James W. Pitton

Construction of positive time-frequency distributions

A general method for constructing nonnegative definite, joint time-frequency distributions (TFDs) satisfying the marginals of time |s(t)|/sup 2/ and frequency |S(f)|/sup 2/ is presented. As nonnegative-definite distributions with the correct marginals, these TFDs are members of the Cohen-Posch class. Several examples illustrating properties of these TFDs are presented for both synthetic and real signals. >

Bilinear time-frequency representations: new insights and properties

An analysis of the interference terms of Cohen-class bilinear time-frequency representations (TFR) of multicomponent signals is presented. Constraints for achieving new interference properties are derived. Imposing these interference time and interference frequency concentration constraints on a TFR guarantees that the TFR will be zero everywhere the signal s(t) is zero, and the TFR will contain only those frequencies that occur in the signal. Thus, these new constraints guarantee strong finite support in a TFR. When these interference concentration properties are combined with interference attenuation, tradeoffs between finite support, the marginals, and the interference properties are shown to be unavoidable. The useful class of product kernels are considered and generalized further to allow TFR with potentially superior interference properties. The interference frequency concentration and attenuation properties allow TFR with spectrogram-like interference suppression, but without the spectrograms inherent time/frequency resolution tradeoff. Other useful combinations of properties are discussed and analyzed, and properties and tradeoffs are illustrated by examples. >

Modulation-scale analysis for content identification

For nonstationary signal classification, e.g., speech or music, features are traditionally extracted from a time-shifted, yet short data window. For many applications, these short-term features do not efficiently capture or represent longer term signal variation. Partially motivated by human audition, we overcome the deficiencies of short-term features by employing modulation-scale analysis for long-term feature analysis. Our analysis, which uses time-frequency theory integrated with psychoacoustic results on modulation frequency perception, not only contains short-term information about the signals, but also provides long-term information representing patterns of time variation. This paper describes these features and their normalization. We demonstrate the effectiveness of our long-term features over conventional short-term features in content-based audio identification. A simulated study using a large data set, including nearly 10 000 songs and requiring over a billion audio pairwise comparisons, shows that modulation-scale features improves content identification accuracy substantially, especially when time and frequency distortions are imposed.

Time-frequency analysis and auditory modeling for automatic recognition of speech

Modern speech processing research may be categorized into three broad areas: statistical, physiological, and perceptual. Statistical research investigates the nature of the variability of the speech waveform from a signal processing viewpoint. This approach relates to the processing of speech in order to obtain measurements of speech characteristics which demonstrate manageable variabilities across a wide range of the talker population, in the presence of noise or competing speakers as well as the interaction of speech with the channel through which it is transmitted, and under the inherent interaction of the information content of speech itself (i.e., the contextual factor). Physiological research aims at constructing accurate models of the articulatory and auditory process, helping to limit the signal space for speech processing. In the perceptual realm, work focuses on understanding the psychoacoustic and possibly the psycholinguistic aspects of the speech communication process that the human so conveniently conducts. By studying this working analysis/recognition system, insights may be garnered that will lead to improved methods of speech processing. Conversely by studying the limitations of this system, particularly how it reduces the information rate of the received signal through, for example, masking and adaptation improvements may be made in the efficiency of speech coding schemes without impacting the quality of the reconstructed speech. Thus comprehension of speech production and perception impacts methods of speech processing, and vice-versa. This paper enunciates such a position, focusing on how modern time-frequency signal analysis methods could help expedite needed advances in these areas.

Approximating time-frequency density functions via optimal combinations of spectrograms

We demonstrate that two previously proposed methods for combining the information content from multiple spectrograms into a single, positive time-frequency function are optimal in a cross-entropy sense. The goal in combining the spectrograms is to obtain an improved approximation of the joint time-frequency signal density by overcoming limitations of any single spectrogram. An example of each method is provided, and results are compared with spectrograms and a Cohen-Posch (1985) time-frequency density (TFD) of a nonstationary pulsed tone signal. The proposed combinations are effective and can be efficiently computed.<<ETX>>

An information-theoretic approach to positive time-frequency distributions

The principle of minimum cross entropy (MCE) is used to generate positive distributions in the Cohen-Posch (1985) class of proper time-frequency distributions (TFDs). The MCE-TFDs are not only intuitively satisfying, but they also yield the correct marginals, have strong finite support, and are everywhere nonnegative. The usual cross-term artifacts that hinder interpretation of other time-frequency representations (most notably, the Wigner-Ville) are not a problem with the MCE-TFDs. Examples of speech and chirps are given and compared to the spectrogram. An interesting observation in the case of speech is that spectrograms more closely resemble time-conditional-frequency distributions (narrowband) or frequency-conditional-time distributions (wideband) than they do joint time-frequency distributions.<<ETX>>

Perceptual Feature Identification for Active Sonar Echoes

This paper presents a novel method of using psychoacoustic information from human listening experiments to generate useful features for automated signal classification or regression. The design and analysis of a similarity experiment using active sonar transient echoes is summarized and two methods are presented for feature identification based on the results of the listening experiment. These methods not only identify novel features but also provide a visual insight into perceptually significant signal attributes. The approach presented is based on perceptual similarity measures collected during formal listening experiments but is applicable to any perceptual similarity experiment (e.g. visual)

Positive time-frequency distributions via maximum entropy deconvolution of the evolutionary spectrum

The relationship between Priestleys definition of the evolutionary densities (TFDs) is explored, and a synthesis method is presented. As defined by Priestley, the ES is not a member of the Cohen-Posch class of TFDs. However, it is shown that by choosing a unit-energy normalization for the envelope function of Priestleys formulation, the energetic ES thus obtained is a member of the Cohen-Posch class of TFDs; this normalization differs from that chosen by Priestley. A method is then presented to obtain an estimate of the energetic ES. This method employs maximum entropy deconvolution of the spectrogram, which is itself a blurred version of the ES. Because the energetic ES is everywhere nonnegative and yields the correct marginal densities, it is a legitimate, joint time-frequency energy density of the signal, unlike the Wigner and other bilinear distributions that go negative.<<ETX>>

Time-frequency spectrum estimation: an adaptive multitaper method

This paper extends Thomsons (1982) adaptive multitaper spectrum estimation method to the nonstationary case. The general approach and the nonadaptive estimation procedure were first presented by Pitton (1998). The method uses time-frequency concentrated basis functions which generalize the properties of the prolate spheroidal waveforms. Individual spectrograms computed with these eigenfunctions form direct time-frequency spectrum estimates, and are combined to form the multitaper time-frequency spectrum estimate. We then develop a new adaptive procedure which reduces the bias of the individual eigenestimates using an estimate of their leakage characteristics. The revised multitaper estimator then has correspondingly improved bias properties. An expression for the variance of the adaptive estimator is also derived, providing a complete characterization of the statistical time-frequency estimator.

Proper time-frequency energy distributions and the Heisenberg uncertainty principle

The Heisenberg uncertainty principle is used for understanding time-frequency distributions (TFDs) or density functions. The relationship between the uncertainty principle and proper TFDs is explored. Specifically, the authors address negative values in a TFD, the interpretation of TFDs as energy density functions, and local time-frequency resolution. This is done in light of having previously devised a method for constructing proper distributions.<<ETX>>