Signal detection using group transforms

It is shown that transforms arising from square integrable group representations can be used for the detection of signals in noise. This class of group transforms includes the Gabor transform and the wavelet transform. These transforms are used to map the reproducing kernel Hilbert space (RKHS) associated with noise covariance into another RKHS; the RKHS formulation of the detection problem is then applied to this new space. Using the discrete form of the Gabor transform or the wavelet transform results in a discrete-parameter correlator structure. It is shown that the use of the wavelet transform for the detection of signals in the presence of 1/f noise results in a structurally simple form for the correlation receiver