The wavelet transform and time-varying tiling of the time-frequency plane

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 change with time. Equivalently, these structures can be considered as time-frequency transforms with a corresponding time-varying tiling of the time-frequency plane and with corresponding time-varying basis functions. This formulation is based on the time domain analysis of the 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