Talk:Discrete Fourier transform

message: I don't believe this addition to the "Definition", made earlier today, is helpful or relevant (to the definition):
http://en.wikipedia.org/w/index.php?title=Discrete_Fourier_transform&diff=527527711&oldid=526485596
--Bob K (talk) 13:38, 11 December 2012 (UTC)
replies: text: I wouldn't include it in the definition either.  However, the connection of the N=2 case to the Hadamard transform should probably be mentioned somewhere in the article.  — Steven G. Johnson (talk) 19:37, 11 December 2012 (UTC)
thread_title:  The N=1 case 

message: The page currently contains this text:
:...yields an eigenvector of the discrete transform:
:*F(m) = \sum_{k\in\mathbb{Z}} \exp\left(-\frac{\pi\cdot(m+N\cdot k)^2}{N}\right).
::A closed form expression for the series is not known, but it converges rapidly.
But I understand \mathbb{Z} as being the set of gaussian integers - complex numbers with integer valued real and imaginary parts. And while this series would converge rapidly if \mathbb{Z} represented regular integers, complex integers mean that -(x^2) will contain arbitrarily large values. In other words, this sum diverges rapidly. Alternatively, if \mathbb{Z} has some other significance this should probably be documented instead of assumed. --Raudelmil (talk) 08:20, 21 April 2014 (UTC)
replies: text: I don't know if you solved your doubts, but {\displaystyle \mathbb {Z} } is the symbol used to refer to integers, representing, in this case, the frequency domain for a continuous periodic system. Anyways, the sentence has been removed by someone, since apparently a closed form can be given in terms of the Jacobi theta function, but the claim about its convergence was accurate. ComandiDosEAltro (talk) 22:56, 1 June 2022 (UTC)
thread_title:  Converges rapidly? 

message: It seems that in this article the Plancherel and Parseval theorems are used interchangeably and inconsitently. In the subsection "The Plancherel theorem and Parseval's theorem" it is stated that the Plancherel theorem is a special case of the Parseval's theorem where y = x and in the subsection on "The unitary DFT" it is stated exactly the other way around where Parseval's theorem is a special case of the Plancherel Theorem (where again y = x). As I understand it, both the Parseval's theorem and Plancherel theorem talk about the "general" case where the inner product <x,y> is preserved under the fourier transformation, the difference being that the Parseval's theorem talks about the summability and unitarity of the Fourier series whereas the the Plancherel theorem more generally talks about the unitarity of any Fourier transform (continuous, multi dimensional etc.).
Doubbleb (talk) 09:29, 18 August 2015 (UTC)
thread_title:  Plancherel and Parseval theorems 

message: Why there j in definition? Should not there be imaginary unit (i)?  — Preceding unsigned comment added by Av life (talk • contribs) 11:28, 24 September 2015 (UTC)
thread_title:  j in definition 

message: The article opens by saying "the discrete Fourier transform (DFT) converts a infinite list of equally spaced samples of a function into the list of coefficients of a finite combination of complex sinusoids", but then goes on to say "[the DFT] deals with a finite amount of data". These statements are contradictory; it appears to be the first statement which is in error. --96.55.224.124 (talk) 05:05, 3 January 2016 (UTC)
replies: text: That was this 22 Dec. vandalism.  Thanks.  Fixed.  Dicklyon (talk) 05:48, 3 January 2016 (UTC)
thread_title:  Input length infinite or finite? 

message: Fourier transform of a gaussian is a gaussian right? KorgBoy (talk) 23:13, 12 May 2016 (UTC)
thread_title:  continuous function and its fourier transform 

message: There seems to be a mistake in the table giving the multiplicities of eigenvalues of DFT, 
cf. http://www.cs.princeton.edu/~ken/Eigenvectors82.pdf  (page 26)
The columns for i and -i should be swapped.  — Preceding unsigned comment added by 31.174.90.50 (talk) 19:03, 5 October 2016 (UTC)
thread_title:  Eigenvalues correct? 

message: Could we include some references for the entries in the "Some discrete Fourier transform pairs" table? Surely they should just be in some stats textbook. 121.121.61.57 (talk) 12:15, 3 July 2020 (UTC)
thread_title: References for entries in "Some discrete Fourier transform pairs" table?

message: I have been working through the dft by hand, I have checked my math multiple times and have used wolfram alpha to provide more checking, but for the input x={1,2,3,4} 
I keep getting X={10, -2+2i, -2, -2-2i} 
and wolfram is giving me 
fft{1,2,3,4} = {5, -1-i, -1,-1+i}, 
but the ifft{1,2,3,4} = {5, -1+i, -1, -1-i} 
This is only one half what I calculated by hand and so this is what makes me think the dft and inverse dft are swapped.
Also there might be something about dividing the result by 2, to be explored. 209.159.200.170 (talk) 20:33, 3 December 2022 (UTC)
thread_title:  Are the equations for the dft and inverse dft swapped?? 

message: Please add a section explaining what this algorithm accomplishes.  I passed an entire undergrad course on this topic, and still don't understand what the purpose of the transform is.  Please help -- I'm not the only one! KatyKathinka (talk) 00:02, 23 April 2023 (UTC)
thread_title:  Motivation 

message: "Further information: Representation theory of finite groups § Discrete Fourier transform" is missing 2A0C:5BC0:40:10C0:DE4A:3EFF:FE6D:C214 (talk) 14:57, 4 March 2024 (UTC)
thread_title:  Link to subsection in Representation theory of finite groups no longer exists