TIME-VARYING FILTER BANKS AND WAVELETS

In this paper, time-varying filter banks and wavelets are studied and a design procedure is presented. In the resulting analysis-synthesis s tructures, the analysis filters and the corresponding synthesis filter s, the number of bands, and the decimation rates can be changed with t ime. Such structures can be considered as time-frequency overlapping b lock transforms. From this viewpoint, the tiling of the time-frequency plane and the corresponding basis functions are changed in time. The time-varying discrete wavelet transforms can be considered a special c ase of time-varying overlapping block transforms and are studied in de tail in this paper. The formulation is based on the time domain formul ation of time-varying analysis-synthesis structures. The design proced ure can be used to design time-varying perfectly invertible transforma tions with a finite number of distinct analysis structures. For adapti ve filter bank application, a least squares design method is also stud ied.