Two drawbacks of pyramidal wavelet transforms for finite-length sequences are the lack of conservation of the support and the boundary effect. In this letter, the structure of cyclic wavelet transforms (CWT) is used to permute the input and output data to map them into a linear array. Systolic realization of cyclic wavelet packet transforms (CWPT) is also presented to adequately deal with finite-length sequences which have dominant information on high or median frequency channels. The VLSI architectures designed in this letter are very attractive because adaptive processing can be achieved by just programming the filter coefficients.