A generating matrix is a matrix such that, when multiplied by an eigenvector of a discrete transform, a new eigenvector is obtained. In this paper, we introduce a family of generating matrices of DFT eigenvectors. We demonstrate that, if a specific initial set of eigenvectors is chosen, using the referred family of matrices, a Hermite-Gaussian-like DFT eigenbasis is obtained. Such an eigenbasis is then employed to define a discrete fractional Fourier transform which numerically approximates the corresponding continuous transform.

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Keywords Eigenstructure of discrete Fourier transform, Fractional Fourier transform, Generating matrices, Hermite-Gaussian-like eigenvectors
Persistent URL dx.doi.org/10.1109/ICASSP.2018.8461637
Conference 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
De Oliveira Neto, J.R. (Jose R.), Lima, J.B. (Juliano B.), & Panario, D. (2018). A Family of Matrices for Generating Hermite-Gaussian-Like DFT Eigenvectors. In ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings (pp. 4379–4383). doi:10.1109/ICASSP.2018.8461637