A unified formulation for detection using time-frequency and time-scale methods

A unified theory is developed for the detection of signals in nonwhite noise using time-frequency and time-scale signal transforms. This class includes the cross-Wigner distribution and certain other members of Cohen´s class, the Gabor transform, and the wavelet transform. Necessary and sufficient conditions are established such that a signal transform is applicable to the nonwhite noise detection problem. Applying this result to the reproducing kernel Hilbert space associated with a finite-dimensional approximation of the noise covariance leads to weighted correlator structures in the time-frequency and time-scale domains. This extends results previously available only for the white noise case