On Stationary and Non-Stationary M-Band Framelet Packets

This paper deals with a construction of both stationary and non-stationary M-band tight framelet packets in L2(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()M() = IM, where M() =  m` ??  + 2p M
M?1 `,p=0