Cyclic wavelet transforms for arbitrary finite data lengths

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, and particularly, the framework has been extended to treat finite length sequences of size 2ⁿ (for positive integers n) over finite fields. The present paper extends this idea further to provide a framework for dealing with arbitrary finite data lengths. This generalization is largely motivated in part by the need for such transforms for building error correcting codes in the wavelet transform domain. Here we extend the previous two-band formulation of the transform to treat a p-band case in general (i.e. for data length pⁿ), where p is a prime number, and we also give a general result for developing transforms over composite-length sequences. Potential applications and computational complexity issues are discussed as well.