On Stationary and Non-Stationary M-Band Framelet Packets

Abstract

This paper deals with a construction of both stationary and non-stationary M-band tight framelet packets in L 2 (R) using extension principles. The approach here is different from the method described by Shah and Debnath in [ Explicit construction of M-band tight framelet packets, Analysis, 32 (2012) 281-294 ] in that we directly decompose the multiresolution space VJ for a fixed level J > 0 to the level 0 with any combined wavelet mask m = [m0, m1, . . . , mL] satisfying the unitary extension principle condition M(ξ)M∗ (ξ) = IM, where M(ξ) =  m` ξ + 2πp M
M−1 `,p=0