Classical wavelet systems over finite fields

This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual is classical full wavelet frame as well, and hence each vector defined over a finite field can be represented as a finite coherent sum of classical wavelet coecients as well.