On Stationary and Non-stationary M-band Framelet Packets

Firdous A Shah


Abstract. This paper deals with a construction of both stationary and nonstationaryM-band tight framelet packets in L2(R) using extension principles.The approach here is different than the method described by Shah and Debnathin [ Explicit construction of M-band tight framelet packets, Analysis,32 (2012) 281-294 ] in that we directly decompose the multiresolution spaceVJ for a fixed level J > 0 to the level 0 with any combined wavelet maskm = [m0,m1, . . . ,mL] satisfying the unitary extension principle conditionM(ξ)M∗(ξ) = IM, where M(ξ) ={mℓ(ξ + 2πpM)}M−1ℓ,p=0.


M-band wavelets; tight wavelet frame; framelet packet; extension principle; Fourier transform

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