Cited by 257Digital Filter Design and ImplementationMathematical Analysis and Transform MethodsMatrix Theory and Algorithms

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Eigenvalue and eigenvector decomposition of the discrete Fourier transform

McClellan, J., Parks, T.·1972·IEEE Transactions on Audio and Electroacoustics

DOI 10.1109/tau.1972.1162342

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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) are{1, -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.

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Authors: McClellan, J., & Parks, T.
Affiliations: Rice University (US)
ORCID: McClellan, J.
Venue: IEEE Transactions on Audio and Electroacoustics
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Published: 1972-03
Volume: 20
Issue: 1
Pages: 66-74
ISSN: 0018-9278 (ISSN-L)
DOI: 10.1109/tau.1972.1162342
OpenAlex: W2102337953
Cited by: 257
References: 4
Citations by year: 2026: 3 · 2025: 5 · 2024: 5 · 2023: 32 · 2022: 5 · 2021: 8 · 2020: 4 · 2019: 9 · 2018: 13 · 2017: 8 · 2016: 3 · 2015: 6 · 2014: 11 · 2013: 11 · 2012: 14
FWCI: 0.54
Type: journal article
Language: en
Open access: closed
Licence: ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)
Locations: IEEE Transactions on Audio and Electroacoustics (publishedVersion)
Topics: Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
Keywords: discrete Fourier transform, eigenvalue decomposition, eigenvalues, eigenvector basis, eigenvalue multiplicity, matrix eigenvalues

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Eigenvalue and eigenvector decomposition of the discrete Fourier transform

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