Eigenvectors and functions of the discrete Fourier transform

1982/02/01 by B. Dickinson, K. Steiglitz · 9 citations
Computer Science · Mathematics · #Digital Filter Design and Implementation #Mathematical Analysis and Transform Methods #Advanced Data Compression Techniques

paper · doi:10.1109/tassp.1982.1163843

openalex publication_date 1982/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can be efficiently computed, and possible applications to multiplexing and transform coding are suggested.

Citations

• Orthogonal transforms for digital signal processing
• Eigenvalue and eigenvector decomposition of the discrete Fourier transform

Cited by

• On the multiangle centered discrete fractional Fourier transform
• Hermite–Gaussian-Like Eigenvectors of the Discrete Fourier Transform Matrix Based on the Singular-Value Decomposition of Its Orthogonal Projection Matrices
• Analytic Expressions of Two Discrete Hermite–Gauss Signals
• On the diagonalization of the discrete Fourier transform
• Fractional Fourier transform as a signal processing tool: An overview of recent developments
• Image rotation, Wigner rotation, and the fractional Fourier transform
• Analytic representation of finite quantum systems
• Minimum-uncertainty states and completeness of non-negative quasiprobability of finite-dimensional quantum systems
• Discrete Fourier transform [wikipedia]