Wavelet transforms associated with finite cyclic groups

Generally speaking, the principal framework within which multiresolution techniques have been studied and applied is the same as that is used in the discrete-time Fourier analysis of sequences of complex numbers. The authors develop an analogous framework for the multiresolution analysis of finite-length sequences of elements from arbitrary fields. As in finite-length Fourier analysis, a cyclic group structure of the index set of such sequences is exploited to characterize the transforms of interest for the particular cases of complex and finite fields. This development is motivated by potential applications in areas such as digital signal processing and algebraic coding, in which cyclic Fourier analysis has found widespread applications.<>