Eigen Analysis of Unitary Matrices Used in Signal Processing


A - Abstracts of IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences (Japanese Edition)   Vol.J90-A   No.5   pp.403-414
Publication Date: 2007/05/01
Online ISSN: 1881-0195
Print ISSN: 0913-5707
Type of Manuscript: PAPER
signal processing,  Fourier transform,  unitary matrix,  eigenspace,  symmetric group,  

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Unitary matrices are available in the area of discrete signal processing. A unitary matrix expands signals to its orthonormal column vectors which consist of a basis, and makes clear how each vector of the basis contributes to make the signal. Inverse transforms by the matrices are their inverse matrices, but, for unitary matrices, inverse matrices are their adjoint ones. Hence, the inverse ones are available only by transposition and complex conjugate without any numerical computation. So far, however, it is still open how eigenvalues and eigensubspaces of a unitary matrix work in this area. From the point of view of eigen analysis of unitary matrices in the area, we describe a relationship between a symmetry of signals steemed from a symmetric group and the unitary matrix, and also consider its role in the area.