## Construction of Orthogonal M-band Wavelets

**DI Shuangliang1,QI Chun1,LIANG Dequn2(1Xi'an Jiaotong University, Xi'an 710049;2Dalian Maritime University, Dalian 116026)**

Study multi-channel wavelet decomposition in L~2(R). Conditions for filter bank F_0(z),F_1(z),...,F_M-1(z) to decompose span {Mg(Mx-n):n∈Z} as an orthogonal sum of span {k(x-n):n∈Z},k=0,1,...,M-1, are given, where M2 is a positive integer, {g(x-n):n∈Z} is an orthonormal family in L~2(R), and ^_k(ω)=M~-1/2 F_k(ω/M)(ω/M). As applications of the general result, M channel Haar, Shannon, and Meyer filter banks are introduced, and M-band Haar, Shannon, and Meyer wavelets are constructed.

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