WEIGHTED TIME-FREQUENCY AND TIME-SCALE TRANSFORMS IN REPRODUCING KERNEL HILBERT-SPACES

Motivated by the time-frequency, time-scale (TF/TS) implementation of a maximum likelihood detector for transient signals in nonstationary G aussian noise, we define weighted TF/TS transforms using reproducing k ernel Hilbert space (RKHS) inner products. Inverses of these weighted TF/TS transforms are also given, The particular case of the weight bei ng the inverse noise covariance is presented. The weighted TF/TS trans forms turn out to be natural transforms for solving nonstationary dete ction, estimation, and filtering problems, and have important applicat ions to transient signal estimation in multipath channels with colored nonstationary Gaussian noise.