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.