Performance analysis of transient detectors based on a class of linear data transforms

The problem of detecting short-duration nonstationary signals, which are commonly referred to as transients, is addressed. Transients are characterized by a signal model containing some unknown parameters, and by a `model mismatch' representing the difference between the model and the actual signal. Both linear and nonlinear signal models are considered. The transients are assumed to undergo a noninvertible linear transformation prior to the application of the detection algorithm. Examples of such transforms include the short-time Fourier transform, the Gabor transform, and the wavelet transform. Closed-form expressions are derived for the worst-case detection performance for all possible mismatch signals of a given energy. These expressions make it possible to evaluate and compare the performance of various transient detection algorithms, for both single-channel and multichannel data. Numerical examples comparing the performance of detectors based on the wavelet transform and the short-time Fourier transform are presented