We describe new two-band filterbanks for wavelet transforms. While extensive research on filterbank design has been conducted in the past, the proposed approach will address filterbank design specifically tailored for the required class of signals. The paper presents new filterbank classes and their optimization methods. The general class of periodically time varying filters discussed allows orthogonality to be preserved, which is good for algorithms, while simultaneously reducing the required bandwidth, which is good for compression. Although not discussed in this paper, extensions of these filters allow us to achieve two desirable features at the same time: (a) orthogonality of the transformations and (b) linear-phase property of the filters. Conventional orthogonal two-band filterbanks cannot have both features. The designed filterbanks are parametric and can be optimized for signal-adapted operation. We present an optimization approach for constructed filterbanks by a backpropagation method. ©2007 IEEE.