharply with an initial increase in separation of the carrier frequencies. They then remained approximately constant when the separation was an octave or above. In the second condition, with carrier pairs of 1 and 2 kHz or 1 and 3.2 kHz and a modulation frequency of 8 Hz, thresholds were little affected as the level of one carrier was decreased relative to the other. With a modulation frequency of 128 Hz, for most subjects there was more of an effect of level disparity on thresholds. In the third condition, when the modulation frequency was 8 Hz, subjects showed relatively constant thresholds whether the signals were presented monotically, dichotically, or dichotically with low- and high-pass noise. Dichotic thresholds were typically higher than monotic when the modulation frequency was 128 Hz. These results suggest that it is not necessary to have information available within a single additive channel to detect envelope phase disparity. In certain circumstances, a comparison across channels may be used to detect such disparities.     

Adjustment on subjective annoyance of low frequency noise by adding additional sound

Structure-borne noise originating from a heat pump unit was selected to study the influence on subjective annoyance of low frequency noise (LFN) combined with additional sound. Paired comparison test was used for evaluating the subjective annoyance of LFN combined with different sound pressure levels (SPL) of pink noise, frequency-modulated pure tones (FM pure tones) and natural sounds. The results showed that, with pink noise of 250-1000 Hz combined with the original LFN, the subjective annoyance value (SAV) first dropped then rose with increasing SPL. When SPL of the pink noise was 15-25 dB, SAV was lower than that of the original LFN. With pink noise of frequency 250-20,000 Hz added to LFN, SAV increased linearly with increasing SPL. SAV and the psychoacoustic annoyance value (PAV) obtained by semi-theoretical formulas were well correlated. The determination coefficient (R²) was 0.966 and 0.881, respectively, when the frequency range of the pink noise was 250-1000 and 250-20,000 Hz. When FM pure tones with central frequencies of 500, 2000 and 8000 Hz, or natural sounds (including the sound of singing birds, flowing water, wind or ticking clock) were, respectively, added to the original sound, the SAV increased as the SPL of the added sound increased. However, when a FM pure tone of 15 dB with a central frequency of 2000 Hz and a modulation frequency of 10 Hz was added, the SAV was lower than that of the original LFN. With SPL and central frequency held invariable, the SAV declined primarily when modulation frequency increased. With SPL and modulation frequency held invariable, the SAV became lowest when the central frequency was 2000 Hz. This showed a preferable correlation between SAV and fluctuation extent of FM pure tones.     

The role of time and place cues in the detection of frequency modulation by hearing-impaired listeners

Frequency modulation detection limens (FMDLs) were measured for five hearing-impaired (HI) subjects for carrier frequencies f(c) = 1000, 4000, and 6000 Hz, using modulation frequencies f(m) = 2 and 10 Hz and levels of 20 dB sensation level and 90 dB SPL. FMDLs were smaller for f(m) = 10 than for f(m) = 2 Hz for the two higher f(c), but not for f(c) = 1000 Hz. FMDLs were also determined with additional random amplitude modulation (AM), to disrupt excitation-pattern cues. The disruptive effect was larger for f(m) = 10 than for f(m) = 2 Hz. The smallest disruption occurred for f(m) = 2 Hz and f(c) = 1000 Hz. AM detection thresholds for normal-hearing and HI subjects were measured for the same f(c) and f(m) values. Performance was better for the HI subjects for both f(m). AM detection was much better for f(m) = 10 than for f(m) = 2 Hz. Additional tests showed that most HI subjects could discriminate temporal fine structure (TFS) at 800 Hz. The results are consistent with the idea that, for f(m) = 2 Hz and f(c) = 1000 Hz, frequency modulation (FM) detection was partly based on the use of TFS information. For higher carrier frequencies and for all carrier frequencies with f(m) = 10 Hz, FM detection was probably based on place cues.     

Evidence for direction-specific channels in the processing of frequency modulation.

Evidence is provided for the existence of at least three feature-specific channels in the auditory system. Thresholds for the detection of small repetitive or nonrepetitive frequency changes were measured following various adapting stimuli using a 2IFC procedure in two subjects at 1 kHz. Thresholds for single linear upward frequency sweeps (up sweeps) were increased by a factor of 2 to 3 following exposure to repetitive (8 Hz) up sweeps but not following exposure to down sweeps or tone bursts; correspondingly, thresholds for down-sweep stimuli were increased only by down sweeps. Sinusoidal FM test stimulus thresholds were elevated by both up-sweeps and down-sweeps and to a lesser extent by tone bursts. These results suggest the existence in the auditory system of channels specific to upward FM, downward FM, and probably repetition rate.     

Behaviors of cubic distortion product otoacoustic emissions evoked by amplitude modulated tones

Distortion product otoacoustic emissions (DPOAEs) were measured using sinusoidal amplitude modulation (AM) tones. When one of the primary stimuli (f(1) or f(2), f(1)?< f(2)) was amplitude modulated, a series of changes in the cubic difference tone (CDT) were observed. In the frequency domain, multiple sidebands were present around the CDT and their sizes grew with the modulation depth of the AM stimulus. In the time domain, the CDT showed different modulation patterns between two major signal conditions: the AM tone was used as the f(1) or the f(2). The CDT amplitude followed the AM tone when the f(1) was amplitude modulated. However, when the AM tone acted as the f(2), the CDT showed a more complex modulation pattern with a notch present at the AM tone peak. The relatively linear dependence of CDT on f(1) and the nonlinear relation with f(2) can be explained with a variable gain-control model representing hair cell functions at the DPOAE generation site. It is likely that processing of AM signals at a particular cochlear location depends on whether the hair cells are tuned to the frequency of the carrier. Nonlinear modulation is related to on-frequency carriers and off-frequency carriers are processed relatively linearly.     

Neuronal responses to amplitude-modulated and pure-tone stimuli in the guinea pig inferior colliculus, and their modification by broadband noise

Neuronal responses were recorded to pure and to sinusoidally amplitude-modulated (AM) tones at the characteristic frequency (CF) in the central nucleus of the inferior colliculus of anesthetized guinea pigs. Temporal (synchronized) and mean-rate measures were derived from period histograms locked to the stimulus modulation waveform to characterize the modulation response. For stimuli presented in quiet, the modulation gain at low frequencies of modulation (approx less than 50 Hz) was inversely proportional to the neuron's mean firing rate in response to both the modulated stimulus and to a pure tone at an equivalent level. In 43% of units the mean discharge rates in response to the AM stimuli were greatest for those modulation frequencies that generated the largest temporal responses. These discharge-rate maxima occurred at signal intensities corresponding to the steeply sloping part of the neuron's pure-tone rate-intensity function (RIF). The change in mean-rate response to modulated stimuli, as a function of intensity, was qualitatively similar to the pure-tone RIF. Adding broadband noise to the modulated stimulus increased the neuron's temporal response to low modulation frequencies. This increase in modulation gain was correlated with mean firing rate in response to the modulation but did not bear a simple relationship to the noise-induced shift in the RIF measured for a pure tone.     

Influence of rate of change of frequency on the overall pitch of frequency-modulated tones

The mechanism(s) determining pitch may assign less weight to portions of a sound where the frequency is changing rapidly. The present experiments explored the possible effect of this on the overall pitch of frequency-modulated sounds. Pitch matches were obtained between an adjustable unmodulated sinusoid and a sinusoidal carrier that was frequency modulated using a highly asymmetric function with the form of a repeating U or inverted U shaped function. The amplitude was constant during the 400-ms presentation time of each stimulus, except for 10-ms raised-cosine onset and offset ramps. In experiment 1, the carrier level was 50 dB SPL and the geometric mean of the instantaneous frequency of the modulated carrier, fc, was either 0.5, 1, 2, or 8 kHz. The modulation rate (fm) was 5, 10, or 20 Hz. The overall depth (maximum to minimum) of the FM was 8% of fc. For all carrier frequencies, the matched frequency was shifted away from the mean carrier frequency, downwards for the U shaped function stimuli and upwards for the repeated inverted U shaped function stimuli. The shift was typically slightly greater than 1% of fc, and did not vary markedly with fc. The effect of fm was small, but there was a trend for the shifts to decrease with increasing fm for fc = 0.5 kHz and to increase with increasing fm for fc = 2 kHz. In experiment 2, the carrier level was reduced to 20 dB SL and matches were obtained only for fc = 2 kHz. Shifts in matched frequency of about 1% were still observed, but the trend for the shifts to increase with increasing fm no longer occurred. In experiment 3, matches were obtained for a 4-kHz carrier at 50 dB SPL. Shifts of about 1% again occurred, which did not vary markedly with fm. The shifts in matched frequency observed in all three experiments are not predicted by models based on the amplitude- or intensity-weighted average of instantaneous frequency (EWAIF or IWAIF). The shifts (and the pitch shifts observed earlier for two-tone complexes and for stimuli with simultaneous AM and FM) are consistent with a model based on the assumption that the overall pitch of a frequency-modulated sound is determined from a weighted average of period estimates, with the weight attached to a given estimate being inversely related to the short-term rate of change of period and directly related to a compressive function of the amplitude.