The influence of carrier level and frequency on modulation and beat-detection thresholds for sinusoidal carriers

This paper is concerned with modulation and beat detection for sinusoidal carriers. In the first experiment, temporal modulation transfer functions (TMTFs) were measured for carrier frequencies between 1 and 10 kHz. Modulation rates covered the range from 10 Hz to about the rate equaling the critical bandwidth at the carrier frequency. In experiment 2, TMTFs for three carrier frequencies were obtained as a function of the carrier level. In the final experiment, thresholds for the detection of either the lower or the upper modulation sideband (beat detection) were measured for "carrier" frequencies of 5 and 10 kHz, using the same range of modulation rates as in experiment 1. The TMTFs for carrier frequencies of 2 kHz and higher remained flat up to a modulation rate of about 100-130 Hz and had similar values across carrier frequencies. For higher rates, modulation thresholds initially increased and then decreased rapidly, reflecting the subjects' ability to resolve the sidebands spectrally. Detection thresholds generally improved with increasing carrier level, but large variations in the exact level dependence were observed, across subjects as well as across carrier frequencies. For beat rates up to about 70 Hz (at 5 kHz) and 100 Hz (at 10 kHz), beat detection thresholds were the same for the upper and the lower sidebands and were about 6 dB higher than the level per sideband at the modulation-detection threshold. At higher rates the threshold for both sidebands increased, but the increase was larger for the lower sideband. This reflects an asymmetry in masking with more masking towards lower frequencies. Only at rates well beyond the maximum of the TMTF did detection for the lower sideband start to be better than that for the upper sideband. The asymmetry at intermediate frequency separations can be explained by assuming that detection always takes place in filters centered above the stimulus spectrum. The shape of the TMTF and the beat-detection data reflects a limitation in resolving fast amplitude variations, which must occur central to the inner-ear filtering. Its characteristic resembles that of a first-order low-pass filter with a cutoff frequency of about 150 Hz.     

Modulation detection for amplitude-modulated bone-conducted sounds with sinusoidal carriers in the high- and ultrasonic-frequency range

Ultrasonic vibration generates a sensation of sound via bone-conduction. This phenomenon is called bone-conducted ultrasonic (BCU) hearing. Complex sounds can also be perceived by amplitude-modulating a BCU stimulus (AM-BCU). The influence of the modulation frequency on the sensitivity to detecting amplitude modulation of sinusoidal carriers of 10, 20, and 30 kHz was examined to clarify the characteristics of the perception of amplitude modulation over the sonic or audio-frequency range and the ultrasonic range. In addition, the detection sensitivity for single-sideband modulation for a 20 kHz carrier was measured. Temporal modulation transfer functions (TMTFs) obtained at each carrier frequency suggest that the auditory system has the ability to process timing information in the envelopes of AM-BCUs at lower modulation frequencies, as is the case with audio-frequency sounds. The possible influence of peripheral filtering on the shape of the TMTF at higher frequencies was examined.     

Monaural and interaural temporal modulation transfer functions measured with 5-kHz carriers

Temporal modulation transfer functions (TMTFs) were measured for detection of monaural sinusoidal amplitude modulation and dynamically varying interaural level differences for a single set of listeners. For the interaural TMTFs, thresholds are the modulation depths at which listeners can just discriminate interaural envelope-phase differences of 0 and 180 degrees. A 5-kHz pure tone and narrowband noises, 30- and 300-Hz wide centered at 5 kHz, were used as carriers. In the interaural conditions, the noise carriers were either diotic or interaurally uncorrelated. The interaural TMTFs with tonal and diotic noise carriers exhibited a low-pass characteristic but the cutoff frequencies changed nonmonotonically with increasing bandwidth. The interaural TMTFs for the tonal carrier began rolling off approximately a half-octave lower than the tonal monaural TMTF (approximately 80 Hz vs approximately 120 Hz). Monaural TMTFs obtained with noise carriers showed effects attributable to masking of the signal modulation by intrinsic fluctuations of the carrier. In the interaural task with dichotic noise carriers, similar masking due to the interaural carrier fluctuations was observed. Although the mechanisms responsible for differences between the monaural and interaural TMTFs are unknown, the lower binaural TMTF cutoff frequency suggests that binaural processing exhibits greater temporal limitation than monaural processing.     

The detection of temporal gaps as a function of frequency region and absolute noise bandwidth.

Temporal gap detection was measured as a function of absolute signal bandwidth at a low-, a mid-, and a high-frequency region in six listeners with normal hearing sensitivity. Gap detection threshold decreased monotonically with increasing stimulus bandwidth at each of the three frequency regions. Given conditions of equivalent absolute bandwidth, gap detection thresholds were not significantly different for upper cutoff frequencies ranging from 600 to 4400 Hz. A second experiment investigated gap detection thresholds at two pressure-spectrum levels, conditions typically resulting in substantially different estimates of frequency selectivity. Estimates of frequency selectivity were collected at the two levels using a notched-noise masker technique. The gap threshold-signal bandwidth functions were almost identical at pressure-spectrum levels of 70 dB and 40 dB for the two subjects in experiment II, while estimates of frequency selectivity showed poorer frequency selectivity at the 70-dB level than at 40 dB. Data from both experiments indicated that gap detection in bandlimited noise was inversely related to signal bandwidth and that gap detection did not vary significantly with changes in signal frequency over the range of 600 to 4400 Hz. Over the range of frequencies investigated, the results indicated no clear relation between gap detection for noise stimuli and peripheral auditory filtering.     

Spectral modulation detection as a function of modulation frequency, carrier bandwidth, and carrier frequency region

The present study investigates the nature of spectral envelope perception using a spectral modulation detection task in which sinusoidal spectral modulation is superimposed upon a noise carrier. The principal goal of this study is to characterize spectral envelope perception in terms of the influence of modulation frequency (cycles/octave), carrier bandwidth (octaves), and carrier frequency region (defined by lower and upper cutoff frequencies in Hz). Spectral modulation detection thresholds measured as a function of spectral modulation frequency result in a spectral modulation transfer function (SMTF). The general form of the SMTF is bandpass in nature, with a minimum modulation detection threshold in the region between 2 to 4 cycles/octave. SMTFs are not strongly dependent on carrier bandwidth (ranging from 1 to 6 octaves) or carrier frequency region (ranging from 200 to 12 800 Hz), with the exception of carrier bands restricted to very low audio frequencies (e.g., 200-400 Hz). Spectral modulation detection thresholds do not depend on the presence of random level variations or random modulation phase across intervals. The SMTFs reported here and associated excitation pattern computations are considered in terms of a linear systems approach to spectral envelope perception and potential underlying mechanisms for the perception of spectral features.     

Basilar-membrane responses to multicomponent (Schroeder-phase) signals: understanding intensity effects

Harmonic complexes comprised of the same spectral components in either positive-Schroeder (+Schr) or negative-Schroeder (-Schr) phase [see Schroeder, IEEE Trans. Inf. Theory 16, 85-89 (1970)] have identical long-term spectra and similar waveform envelopes. However, localized patterns of basilar-membrane (BM) excitation can be quite different in response to these two stimuli. Measurements in chinchillas showed more modulated (peakier) BM excitation for +Schr than -Schr complexes [Recio and Rhode, J. Acoust. Soc. Am. 108, 2281-2298 (2000)]. In the current study, laser velocimetry was used to examine BM responses at a location tuned to approximately 17 kHz in the basal turn of the guinea-pig cochlea, for +Schr and -Schr complexes with a 203-Hz fundamental frequency and including 101 equal-amplitude components from 2031 to 22,344 Hz. At 35-dB SPL, +Schr response waveforms showed greater amplitude modulation than -Schr responses. With increasing stimulation level, internal modulation decreased for both complexes. To understand the observed phenomena quantitatively, responses were predicted on the basis of a linearized model of the cochlea. Prediction was based on an "indirect impulse response" measured in the same animal. Response waveforms for Schroeder-phase signals were accurately predicted, provided that the level of the indirect impulse used in prediction closely matched the level of the Schroeder-phase stimulus. This result confirms that the underlying model, which originally was developed for noise stimuli, is valid for stimuli that produce completely different response waveforms. Moreover, it justifies explanation of cochlear filtering (i.e., differential treatment of different frequencies) in terms of a linear system.     

Intensity difference limens at high frequencies

Thresholds for amplitude modulation detection were obtained from four subjects at frequencies of 2, 4, 6, 8, and 10 kHz for sensation levels of 15, 30, 45, and 60 dB and modulation rates of 2, 4, and 8 Hz. High-frequency difference limens calculated from amplitude modulation thresholds were found to change nonmonotonically as a function of sensation level, independent of modulation rate. This nonmonotonic relation stemmed mainly from a gradual reduction of the difference limen at the lowest sensation level with increasing frequency. Difference limens for pulsed tone discrimination were also measured in two of the subjects at 2, 6, and 10 kHz and sensation levels of 15, 30, 45, and 60 dB. The relation between intensity discrimination and sensation level was similar to that found for amplitude modulation detection. These findings are interpreted as indicating that the nonmonotonic relation between sensation level and intensity resolution is a general characteristic of stimulus processing at higher frequencies.     

Bottlenose dolphin (Tursiops truncatus) steady-state evoked responses to multiple simultaneous sinusoidal amplitude modulated tones

Auditory steady-state evoked potentials were measured in a bottlenose dolphin (Tursiops truncatus) in response to single and multiple sinusoidal amplitude modulated (SAM) tones. Tests were conducted in air using a "jawphone" sound projector. Evoked potentials were recorded noninvasively using surface electrodes embedded in suction cups. Sound stimuli consisted of SAM tones with 1, 2, 3, or 4 carrier frequencies (10, 20, 30, 40 kHz), each with a unique modulation frequency. Stimulus sound pressure levels were varied in 5-dB steps from approximately 120 to 60-75 dB re 1 microPa, depending on frequency. Evoked potentials followed the temporal envelope of each stimulus, resulting in spectral components at each unique modulation frequency. Spectral analysis was used to evaluate the response amplitude for each carrier as a function of stimulus level. There were no significant differences between thresholds obtained with single and multiple stimuli at 10, 30, and 40 kHz. At 20 kHz, thresholds obtained with three components were higher than those obtained with four components, possibly revealing interactions between stimuli with less than one octave frequency separation. The use of multiple SAM stimuli may offer substantial advantages for studies of marine mammal hearing, where testing time and access to subjects are typically limited.     

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.     

The acoustical cues to sound location in the rat: measurements of directional transfer functions

The acoustical cues for sound location are generated by spatial- and frequency-dependent filtering of propagating sound waves by the head and external ears. Although rats have been a common model system for anatomy, physiology, and psychophysics of localization, there have been few studies of the acoustical cues available to rats. Here, directional transfer functions (DTFs), the directional components of the head-related transfer functions, were measured in six adult rats. The cues to location were computed from the DTFs. In the frontal hemisphere, spectral notches were present for frequencies from approximately 16 to 30 kHz; in general, the frequency corresponding to the notch increased with increases in source elevation and in azimuth toward the ipsilateral ear. The maximum high-frequency envelope-based interaural time differences (ITDs) were 130 mus, whereas low-frequency (<3.5 kHz) fine-structure ITDs were 160 mus; both types of ITDs were larger than predicted from spherical head models. Interaural level differences (ILDs) strongly depended on location and frequency. Maximum ILDs were <10 dB for frequencies <8 kHz and were as large as 20-40 dB for frequencies >20 kHz. Removal of the pinna eliminated the spectral notches, reduced the acoustic gain and ILDs, altered the acoustical axis, and reduced the ITDs.     

Temporal resolution in frog auditory-nerve fibers

Sinusoidally amplitude-modulated (SAM) noise was monaurally presented to the neotropical frog, Eleutherodactylus coqui, while recording intracellularly from auditory-nerve fibers. Neuronal phase locking was measured to the SAM noise envelope in the form of a period histogram. The modulation depth was changed (in 10% steps) until the threshold modulation depth was determined. This was repeated for various modulation frequencies (20-1200 Hz) and different levels of SAM noise (34-64 dB/Hz). From these data, temporal modulation transfer functions (TMTFs) were produced and minimum integration time (MIT) for each auditory fiber was calculated. The median MIT was 0.42 ms (lower quartile 0.32, upper quartile 0.68 ms). A noise level-dependent effect was noted on the shape of the TMTF as well as the minimum integration time. The latter results may be explained as a loss in spectral resolution with increasing noise level, which is consistent with the correlation that was found between minimum integration time and bandwidth.     

An autocorrelation model with place dependence to account for the effect of harmonic number on fundamental frequency discrimination

Fundamental frequency (f0) difference limens (DLs) were measured as a function of f0 for sine- and random-phase harmonic complexes, bandpass filtered with 3-dB cutoff frequencies of 2.5 and 3.5 kHz (low region) or 5 and 7 kHz (high region), and presented at an average 15 dB sensation level (approximately 48 dB SPL) per component in a wideband background noise. Fundamental frequencies ranged from 50 to 300 Hz and 100 to 600 Hz in the low and high spectral regions, respectively. In each spectral region, f0 DLs improved dramatically with increasing f0 as approximately the tenth harmonic appeared in the passband. Generally, f0 DLs for complexes with similar harmonic numbers were similar in the two spectral regions. The dependence of f0 discrimination on harmonic number presents a significant challenge to autocorrelation (AC) models of pitch, in which predictions generally depend more on spectral region than harmonic number. A modification involving a "lag window"is proposed and tested, restricting the AC representation to a limited range of lags relative to each channel's characteristic frequency. This modified unitary pitch model was able to account for the dependence of f0 DLs on harmonic number, although this correct behavior was not based on peripheral harmonic resolvability.     

Frequency specificity of chirp-evoked auditory brainstem responses

This study examines the usefulness of the upward chirp stimulus developed by Dau et al. [J. Acoust. Soc. Am. 107, 1530-1540 (2000)] for retrieving frequency-specific information. The chirp was designed to produce simultaneous displacement maxima along the cochlear partition by compensating for frequency-dependent traveling-time differences. In the first experiment, auditory brainstem responses (ABR) elicited by the click and the broadband chirp were obtained in the presence of high-pass masking noise, with cutoff frequencies of 0.5, 1, 2, 4, and 8 kHz. Results revealed a larger wave-V amplitude for chirp than for click stimulation in all masking conditions. Wave-V amplitude for the chirp increased continuously with increasing high-pass cutoff frequency while it remains nearly constant for the click for cutoff frequencies greater than 1 kHz. The same two stimuli were tested in the presence of a notched-noise masker with one-octave wide spectral notches corresponding to the cutoff frequencies used in the first experiment. The recordings were compared with derived responses, calculated offline, from the high-pass masking conditions. No significant difference in response amplitude between click and chirp stimulation was found for the notched-noise responses as well as for the derived responses. In the second experiment, responses were obtained using narrow-band stimuli. A low-frequency chirp and a 250-Hz tone pulse with comparable duration and magnitude spectrum were used as stimuli. The narrow-band chirp elicited a larger response amplitude than the tone pulse at low and medium stimulation levels. Overall, the results of the present study further demonstrate the importance of considering peripheral processing for the formation of ABR. The chirp might be of particular interest for assessing low-frequency information.     

Intensity discrimination as a function of level and frequency and its relation to high-frequency hearing

This paper examines how intensity discrimination depends on the test frequency, the level, and the subjects's high-frequency hearing. Three experiments were performed. In the first experiment, intensity discrimination of pulsed tones was measured as a function of level at 1 and 14 kHz in five listeners. Results show less deviation from Weber's law at 14 kHz than at 1 kHz. In the second experiment, intensity discrimination was measured for a 1-kHz tone at 90-dB SPL as a function of the cutoff frequency of a high-pass masking noise in two listeners. Results show that the audibility of very high frequencies is important for frequency discrimination at 1 kHz. The DL increased by a factor between 1.5 and 2.0 as the cutoff frequency of the noise was lowered from 19 to 6 kHz. In the third experiment, thresholds from 6 to 20 kHz and intensity discrimination for a 1-kHz tone was measured in 12 listeners. Results show that the DLs at 80-dB SPL are correlated with the ability to hear very high frequencies. Results of all three experiments are consistent with the multiband version of the excitation-pattern model for intensity discrimination [Florentine and Buus, J. Acoust. Soc. Am. 70, 1646-1654 (1981)].     

Intrinsic envelope fluctuations and modulation-detection thresholds for narrow-band noise carriers

A model is presented which calculates the intrinsic envelope power of a bandpass noise carrier within the passband of a hypothetical modulation filter tuned to a specific modulation frequency. Model predictions are compared to experimentally obtained amplitude modulation (AM) detection thresholds. In experiment 1, thresholds for modulation rates of 5, 25, and 100 Hz imposed on a bandpass Gaussian noise carrier with a fixed upper cutoff frequency of 6 kHz and a bandwidth in the range from 1 to 6000 Hz were obtained. In experiment 2, three noises with different spectra of the intrinsic fluctuations served as the carrier: Gaussian noise, multiplied noise, and low-noise noise. In each case, the carrier was spectrally centered at 5 kHz and had a bandwidth of 50 Hz. The AM detection thresholds were obtained for modulation frequencies of 10, 20, 30, 50, 70, and 100 Hz. The intrinsic envelope power of the carrier at the output of the modulation filter tuned to the signal modulation frequency appears to provide a good estimate for AM detection threshold. The results are compared with predictions on the basis of the more complex auditory processing model by Dau et al.     

Spectral modulation masking patterns reveal tuning to spectral envelope frequency

Auditory processing appears to include a series of domain-specific filtering operations that include tuning in the audio-frequency domain, followed by tuning in the temporal modulation domain, and perhaps tuning in the spectral modulation domain. To explore the possibility of tuning in the spectral modulation domain, a masking experiment was designed to measure masking patterns in the spectral modulation domain. Spectral modulation transfer functions (SMTFs) were measured for modulation frequencies from 0.25 to 14 cycles/octave superimposed on noise carriers either one octave (800-1600 Hz, 6400-12,800 Hz) or six octaves wide (200-12,800 Hz). The resulting SMTFs showed maximum sensitivity to modulation between 1 and 3 cycles/octave with reduced sensitivity above and below this region. Masked spectral modulation detection thresholds were measured for masker modulation frequencies of 1, 3, and 5 cycles/octave with a fixed modulation depth of 15 dB. The masking patterns obtained for each masker frequency and carrier band revealed tuning (maximum masking) near the masker frequency, which is consistent with the theory that spectral envelope perception is governed by a series of spectral modulation channels tuned to different spectral modulation frequencies.     

Detection of temporal gaps in bandlimited noise: effects of variations in bandwidth and signal-to-masker ratio

Thresholds were measured for the detection of a temporal gap in a bandlimited noise signal presented in a continuous wideband masker, using an adaptive forced-choice procedure. In experiment I the ratio of signal spectrum level to masker spectrum level (the SMR) was fixed at 10 dB and gap thresholds were measured as a function of signal bandwidth at three center frequencies: 0.4, 1.0, and 6.5 kHz. Performance improved with increasing bandwidth and increasing center frequency. For a subset of conditions, gap threshold was also measured as bandwidth was varied keeping the upper cutoff frequency of the signal constant. In this case the variation of gap threshold with bandwidth was more gradual, suggesting that subjects detect the gap using primarily the highest frequency region available in the signal. At low center frequencies, however, subjects may have a limited ability to combine information in different frequency regions. In experiment II gap thresholds were measured as a function of SMR for several signal bandwidths at each of three center frequencies: 0.5, 1.0, and 6.5 kHz. Gap thresholds improved with increasing SMR, but the improvement was minimal for SMRs greater than 12-15 dB. The results are used to evaluate the relative importance of factors influencing gap threshold.     

Detection of modulation in spectral envelopes and linear-rippled noises by budgerigars (Melopsittacus undulatus)

Budgerigars were trained to discriminate complex sounds with two different types of spectral profiles from flat-spectrum, wideband noise. In one case, complex sounds with a sinusoidal ripple in (log) amplitude across (log) frequency bandwidth were generated by combining 201 logarithmically spaced tones covering the frequency region from 500 Hz to 10 kHz. A second type of rippled stimulus was generated by delaying broadband noise and adding it to the original noise in an iterative fashion. In each case, thresholds for modulation depth (i.e., peak-to-valley in dB) were measured at several different ripple frequencies (i.e., cycles/octave for logarithmic profiles) or different repetition pitches (i.e., delay for ripple noises). Budgerigars were similar to humans in detecting ripple at low spatial frequencies, but were considerably more sensitive than humans in detecting ripples in log ripple spectra at high spatial frequencies. Budgerigars were also similar to humans in detecting linear ripple in broadband noise over a wide range of repetition pitches. Taken together, these data show that the avian auditory system is at least as good, if not better, than the human auditory system at detecting spectral ripples in noise despite gross anatomical differences in both the peripheral and central auditory nervous systems.     

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.