Gregory H. Wakefield

Comparison of electrode discrimination, pitch ranking, and pitch scaling data in postlingually deafened adult cochlear implant subjects

The goal of this study was to investigate the relationship between variation in electrode site of stimulation and the perceptual dimensions along which such stimuli vary. This information may allow more effective use of electrode place when encoding speech information. To achieve this goal, two procedures which measure pitch in subjects implanted with the Nucleus/Cochlear Corporation multichannel device were performed. Estimates of electrode discriminability that can be obtained from these procedures were compared to a more direct measure of electrode discriminability that was obtained in a previous study [Collins et al., Assoc. Res. Otolaryng. Abstracts, No. 642 (1994)]. In the first task, subjects performed a pitch ranking procedure similar to that used in previous studies [Townshend et al., J. Acoust. Soc. Am. 82, 106-115 (1987); Nelson et al., J. Acoust. Soc. Am. 98, 1987-1999 (1995)]. Estimates of the pitch percept elicited by stimulation of each electrode as well as the discriminability of the electrodes were generated from the data using two different statistical analyses. In the second task, subjects performed a pitch scaling procedure similar to one used in a previous study [Busby et al., J. Acoust. Soc. Am. 95, 2658-2669 (1994)]. Again, two different statistical analyses were performed to generate estimates of the pitch percept corresponding to stimulation of each electrode and to generate estimates of electrode discriminability. In general, the estimates of the relationships between the pitch percepts obtained from the two procedures were not identical. In addition, the estimates of electrode discriminability were not equivalent to the electrode discrimination measures obtained from the same subjects during the previous study. Signal detection theory has been used to model the decision processes required by each of the procedures described above [e.g., Jesteadt and Bilger, J. Acoust. Soc. Am. 55, 1266-1276 (1974)]. However, these models do not predict the differences that were observed between the data sets obtained during this study. An alternate model is proposed which may explain the data obtained from these subjects. This model is based on the assumption that the percept that is elicited by electrical stimulation of an electrode is multidimensional, as opposed to unidimensional in nature. Therefore, the perceived signal is more appropriately modeled using a multidimensional random vector, where each element of the vector represents the perceived value of one of the dimensions of the signal.

Mathematical representation of joint time-chroma distributions

Originally coined by the sensory psychologist Roger Shepard in the 1960s, chroma transforms frequency into octave equivalence classes. By extending the concept of chroma to chroma strength and how it varies over time, we have demonstrated the utility of chroma in simplifying the processing and representation of signals dominated by harmonically-related narrowband components. These investigations have utilized an ad hoc procedure for calculating the chromagram from a given time-frequency distribution. The present paper is intended to put this ad hoc procedure on more sound mathematical ground.

Special problems in the estimation of power-law spectra as applied to topographical modeling

An increasing number of topographical studies find that natural surfaces possess power-law roughness spectra. Power-law spectra introduce unique difficulties in the spectral estimation process. The authors describe how an improper window choice allows leakage that yields a spectral estimate that is insensitive to the spectral slope. In addition, the commonly used Fourier-based spectral estimates have higher variances than other available estimators. Higher variance is particularly problematic when data records are short, as is often the case in remote sensing studies. The authors show that Capons spectral estimator has less variance than Fourier-based estimators and measures the spectral slope more accurately. The authors also show how estimates of a 2D roughness spectrum can be obtained from estimates of the 1D spectrum for the isotropic power-law case. >

Discrimination of modulation depth of sinusoidal amplitude modulation (SAM) noise

The detection of sinusoidal amplitude modulation (SAM) provides a lower bound on the degree to which temporal information in the envelope of complex waveforms is encoded by the auditory system. The extent to which changes in the amount of modulation are discriminable provides additional information on the ability of the auditory system to utilize envelope fluctuations. Results from an experiment on the discrimination of modulation depth of broadband noise are presented. Discrimination thresholds, expressed as differences in modulation power, increase monotonically with the modulation depth of the standard, but do not obey Webers law. The effects of carrier level and of modulation frequency are consistent with those observed in modulation detection: Changes in carrier level have little effect on modulation discrimination; changes in modulation frequency also have little effect except for standards near the modulation detection threshold. The discrimination of modulation depth is consistent with the leaky-integrator model of modulation detection for standards below--10 dB (20 log ms); for standards greater than--10 dB, the leaky integrator predicts better performance than that observed behaviorally.

Pole-zero approximations for head-related transfer functions using a logarithmic error criterion

Pole-zero approximations of human free-field-to-eardrum transfer functions-i.e., head-related transfer functions (HRTFs)-can be used to synthesize binaural acoustic fields over headphones with fewer parameters, and therefore, lower computational complexity than is typically achieved by all-zero approximations. While standard pole-zero designs minimize the squared difference between the desired and designed frequency responses, the synthesis of binaural acoustic fields is more likely to be sensitive to relative, rather than absolute, differences in the HRTF approximations. The paper proposes a new design algorithm that minimizes an error criterion based on complex logarithms. As a result, both log-magnitude and phase errors are minimized. Slight modifications to the proposed algorithm result in one for which the phase error can be ignored. A comparison of this modified algorithm to others that have been developed to minimize the log-magnitude error shows implementation advantages without sacrificing performance. In achieving comparable errors, application of the proposed algorithm to the HRTF approximation results in pole-zero model orders smaller than those required for approximating the HRTFs using a least-squares error criterion.

The time-frequency characteristics of violin vibrato: Modal distribution analysis and synthesis

A high-resolution time-frequency distribution, the modal distribution, is applied to the study of violin vibrato. The analysis indicates that the frequency modulation induced by the motion of the stopped finger on the string is accompanied by a significant amplitude variation in each partial of that note. Amplitude and frequency estimates for each partial are extracted from the modal distribution of ten pitches that span the range of the violin instrument. The frequency modulation is well-represented by a single sinusoid with a mean rate of 5.9 Hz and a mean excursion of +/- 15.2 cents. A spectral decomposition of the amplitude envelopes of the partials shows that the peaks lie primarily at integer multiples of the vibrato rate. These amplitude and frequency estimates are used in an additive synthesis model to generate synthetic replicates of violin vibrato. Simple approximations to these estimates are created, and synthesized sounds using these are evaluated perceptually by seven subjects using discrimination, nonmetric multidimensional scaling (MDS), and sound quality scoring tasks. It is found that the absence of frequency modulation has little effect on the perceptual response to violin vibrato, while the absence of amplitude modulation causes marked changes in both sound quality and MDS results. Low-order spectral decompositions of the amplitude and frequency estimates also occupy the same perceptual space as the original recording for a subset of the pitches studied.

A high‐resolution time–frequency representation for musical instrument signals

Analyzing musical signals to obtain the time‐varying magnitudes and frequencies of instruments’ partial frequency components is important for resynthesis, transcription, and instrument physics. Windowing techniques, including Fourier series extensions, short‐time Fourier transforms, and constant‐Q transforms, generate bias in time and frequency dictated by the uncertainty principle. This is significant to analysis requirements of such properties as attack, which involve changes over millisecond time ranges and require frequency accuracy on the order of cents. Alternatives such as the Wigner distribution avoid the uncertainty principle restriction and associated bias, but nonlinear cross products of magnitude and frequency computations are not smoothed as with windowing methods, increasing those sources of bias. All these techniques belong to Cohen’s class, a framework where this paper develops the modal distribution, exhibiting decreased total bias. Computation of the modal distribution and a constant‐Q v...

Singing voice identification using spectral envelope estimation

In this paper, we present a spectrum-based system for singer identification that operates for the ideal case in which audio samples contain only the singers voice. Our method begins with the computation of a robust estimate of the spectral envelope called the composite transfer function (CTF). The CTF is derived from the instantaneous amplitude and frequency of the sinusoidal partials which make up the vocal signal. Unlike traditional source-filter theory , the CTF does not explicitly separate the spectral characteristics of the vocal source and the vocal tract filter. The principal components of the CTFs are used as features for a quadratic classifier to identify singers. The approach is validated on a database containing samples from twelve classically trained singers. In cross validation experiments, test set accuracies of approximately 95% are found for a baseline case. The classifiers performance is not degraded when different vowels are included in classifier training and evaluation. Restricting the frequency range of the CTFs and using a test set containing samples extracted from solo performances of Italian arias reduces the test set accuracy to 70-80%.

A comparison of head related transfer function interpolation methods

In order to achieve realistic synthesized 3-dimensional acoustic fields over headphones, low-order approximations of head related transfer functions (HRTFs) are desirable not only because of the computational complexity reduction, but also because of the potential for allowing listeners to modify the low-order approximation parameters in order to generate interpolated HRTFs that optimize the source localization percept. By fitting the directional component of a HRTF, commonly known as the directional transfer function (DTF), it is possible to achieve low-order systems for the purpose of interpolating HRTFs even if the number of parameters required to approximate the entire HRTF is relatively large. The present paper compares the relative performance of interpolation methods for both all-zero and pole-zero modelling of the DTFs. With the goal of developing better interpolation methods by incorporating subjective preferences, active sensory tuning (AST), which has been previously shown to provide an efficient means of searching through moderate dimensional parameter spaces using subjective feedback, is proposed as a method of providing high quality interpolated DTFs within reasonable time constraints.

On the design of pole-zero approximations using a logarithmic error measure

For obtaining a pole-zero approximation of a linear, discrete-time system, a new method is presented which minimizes the squared difference between the log-magnitude spectrum of the system and that of the approximation. Using an iterative procedure, a locally optimal solution is found for the poles and zeros of the system approximation. >