Multiband cyclic wavelet transforms

Multiresolution analysis via decomposition into wavelets has been established as an important transform technique in signal processing. A wealth of results is available on this subject, the framework has been extended to treat finite length sequences of size 2ⁿ (for positive integers n) over finite fields. The paper extends this idea further to provide a framework for dealing with data lengths pⁿ for any prime p. This generalization is motivated in part by the need for such transforms for building error correcting codes in the wavelet transform domain. Potential applications and computational complexity issues are discussed as well. We focus on the description of wavelet transforms in terms of perfect reconstruction filter banks