Detection of transient signals by the Gabor representation

This paper proposes to use the Gabor representation for the detection of transient signals with unknown arrival times. We introduce a one-sided exponential window function, which seems to the most appropriate for transient modeling. Explicit expressions for the Gabor coefficients are given for this window function. When the given signal is random, so are the coefficients. The second-order moments of the Gabor coefficients are computed for a white noise signal. These are then used to introduce a detection statistic based on the Gabor coefficients. The proposed detector is capable of separating transients having different arrival times, even in the case where their waveforms partially overlap.