Detection of a transient signal of unknown scaling and arrival time using the discrete wavelet transform

The authors compare the output of a certain generalized matched filter to a threshold for detection of a signal of known waveshape, but unknown arrival time and time-scaling factor in white Gaussian noise. It is shown that this generalized matched filter is actually the wavelet transform, and the authors suggest implementing the proposed detector using the discrete wavelet transform. The performance of the proposed detector is studied, and it is shown that, under proper design of the parameter grid, its performance is near-optimal