Time-varying filter banks and wavelets

Time-varying filter banks and wavelets are studied and a design procedure is presented. In the resulting analysis-synthesis structures, the analysis filters and the corresponding synthesis filters, the number of bands, and the decimation rates can be changed with time. Such structures can be considered as time-frequency overlapping block 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 case of time-varying overlapping block transforms and are studied in detail. The formulation is based on the time domain formulation of time-varying analysis-synthesis structures. The design procedure can be used to design time-varying perfectly invertible transformations with a finite number of distinct analysis structures. For adaptive filter bank application, a least squares design method is also studied