Spectral Feature Extraction Using Poisson Moments

We propose to use the Gamma filter [1] as a feature extractor for the preprocessing of speech signals. Gamma filter which can be implemented as a cascade of identical first order lowpass filters generates at its taps the Poisson Moments of an input signal. These moments carry spectral information about the recent history of the input signal. They can be used to construct time-frequency representations as an alternative to the conventional methods of short term Fourier transform, cepstrum, etc. In this study it is shown that when the time scale of the Gamma filter is chosen properly, the Poisson moments correspond to the Taylor’s series expansion coefficients of the input signal spectra. The appeal of the proposed method comes from the fact that in the analog domain the moments are available as a continuous time electrical signal and can be physically measured, rather than computed off-line by a digital computer. With this convenience, the speed of the discrete time processor following the preprocessor is independent of the highest frequency of the input signal, but is constrained with the stationarity duration of the signal. INTRODUCTION Classification of temporal patterns is one of the areas where artificial neural networks (ANNs) are frequently utilized. Speech recognition is a special case to that problem. In order to simplify the classification task undertaken by an ANN preprocessing of the temporal pattern is vital. The goal of the preprocessing should be to capture the features of the pattern and to express them in a low dimensional space. If this is achieved, then a big deal of computational and structural burden over the neural network can be removed. One method suggested for the preprocessing of speech signals is the Focused Gamma Network [2][3]. This is a generalized feedforward structure with adjustable feedback which is responsible for changing the time scale (or the memory depth) of the preprocessor. Adjusting the time scale allows one to focus the representation space on the signal of interest such that a low dimensional, but a faithful representation is obtained. Well known Time Delay Neural Network (TDNN) [4] is a special case of the Gamma Network where the time scale is frozen to be unity. In their isolated word speech recognition task Tracey and Principe [2] showed that the Gamma Network is superior to TDNN both in terms of the size of the neural network required and the time it took to learn the given patterns. In this paper we analyze the Gamma Network and show that the features fed into the ANN are basically the Taylor’s series expansion coefficients of the recent speech spectra. Taking into account the practicality of obtaining these features, a time-frequency representation can easily be constructed by concatenating the feature vectors of different times together. An analog implementation of the filter can be pursued in analog VLSI. Since the moment vectors are obtained in the analog domain, a digital processor that operates on these vectors is not bound by the Nyquist rate of the input signal, but by the rate the moments vary. POISSON MOMENTS Fairman and Shen [5] proposed that a distribution f(t) can be expanded in terms of the derivatives of Dirac’s delta function as follows