Tridiagonal Commuting Matrices and Fractionalizations of DCT and DST Matrices of Types I, IV, V, and VIII

Authors:
Soo-Chang Pei;Wen-Liang Hsue
Affiliations:
Grad. Inst. of Commun. Eng., Nat. Taiwan Univ., Taipei;-
Venue:
IEEE Transactions on Signal Processing
Year:
2008

Citing 0
Cited 2

Linear summation of fractional-order matrices

IEEE Transactions on Signal Processing
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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.