Abhijit Kulkarni

Role of spectral detail in sound-source localization

Sounds heard over headphones are typically perceived inside the head (internalized), unlike real sound sources which are perceived outside the head (externalized). If the acoustical waveforms from a real sound source are reproduced precisely using headphones, auditory images are appropriately externalized and localized. The filtering (relative boosting, attenuation and delaying of component frequencies) of a sound by the head and outer ear provides information about the location of a sound source by means of the differences in the frequency spectra between the ears as well as the overall spectral shape. This location-dependent filtering is explicitly described by the head-related transfer function (HRTF) from sound source to ear canal. Here we present sounds to subjects through open-canal tube-phones and investigate how accurately the HRTFs must be reproduced to achieve true three-dimensional perception of auditory signals in anechoic space. Listeners attempted to discriminate between ‘real’ sounds presented from a loudspeaker and ‘virtual’ sounds presented over tube-phones. Our results show that the HRTFs can be smoothed significantly in frequency without affecting the perceived location of a sound. Listeners cannot distinguish real from virtual sources until the HRTF has lost most of its detailed variation in frequency, at which time the perceived elevation of the image is the reported cue.

SENSITIVITY OF HUMAN SUBJECTS TO HEAD-RELATED TRANSFER-FUNCTION PHASE SPECTRA

Head-related transfer functions (HRTFs) for human subjects in anechoic space were modeled with modified phase spectra, including minimum-phase-plus-delay, linear-phase, and reversed-phase-plus-delay functions. The overall (wide-band) interaural time delay (ITD) for the modeled HRTFs was made consistent with that of the empirical HRTFs by setting the position-dependent, frequency-independent delay in the HRTF for the lagging ear. Signal analysis of the minimum-phase-plus-delay reconstructions indicated that model HRTFs deviate from empirical HRTF measurements maximally for contralateral azimuths and low elevations. Subjects assessed the perceptual validity of the model HRTFs in a four-interval, two-alternative, forced-choice discrimination paradigm. Results indicate that monaural discrimination performance of subjects was at chance for all three types of HRTF models. Binaural discrimination performance was at chance for the linear-phase HRTFs, was above chance for some locations for the minimum-phase-plus-delay HRTFs, and was above chance for all tested locations for the reversed-phase-plus-delay HRTFs. An analysis of low-frequency timing information showed that all of these results are consistent with efficient use of interaural time differences in the low-frequency components of the stimulus waveforms. It is concluded that listeners are insensitive to HRTF phase spectra as long as the overall ITD of the low-frequency components does not provide a reliable cue. In particular, the minimum-phase-plus-delay approximation to the HRTF phase spectrum is an adequate approximation as long as the low-frequency ITD is appropriate. These results and conclusions are all limited to the anechoic case when the HRTFs correspond to brief impulse responses limited to a few milliseconds.

Infinite-impulse-response models of the head-related transfer function

Head-related transfer functions (HRTFs) measured from human subjects were approximated using infinite-impulse-response (IIR) filter models. Models were restricted to rational transfer functions (plus simple delays) so that specific models are characterized by the locations of poles and zeros in the complex plane. The all-pole case (with no nontrivial zeros) is treated first using the theory of linear prediction. Then the general pole-zero model is derived using a weighted-least-squares (WLS) formulation of the modified least-squares problem proposed by Kalman (1958). Both estimation algorithms are based on solutions of sets of linear equations and result in efficient computational schemes to find low-order model HRTFs. The validity of each of these two low-order models was assessed in psychophysical experiments. Specifically, a four-interval, two-alternative, forced-choice paradigm was used to test the discriminability of virtual stimuli constructed from empirical and model HRTFs for corresponding locations. For these experiments, the stimuli were 80 ms, noise tokens generated from a wideband noise generator. Results show that sounds synthesized through model HRTFs were indistinguishable from sounds synthesized from original HRTF measurements for the majority of positions tested. The advantages of the techniques described here are the computational efficiencies achieved for low-order IIR models. Properties of the all-pole and pole-zero estimators are discussed in the context of low-order HRTF representations, and implications for basic and applied contexts are considered.

On the minimum-phase approximation of head-related transfer functions

The head-related transfer function embodies the amplitude and phase transformations accompanying a sound source from a fixed position in space to the eardrum. These transformations, which primarily result from the interaction of the acoustic wave with the complex geometry of the head and pinna, are known to be the principal determinants of source location. It is especially known that the interaural time differences (ITDs) are encoded by the phase spectra of the HRTFs at the two ears. In this study we explore a model of the HRTF which approximates the HRTF as a minimum phase function. The model is tested both theoretically and through psychophysical experiments. Results suggest that a minimum phase representation of the phase spectra, augmented by a position-dependent, frequency-independent ITD, is an adequate description of the HRTF phase. Both the scientific and the practical consequences of this result shall be discussed.

Variability in the characterization of the headphone transfer-function

In simulations of virtual acoustic space, stimuli are filtered with HRTFs and presented over headphones. An equalization filter is specified to compensate for the spurious coloration introduced by the headphone delivery system on the stimulus at the listener’s eardrum. The purpose of this letter is to report the variability in the response of supra-aural headphones arising from the positioning of the headphone cushion during normal usage. The headphone responses were obtained on the KEMAR acoustical mannequin. It is shown that the variability in the measurements due to headphone cushion placements makes it difficult to specify a compensation filter for canceling the headphone characteristics. This makes the stimulus waveform at a listener’s eardrum unpredictable and could have an important consequence on the perceptual adequacy of virtual displays.

Efficient finite‐impulse‐response filter models of the head‐related transfer function

The head‐related transfer function (HRTF) is empirically measured as a finite‐impulse‐response (FIR) filter e.g., Wightman and Kistler, 1989. In this study we explore reduced‐order approximations of measured HRTFs for use in virtual acoustical displays. The HRTFs tested were measured from human subjects and provided by Dr. Fred Wightman. In all model reconstructions it is assumed that HRTFs can be approximated as minimum‐phase functions. Theoretical results are derived which allow for two model‐order reduction strategies with optimal criteria. First, we demonstrate that the partial energy contained in the first n taps of a minimum‐phase FIR filter is optimal in the Parseval sense. Secondly, we demonstrate that the HRTF expressed by its cepstral coefficients (Oppenheim and Schafer, 1979) constitutes a Fourier series. A partial sum from this Fourier series then provides the best mean‐square approximation to the log‐magnitude function of the HRTF. The validity of the reconstructed HRTFs was assessed psychoph...

Influence of autoregressive model parameter uncertainty on spectral estimates of heart rate dynamics

Linear autoregressive (AR) model-based heart rate (HR) spectral analysis has been widely used to study HR dynamics. Owing to system and measurement noise, the parameters of an AR model have intrinsic statistical uncertainty. In this study, we evaluate how this AR parameter uncertainty can translate to uncertainty in HR power spectra. HR time series, obtained from seven subjects in supine standing positions, were fitted to AR models by least squares minimization via singular value decomposition. Spectral uncertainty due to inexact parameter estimation was assessed through a Monte Carlo study in which the AR model parameters were varied randomly according to their Gaussian distributions. Histogram techniques were used to evaluate the distribution of 50,000 AR spectral estimates of each HR time series. These Monte Carlo uncertainties were found to exceed those predicted by previous theoretical approximations. It was determined that the uncertainty of AR HR spectral estimates, particularly the locations and magnitudes of spectral peaks, can often be large. The same Monte Carlo analysis was applied to synthetic AR time series and found levels of spectral uncertainty similar to that of the HR data, thus suggesting that the results of this study are not specific to experimental HR data. Therefore, AR spectra may be unreliable, and one must be careful in assigning pathophysiological origins to specific spectral features of any one spectrum.

Evaluation of a linear interpolation scheme for approximating HRTFs

As part of a study of virtual acoustical environments, the ability of subjects to distinguish interpolated HRTFs from empirical HRTFs in the horizontal plane was investigated. Each interpolated HRTF was obtained by averaging empirical HRTFs from two positions chosen symmetrically about the location of interest. Empirical HRTFs were measured from the KEMAR mannequin in anechoic space. Subjects were tested using a 4I, 2AFC paradigm for several angles of interpolation using lowpass noise stimuli. Theoretical analysis predicted a useful lateralization cue for large interpolation angles. For a 2.2‐kHz lowpass stimulus, subjects reported the use of such a cue and performed at 96% correct (averaged across four subjects) for a 30‐deg angle. For a 10‐deg angle, subjects reported no lateralization cue and performed near chance (53% correct), until they discovered a spectral cue increasing performance significantly (69% correct). Monaural performance was comparable to binaural performance, consistent with prediction...

Uncertainty of AR spectral estimates

The statistical uncertainty of autoregressive (AR) model heart rate (HR) power spectra was investigated. HR time series, obtained from 9 subjects in supine and standing positions, were fit to AR models by least squares minimization via singular value decomposition (SVD). AR spectral uncertainty due to inexact parameter estimation was assessed in a Monte Carlo study. For each of 50000 spectral realizations, all AR parameters were varied randomly within 1 standard deviation of their SVD estimated values. Histogram techniques were used to evaluate the resulting distribution of spectral estimates. It was determined that the uncertainty of HR AR spectral estimates can be quite high, especially at the locations of spectral peaks. Thus, AR spectra may be unreliable and assigning physiological origins to specific spectral features may be inappropriate.<<ETX>>

Binaural recordings from KEMAR mannequin in several acoustical environments

In the development and evaluation of virtual acoustic displays, the relative importance of factors such as head movement, listener‐specific pinna responses, and naturalness of the environment to the veridical localization of sound (including externalization) remains unclear. In this poster demonstration, the role of reverberation is explored through a series of recordings from an artificial head in a variety of acoustical environments. Specifically, several binaural recordings have been made on the acoustical mannequin KEMAR for single and multiple talker configurations in a variety of different environments and in a number of different conditions. The signals from KEMAR’s microphones (Etymotic ER−1/2 in.) were amplified (ER‐11 amplifiers provided with microphones) and fed directly to a commercially available digital audio tape (DAT) machine. These recordings will be available for listening and discussion at the poster. [Work supported by NIDCD.]