双正交小波矩阵

Matrices on Biorthogonal Wavelets

本文引进了双正交（半正交）小波矩阵及对偶的概念。讨论了这些矩阵的一些性质，尤其是给出了利用小波矩阵的元素将离散函数展开为级数形式的结果，进而建立了半正交小波矩阵与［８］中正交小波矩阵，双正交小波矩阵与对偶双正交小波矩阵的关系。最后举例说明了本文引进双正交（半正交）小波矩阵及对偶概念和方法的合理性。

In this paper we introduce the concepts of matrices on biorthogonal (semiorthogonal)wavelets and their duals.some properties of these matrices are discussed.In especial we show that any discrete function admits a series representation in terms of the rows of a given wavelet matrix.Furthermore the nelationships between semiorthogonal wavelet mathrices and orthogonal wavelet matrices in [8].Biorthogonal wavelet matrices and their duals are founded.At last we repesent some ezamples which show the reasonableners of methods and concepts of matrices on bionthogonal (semiorthognal) wavelets introduced in this paper.