Editing Discrete Fourier transform (section)

==Further reading==
* {{cite book
 | last = Brigham | first = E. Oran
 | title=The fast Fourier transform and its applications
 | location = Englewood Cliffs, N.J.
 | publisher = Prentice Hall
 | year=1988
 | isbn=978-0-13-307505-2
 }}
* {{cite book
 | last = Smith | first = Steven W.
 | chapter-url = http://www.dspguide.com/ch8/1.htm
 | title = The Scientist and Engineer's Guide to Digital Signal Processing
 | edition = Second
 | location = San Diego, Calif.
 | publisher = California Technical Publishing
 | year=1999
 | isbn=978-0-9660176-3-2
 | chapter = Chapter 8: The Discrete Fourier Transform
}}
* {{cite book
 | first = Thomas H. | last = Cormen | author-link = Thomas H. Cormen |author2=Charles E. Leiserson | author3-link = Ronald L. Rivest |author3=Ronald L. Rivest | author4-link = Clifford Stein |author4=Clifford Stein
 | year = 2001
 | title = Introduction to Algorithms
 | edition = Second
 | publisher = MIT Press and McGraw-Hill
 | isbn = 978-0-262-03293-3
 | chapter = Chapter 30: Polynomials and the FFT
 | pages = [https://archive.org/details/introductiontoal00corm_691/page/n844 822]–848
 | title-link = Introduction to Algorithms | author2-link = Charles E. Leiserson }} esp. section 30.2: The DFT and FFT, pp.&nbsp;830–838.
* {{cite journal
 |author1=P. Duhamel |author2=B. Piron |author3=J. M. Etcheto | title = On computing the inverse DFT
 | journal =IEEE Transactions on Acoustics, Speech, and Signal Processing
 | volume = 36 | issue = 2 | pages = 285–286 | year = 1988
 | doi = 10.1109/29.1519
 }}
* {{cite journal
 |author1=J. H. McClellan |author2=T. W. Parks | title = Eigenvalues and eigenvectors of the discrete Fourier transformation
 | journal =IEEE Transactions on Audio and Electroacoustics
 | volume = 20 | issue = 1 | pages = 66–74 | year = 1972
 | doi = 10.1109/TAU.1972.1162342
 }}
* {{cite journal
 |author1=Bradley W. Dickinson |author2=Kenneth Steiglitz | title = Eigenvectors and functions of the discrete Fourier transform
 | journal =IEEE Transactions on Acoustics, Speech, and Signal Processing
 | volume = 30 | issue = 1 | pages = 25–31 | year = 1982
 | doi = 10.1109/TASSP.1982.1163843
 | url = http://www.cs.princeton.edu/~ken/Eigenvectors82.pdf|citeseerx=10.1.1.434.5279 }} (Note that this paper has an apparent typo in its table of the eigenvalue multiplicities: the +''i''/−''i'' columns are interchanged.  The correct table can be found in McClellan and Parks, 1972, and is easily confirmed numerically.)
* {{cite journal
 | author = F. A. Grünbaum
 | title = The eigenvectors of the discrete Fourier transform
 | journal =Journal of Mathematical Analysis and Applications
 | volume = 88 | issue = 2 | pages = 355–363 | year = 1982
 | doi = 10.1016/0022-247X(82)90199-8
 | doi-access = free
 }}
* {{cite journal
 |author1=Natig M. Atakishiyev |author2=Kurt Bernardo Wolf | title = Fractional Fourier-Kravchuk transform
 | journal =Journal of the Optical Society of America A
 | volume = 14 | issue = 7 | pages = 1467–1477 | year = 1997
 | doi = 10.1364/JOSAA.14.001467
 |bibcode = 1997JOSAA..14.1467A }}
* {{cite journal
 |author1=C. Candan |author2=M. A. Kutay |author3=H. M.Ozaktas | title = The discrete fractional Fourier transform
 | journal = IEEE Transactions on Signal Processing
 | volume = 48 | issue = 5 | pages = 1329–1337 | year = 2000
 | doi = 10.1109/78.839980
 |bibcode = 2000ITSP...48.1329C |url=http://www.ee.bilkent.edu.tr/~haldun/publications/ozaktas166.pdf |archive-url=https://web.archive.org/web/20170921231500/http://www.ee.bilkent.edu.tr/~haldun/publications/ozaktas166.pdf |archive-date=2017-09-21 |url-status=live|hdl=11693/11130 | hdl-access = free }}
* {{cite journal
 | author = Magdy Tawfik Hanna, Nabila Philip Attalla Seif, and Waleed Abd El Maguid Ahmed
 | title = Hermite-Gaussian-like eigenvectors of the discrete Fourier transform matrix based on the singular-value decomposition of its orthogonal projection matrices
 | journal =IEEE Transactions on Circuits and Systems I: Regular Papers
 | volume = 51 | issue = 11 | pages = 2245–2254 | year = 2004
 | doi = 10.1109/TCSI.2004.836850
 | s2cid = 14468134
 }}
* {{cite journal
 |author1=Shamgar Gurevich |author2=Ronny Hadani | title=On the diagonalization of the discrete Fourier transform
 | id=preprint at
 | journal=Applied and Computational Harmonic Analysis
 | volume = 27 | issue = 1 | year=2009
 | pages=87–99
 | doi=10.1016/j.acha.2008.11.003
 | arxiv=0808.3281
|s2cid=14833478 }}
* {{cite journal
 |author1=Shamgar Gurevich |author2=Ronny Hadani |author3=Nir Sochen | title=The finite harmonic oscillator and its applications to sequences, communication and radar
 | id=preprint at
 | journal= IEEE Transactions on Information Theory
 | volume = 54 | issue = 9 | pages = 4239–4253 | year=2008
 | doi=10.1109/TIT.2008.926440
 | arxiv=0808.1495
|bibcode=2008arXiv0808.1495G |s2cid=6037080 }}
* {{cite journal
 |author1=Juan G. Vargas-Rubio |author2=Balu Santhanam | title = On the multiangle centered discrete fractional Fourier transform
 | journal =IEEE Signal Processing Letters
 | volume = 12 | issue = 4 | pages = 273–276 | year = 2005
 | doi = 10.1109/LSP.2005.843762
 |bibcode = 2005ISPL...12..273V |s2cid=1499353 }}
* {{cite journal
 | author = F.N. Kong
 | title = Analytic Expressions of Two Discrete Hermite-Gaussian Signals
 | journal =IEEE Transactions on Circuits and Systems II: Express Briefs
 | volume = 55 | issue = 1 | pages = 56–60 | year = 2008
 | doi = 10.1109/TCSII.2007.909865
| s2cid = 5154718
 }}
* {{cite arXiv
 | last1 = Casper
 | first1 = William
 | last2 = Yakimov
 | first2 = Milen
 | date = 2024
 | title = The restricted discrete Fourier transform
 | eprint = 2407.20379
 | class = math.CA
}}
* "Digital Signal Processing<ref>{{Cite web |title=Digital Signal Processing |url=https://r.search.yahoo.com/_ylt=AwrOtbNIhxZn4TASxeJXNyoA;_ylu=Y29sbwNncTEEcG9zAzQEdnRpZAMEc2VjA3Ny/RV=2/RE=1730739273/RO=10/RU=https://assets.cambridge.org/97811084/18447/frontmatter/9781108418447_frontmatter.pdf/RK=2/RS=sx950n9ftvPcKIy.eiDqv6gBrW8- |website=r.search.yahoo.com}}</ref>" by Thomas Holton.