Detection of transient signals by the Gabor representation

Gabor representation is used for the detection of transient signals with unknown arrival times. A one-sided exponential window function is used which seems to be most appropriate for transient modelling. 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 this case where their waveforms partially overlap