Classes of smoothed Weyl symbols

We propose a new class of time frequency (TF) symbols covariant to time shifts and frequency shifts on a random process. The new TF symbols are useful for analyzing linear time-varying systems or nonstationary random processes, and they are defined as TF-smoothed versions of the narrowband Weyl symbol. We derive kernel constraints for the new TF symbols to satisfy the unitarity property and the quadratic form. We also propose a new class of TF symbols covariant to time shifts and scale changes on a random process. These new TF symbols can be interpreted as affine-smoothed versions of the narrowband Weyl symbol or of the wideband P/sub 0/-Weyl symbol.