Signal representation and processing in the mixed time-frequency domain

This paper is concerned with mixed time-frequency signal processing using Wigner Distribution Function (WDF). This approach is based upon the generation of the mixed time-frequency representation (MTFR) of a signal, processing of that representation in the mixed time-frequency domain, and obtaining a filtered output by an inverse operation or approximation procedure. Various signal processing operations are formulated. Validity condition for the resulting MTFR are investigated. An inverse operation can be applied as an exact procedure if the output MTFR is a valid WDF, it can be regarded as an approximation procedure if the resulting MTFR is not admissible. Other approximations can be formulated. One scheme depends on the projection of the MTFR onto the space of valid WDF. The other scheme depends on the modification of the filtering function in a minimal way such that the resulting MTFR is valid.