Tridiagonal commuting matrices and fractionalizations of DCT and DST matrices of typesI, IV, V and VIII
Journal
IEEE Transactions on Signal Processing
Journal Volume
56
Journal Issue
6
Pages
2357-2369
Date Issued
2008-06
Author(s)
W. L. Hsue
Abstract
In this paper, we first establish new relationships in matrix forms among discrete Fourier transform (DFT), generalized DFT (GDFT), and various types of discrete cosine transform (DCT) and discrete sine transform (DST) matrices. Two new independent tridiagonal commuting matrices for each of DCT and DST matrices of types I, IV, V, and VIII are then derived from the existing commuting matrices of DFT and GDFT. With these new commuting matrices, the orthonormal sets of Hermite-like eigenvectors for DCT and DST matrices can be determined and the discrete fractional cosine transform (DFRCT) and the discrete fractional sine transform (DFRST) are defined. The relationships among the discrete fractional Fourier transform (DFRFT), fractional GDFT, and various types of DFRCT and DFRST are developed to reduce computations for DFRFT and fractional GDFT.
Type
journal article