Julius L. Goldstein

An optimum processor theory for the central formation of the pitch of complex tones

A theory was formulated for the central formation of the pitch of complex tones, i.e., periodicity pitch. This theory is a logical deduction from statistical estimation theory of the optimal estimate for fundamental frequency, when this estimate is constrained in ways inferred from empirical phenomena. These constraints are (1) the estimator receives noisy information on the frequencies, but not amplitudes and phases, of aurally resolvable simple tones from the stimulus and its aural combination tones, and (2) the estimator presumes all stimuli are periodic with spectra comprising successive harmonics. The stochastic signals representing the frequencies of resolved tones are characterized by independent Gaussian distributions with mean equal to the frequency represented and a variance that serves as free parameter. The theory is indifferent to whether frequency is coded by place or time. Optimum estimates of fundamental frequency and harmonic numbers are calculated upon each stimulus presentation. Multimo...

Neural correlates of the aural combination tone 2f 1 - f 2

Physiological studies confirm the nineteenth-century view that the phenomenon of aural combination tones has important implications for the understanding of the auditory system. Responses of single fibers in the auditory nerve of anesthetized cats were studied for evidence of combination tones when the acoustic stimulus consisted of two sinusoidal tones. The stimulus frequencies were chosen so that the combination frequency 2f 1 - f 2 , where 1 2 /f 1 1 - f 2 ) were found for every fiber, 2) the time-locked response could be cancelled by adding a combination tone (2f 1 - f 1 ) to the stimulus, 3) the stimulus frequencies could be chosen to obtain responses that were predominantly time locked to the reference combination tone, and 4) the rates of discharge for both single and two-tone stimuli show a similar dependence upon sound level. These characteristics of the neural responses are similar to those expected from acoustic stimuli that contain a combination tone (2f 1 - f 2 ) of amplitude approximately proportional to the actual stimulus amplitude. Therefore, these findings do not reflect an overloading type of distortion but rather some normal operating property of the auditory system. The physiological findings bear a close relation to those of psychophysical experiments on combination tones.

A cochlear nonlinear transmission‐line model compatible with combination tone psychophysics

Human psychophysical measurements of the cubic combination tone (2f1-f2) have shown that at low and moderate stimulus levels its phase decreases at 6 degrees-12 degrees per dB increase in stimulus level. This finding contrasts with physiological measurements in anaesthetized animals where the CT phase is insensitive to stimulus level. We have characterized quantitatively the difference in cochlear nonlinear response between humans and animals in terms of a cochlear nonlinear transmission line model having different nonlinear elements for human and animal. Following Hall [J. Acoust. Soc. Am. 56, 1818-1828 (1974)], a nonlinearity was introduced in the resistance of the cochlear partition (model A) for describing the animal cochlea. To model the human cochlea, we found that adding a nonlinear stiffness to the nonlinear mechanical loading of the basilar membrane gave the correct phase-amplitude dependence (model B). Simulation was used to solve the nonlinear models in the time domain. For high amplitude stimuli, both models predict similar results, mainly saturation in the response. The significant differences between the models occur at low and moderate stimulus intensities. According to model B the site of the resonant frequency along the basilar membrane depends on the stimulus level, while it is independent of stimulus level according to model A. As a result of the shift in the resonant site location in model B, the phase response profile is shifted as well, so that the phase response at the original resonant site depends on stimulus level. The psychophysical data on CT cancellation were predicted by model B, while physiological data on CT cancellation are predicted by model A.

Scalar LPC quantization based on format JND's

Efficient scalar quantization tables for LPC k-parameters were developed using a distortion measure based on just-noticeable-differences (JNDs) in formant parameters of the speech spectrum envelope. Forty percent fewer bits were required than the 41/frame used in conventional approaches. An empirical technique was developed for relating perturbations in k-parameters and formant parameters. New estimates were obtained for the values of the formant JNDs: they are about four times the steady-state values reported by Flanagan [6] and increase sharply above approximately 1.5 kHz.

Modeling the nonlinear cochlear mechanical basis of psychophysical tuning.

The multiple‐bandpass‐nonlinearity (MBPNL) model of nonlinear cochlear mechanical response [J. Goldstein, Hear. Res. 49, 39–60 (1990)] was used to study the basis for sound‐level dependence of human psychophysical tuning [R. Wegel and C. Lane, Phys. Rev. 23, 226–285 (1924)]. Comprehensive psychophysical tuning curve (PTC) data reported by P. Stelmachowicz and W. Jesteadt [J. Speech and Hear. Res. 27, 396–402 (1984)] and supplemented by Nelson and Fortune [J. Speech Hear. Res. 34, 360–373 (1991)] were simulated with a single MBPNL filter channel tuned to the 2‐kHz probe tone and detected by a classical Weber–Fraction energy detector. Accurate simulation of most of the PTC data was obtained with MBPNL parameters similar to values estimated earlier from physical cochlear measurements. Nelson and Fortune showed that masking of aural combination tones significantly broadens the PTCs at high probe levels. The model simulations confirm their finding by providing better agreement with their broader high‐level PTC...

Comparison of peak and energy detection for auditory masking of tones by narrow‐band noise

Classical energy‐detection theory [Green and Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966)] predicts that masking of tones by Gaussian noise is limited by the variability of detector responses and by internal auditory noise. It elegantly relates detection variability to masker duration–bandwidth product (TW). The theory accounts reasonably for Gaussian maskers with fixed RMS levels, but fails when the level is randomly roved with each stimulus presentation, suggesting that the auditory system detects waveform cues. A solution to this problem is proposed in which energy detection is replaced with the dual cues of envelope peak detection and normalized envelope peak detection, which are optimally processed as in classical theory [Goldstein and Hall, J. Acoust. Soc. Am. 97, 3330(A) (1995)]. The model was studied with periodic noise maskers comprising successive harmonics having uniform amplitudes and random phases, and with Gaussian noise maskers. Fixed‐level masked threshold predi...

Peak detection for auditory sound discrimination

Auditory detection of envelope maxima in temporal responses of cochlear frequency‐analyzing filters has been hypothesized to account for phase effects in psychophysical discrimination [J. L. Goldstein, 458–479 (1967)]. Re‐examination of this hypothesis in the context of asymmetry of masking [R. Hellman, Percept. Psychophys. 11, 241–246 (1972)] reveals that it also provides an adequate explanation for this phenomenon. Peak discrimination between a tone and tone masker plus narrow‐band‐noise probe is more sensitive to probe energy than is the inverse discrimination between noise and noise masker plus tone probe, in agreement with psychophysics. Simulations of this model indicate that asymmetry of masking is a function of the product of noise bandwidth and temporal duration. Psychophysical experiments on masking asymmetry were performed with both masker and probe bandwidth ranging from pure tone to supracritical band. The experimental design included both fixed and roving levels, with random phases fixed thr...

Changing roles in the cochlea: Bandpass filtering by the organ of Corti and additive amplification on the basilar membrane

The classical role of the basilar membrane in cochlear sound analysis is being reassessed on the basis of quantitative models of cochlear nonlinear responses and biophysical evidence for tonotopically organized tuning by outer hair cells. It is hypothesized that the primary function of cochlear bandpass filtering is performed by the organ of Corti, whose nonlinear responses to stapes signals are collected by the basilar membrane. Bilateral nonlinear signal processing characteristics for the organ‐of‐Corti filters are quantified with a new feedback reconfiguration of the multiple‐bandpass nonlinearity (MBPNL) model [J. Goldstein, Hear. Res. 49, 39–60 (1990)]. The basilar membrane is modeled classically, but its role is hypothesized to be analogous to the transmission‐line collector of a distributed amplifier. Traveling waves on the basilar membrane provide a means for coherent addition of responses to a given tone from different organ‐of‐Corti filters. Computations with the model using biophysical knowledge of the density of outer hair cells and the tonotopic map yield a maximum distributed gain of 43 dB, which agrees with known data. Bilateral nonlinear transduction in the cochlear model is responsible for an I/O response versus level for tones that compresses at much lower sound levels than the isolated organ‐of‐Corti filter, also consistent with data. These results encourage further modeling research with our working hypothesis that redefines the roles of basilar membrane and organ of Corti in cochlear function. [Work supported by NIDCD Grant No. DC00737.]

Statistical theory of peak detection for human hearing

Envelope peaks and peak factors of narrow‐band sounds have been found in simulation studies to explain a wide range of experiments on sound discrimination [e.g., J. L. Goldstein, J. Acoust. Soc. Am. 99, 2541(A) (1996)]. To extend understanding of peak detection, mathematical approximations were developed for the first and second moments of log (dB) envelope statistics of a tone centered in noise with duration T and bandwidth W. Noises considered are: uniform periodic noise (UPN) having uniform amplitudes and random phases, Gaussian periodic noise (GPN) having random amplitudes and phases, and true Gaussian noise (TGN). Key properties quantified include: (1) Three nearly independent causes of waveform fluctuation underlie peak variance, viz., phase noise, energy noise, and interaction of tone with common frequency noise (energy cross term). (2) The energy variances in peak detection are similar as for energy detection. (3) Peak factor variance is primarily phase noise, which, for noise alone, is ∼1 dB for ...

Temporal factors in auditory peak detection of modulation of tones

Auditory detection of tone modulation has been modeled as envelope‐peak detection of the cochlear filterbank responses [J. L. Goldstein, J. Acoust. Soc. Am. 41, 458–479 (1967)]. To study the ability of this model to quantify temporal smoothing in detection, new psychophysical experiments using a 4IFC paradigm were conducted, with the authors as subjects. AM or quasi‐FM sinusoidally modulated tones were discriminated from the carrier tone. Only one should was modulated among the four pushed sounds in the paradigm. The first series of exploratory experiments (1994) focused on low modulation frequencies (4–16 Hz). A second series of systematic experiments (1996) with a wide range of modulation frequencies allowed estimation of detector smoothing at carrier frequencies of 0.25, 1, and 4 kHz. Despite differences between subjects in estimated spectral filtering, modulation thresholds for both subjects gave similar estimates of smoothing at each carrier frequency. At modulation frequencies above 20 Hz, the smoot...