The use of the wavelet transform in the detection of an unknown transient signal

For the detection of a not-perfectly-known signal in noise, usually no uniformly most powerful test exists, and thus a detector performance depends on the signal representation. The use of the wavelet representation of signals to perform a new detection scheme is discussed. The advantage of using this particular representation is shown. It is shown that prior information regarding the relative bandwidth and the time-bandwidth-product of the signal to be detected is efficiently incorporated into the detection problem formulation. Thus, the proposed detection scheme is most suitable for detection of unknown transient signals when prior information about the signal time-bandwidth product and relative bandwidth exists. In these cases, the wavelet-representation-based detector performs better than any other. The structure of the proposed detectors is discussed and its performance is evaluated using Monte Carlo simulations.<>