【摘要】 设{g(x-n):n∈Z}是L2(R)的规范正交系,Fl(z)=∑n∈Zfl(n)z-n,l=0,1,…,M-1,是M个滤波器(M 2),定义l(x)=M∑n∈Zfl(n)g(Mx-n),l=0,1,…,M-1。考虑了在什么条件下,{l(x-n):n∈Z;l=0,…,M-1}构成span{Mg(Mx-n):n∈Z}的规范正交基。给出了一个定理,该定理描述了与前面所述的"规范正交基底性"相等价的条件。在这些等价性条件的指导下,讨论了M通道的Haar,Shannon,和Meyer滤波器组以及与之相联系的M带正交小波,构造了正交的M带Haar,Shannon,及Meyer小波。更多还原

【Abstract】 Study multi-channel wavelet decomposition in L²（R）. Conditions for filter bank F₀（z）,F₁（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 M2 is a positive integer, {g（x-n）:n∈Z} is an orthonormal family in L²（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.更多还原