DFT-commuting matrix with arbitrary or infinite order second derivative approximation
IEEE Transactions on Signal Processing
Discrete Fractional Fourier Transform Based on New Nearly Tridiagonal Commuting Matrices
IEEE Transactions on Signal Processing
The discrete rotational Fourier transform
IEEE Transactions on Signal Processing
Discrete fractional Fourier transform based on orthogonalprojections
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing - Part II
The discrete fractional Fourier transform
IEEE Transactions on Signal Processing
The discrete fractional Fourier transform based on the DFT matrix
Signal Processing
Eigenvectors of the discrete Fourier transform based on the bilinear transform
EURASIP Journal on Advances in Signal Processing - Special issue on applications of time-frequency signal processing in wireless communications and bioengineering
Signal-adaptive discrete evolutionary transform as a sparse time-frequency representation
Digital Signal Processing
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In order to define the discrete fractional Fourier transform, Hermite Gauss-like eigenvectors are needed and one way of extracting these eigenvectors is to employ DFT commuting matrices. Recently, Pei et al. exploited the idea of obtaining higher order DFT-commuting matrices, which was introduced by Candan previously. The upper bound of O(h^2^k) approximation to NxN commuting matrix is 2k+1@?N in Candan's work and Pei et al. improved the proximity by removing this upper bound at the expense of higher computational cost. In this paper, we derive an exact closed form expression of infinite-order Taylor series approximation to discrete second derivative operator and employ it in the definition of excellent DFT commuting matrices. We show that in the limit this Taylor series expansion converges to a trigonometric function of second-order differentiating matrix. The commuting matrices possess eigenvectors that are closer to the samples of Hermite-Gaussian eigenfunctions of DFT better than any other methods in the literature with no additional computational cost.