For the detection of a not-perfectly-known signal in noise, usually no uniformly most powerful (UMP) 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. 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 un known transient signals, when prior information about the signal time-bandwidth-productand relative bandwidth exist. In these cases, the wavelet-representation-based detector performs better than any other. The structure of the proposed detector is discussed and its performance is evaluated, using Monte Carlo simulations.