Non-stationary, narrowband Gaussian signal discrimination in time-frequency space

Abstract

The problem of signal classification can be divided into three consecutive sub-problems: detection of the presence of a signal; segmentation to determine the time interval of the signal; and classification of the signal into one of a finite number of classes. We assume that a signal is observed and its time interval is known and focus on the classification problem. In this paper we extend a frequency domain classifier for stationary signals [8] to a time-frequency classifier for non-stationary signals. The motivation for this extension is straightforward: the classical technique is only optimal (in the sense of minimising the probability of misclassifying an observation of one kind for a fixed misclassification rate of the other kind) if the signal is stationary. This leads us to consider a technique that does not require the signal to be stationary. In particular, we introduce a time-varying quadratic discriminant function using the spectrogram. We apply the generalised sequentially rejective Bonferroni test to the mUltiple hypotheses that can be constructed at different points in time from this discriminant function. Other classification techniques have been suggested recently using time-frequency distributions (TFD). In [10] the authors extended the log-spectral distance to the time-frequency case and in the authors proposed a technique based on the cross Wigner-Ville distribution. In the sequel we will discuss how our method deviates from the existing solutions.