Performance analysis of a class of transient detection algorithms-a unified framework

The detection of short-duration nonstationary signals, which are commonly referred to as transients, is often performed in the time-frequency-transform domain. An analytical framework within which the performance of different detectors based on linear transforms can be easily compared, for different classes of signals, is developed. A given class of transients is modeled as a signal existing in a linear subspace, plus a mismatch signal. Closed-form expressions are derived for the best and the worst detection performance for all possible transients in a given class. Using this framework, the performance of detectors based on the Gabor transform and on the short-time Fourier transform is evaluated and compared.>