A class of time-varying wavelet transforms

The concept of the time-varying discrete-time wavelet transform is introduced. In the time-varying wavelet transform, the basic tiling of the time-frequency plane stays unchanged and only the properties of the analysis wavelets are changed in time. The authors´ primary objective in designing such analysis-synthesis structures is to insure that the transform is invertible at all times. Two design procedures are developed based on the time-varying filter bank design. The first approach uses a time-varying two-band filter bank tree structure, and the second approach is based on parallel nonuniform filter banks. The concept can easily be extended to general tree structures and wavelet packets.<>