Detection of a known transient signal of unknown scaling and arrival time

This paper discusses the problem of detecting a known waveshape transient signal of unknown arrival time and duration in additive, white Gaussian noise. The limited duration transient is modeled by the known waveshape and by unknown attenuation and time-scaling factors. We show that the intuitive generalized matched filter can be interpreted as a wavelet-based detector, with the known waveshape serving as the wavelet `mother´ function. Using results from wavelet theory we then suggest a procedure for designing a `bank of filters´ detector, in which the filters are logarithmically distributed in the frequency domain. We show the tradeoff between the performance and the number of filters and we find the minimal number of filters which guarantee performance improvement relative to the energy detector. We also find the number of filters which obtain close to best attainable performance. The study was done using Monte-Carlo simulation