Implementation and optimization of time-varying linear-phase and nonlinear-phase orthogonal two-band filter banks for wavelet transforms

We describe the implementation and optimization of new two-band filter banks for wavelet transforms. While extensive research on filter bank design has been conducted in the past, the work here will address an implementation of a filter bank design specifically tailored for the required class of signals. This work presents new filter bank classes and an optimization method. We achieve two desirable features at the same time: (a) orthogonality of the transformations and (b) linear-phase property of the filters by using periodically time-varying filters. Conventional orthogonal two-band filter banks can not have both features. The designed filter banks are parametric and are optimized for signal-adapted operation. We present an optimization implementation for constructing filter banks by a back propagation method via a simulator to allow investigation of its properties.