The generalised sequentially rejective Bonferroni test applied to non-stationary, random signal classification

We present a new non-stationary signal classification algorithm based on a time-frequency distribution and multiple hypothesis testing. The time-frequency distribution is used to construct a time-dependent quadratic discriminant function. At selected points in time we evaluate the discriminant function and form a set of statistics which are used to test multiple hypotheses. We show that the statistics are a linear combinations of chi square random variables with constant coefficients and hence are not normally distributed. The multiple hypotheses are treated simultaneously using the generalised sequentially rejective Bonferroni test to control the probability of incorrect classification of one class. Finally, we show the results of classifying time-varying AR(1) processes which have identical expected instantaneous power and power spectral densities but different time-frequency representations