Time-variant filtering in the time-frequency space: performance analysis and filter design

Signal representation in the combined time-frequency space facilitates the analysis and synthesis of time-varying systems. A new approach to such filtering tasks is introduced, based on the Gabor representation. In order to assess the performance of this filtering scheme and compare it to alternative approaches, a new quality criterion is developed for filters characterized in the time-frequency plane. This criterion affords a quantitative objective comparison, irrespective of the specific time-frequency representation used. Consequently an optimal filter design is induced. A comparison between the Wigner and Gabor approaches is carried out, and the relationships between traditional methods and the optimal filters obtained by the criterion are discussed.