Multirate systems with shortest spline-wavelet filters

Motivated by the need of short FIR filters for perfect-reconstruction multirate systems, the main objective of this paper is to derive the shortest filters for such filter banks with MM channels, for any integer M⩾2M⩾2, based on the MM-dilated refinement sequence pmpm of the mth order cardinal B-spline. By imposing the additional constraint of ℓ  th order sum rule on the MM-dual low-pass sequence amam, the smoothness property of the MM-dual scaling function, along with its corresponding analysis wavelets, is studied, and consequently yielding the ℓ  th order vanishing moment for each of the M−1M−1 synthesis (spline) wavelets. Several illustrative examples and tables of the filter systems are also included in this paper.