Spectrograms and generalized spectrograms for classification of random processes

A maximum likelihood (ML) classifier for discriminating between nonstationary Gaussian time series can be implemented by correlating the data spectrogram with templates that are constructed from ensemble average reference spectrograms. The time window used to synthesize the spectrograms must have a duration that is longer than the decorrelation time of the data in the neighborhood of the window. If the data time series exhibits significant nonstationarity within this decorrelation time, Karhunen-Loéve (K-L) basis functions should ideally be used to construct a generalized spectrogram, rather than using a standard spectrogram constructed with the usual sinusoidal basis functions. Utilization of a standard spectrogram imposes forced, pseudo-stationarity by approximating the autocovariance function of the data by the short-time autocorrelation function. This forced stationarity is routinely used to obtain linear prediction coefficients (LPC). When signal to interference ratio (SNR) is large, the templates that are used to classify a data spectrogram are sensitive to differences in the locations of nulls or zeroes in the expected signal spectrograms from different data classes. This null sensitivity seems to imply that peak-oriented models of random processes, e.g. , the all pole representation that is associated with LPC, are suboptimum for ML classification under high SNR conditions. Compensation for time warping is especially necessary if window durations are data dependent. Spectrogram implementation of the ML classifier yields a new similarity index for time warp compensation.