Eigenvalue and eigenvector decomposition of the discrete Fourier transform

1972/03/01 by James H. McClellan, T.W. Parks · 6 citations
Computer Science · Mathematics · #Digital Filter Design and Implementation #Mathematical Analysis and Transform Methods #Numerical Methods and Algorithms

paper · doi:10.1109/tau.1972.1162342

openalex publication_date 1972/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The principal results of this paper are listed as follows. 1) The eigenvalues of a suitably normalized version of the discrete Fourier transform (DFT) are1, -1,j, -j. 2) An eigenvector basis is constructed for the DFT. 3) The multiplicities of the eigenvalues are summarized for an N×N transform as follows.

Citations

• The finite Fourier transform

Cited by

• Eigenvectors and functions of the discrete Fourier transform
• 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
• Is computing with the finite Fourier transform pure or applied mathematics?
• Discrete Fourier transform [wikipedia]