Automatic Classification of Positive Time- Frequency Distributions

A method of performing automatic classification of positive time-frequency distributions is presented. These distributions are computed via constrained optimization, minimizing the cross-entropy of the distribution subject to a set of constraints. An algorithm for clustering using cross-entropy as the distance measure between vectors was derived by Shore and Gray [14]. We apply this method to the time-frequency case, and derive an efficient classification scheme. An advantage of this method is that the time-frequency distributions of the data to be classified do not need to be directly computed; thus, the method can be applied to real-time classification. INTRODUCTION Signals with time-varying spectral content such as speech are not adequately represented by the spectral energy density , in that the spectral density indicates the frequency content of the signal, but it does not reveal when individual frequencies occurred. For the spectral analysis of such time-varying, or nonstationary, signals, a joint time-frequency energy density, or distribution, of the signal is desired [4]. For to be interpreted as a valid energy density, it must be everywhere nonnegative, with marginal densities and . The latter requirement is an energy-conservation constraint, which ensures that the temporal, spectral and total signal energies are accurately represented by . Without loss of generality, we may assume unit-energy signals. Cohen and Posch [5] have shown that positive timefrequency distributions, or TFDs, exist for any finite energy signal . General methods have recently been given for generating these TFDs for arbitrary signals via optimization methods [8]-[11]. The resulting TFDs demonstrate that improvements in time and frequency resolution over that of quasi-stationary methods such as the spectrogram may be obtained without suffering the drawbacks of “negative energy” or spurious artifacts. S ω ( ) 2 P t ω , ( ) P t ω , ( )