An undecimated wavelet transform based detector for transients in 1/f noise

We consider the detection in the presence of 1/f noise of a known transient signal of unknown amplitude, scale and delay. We introduce a generalized likelihood ratio test (GLRT) method based on pattern matching in the undecimated discrete wavelet transform (UDWT) domain. In many cases, the computational complexity of the detector can be reduced with minimal performance impact by limiting the pattern matching operations to locations in the UDWT domain that correspond to the existence of transform local maxima. As examples of our approach, we simulate the detection of transients that are modeled either by scaling functions, Gaussian functions, or two-sided exponential functions.