Talk:Short-time Fourier transform

message: Now I hear that the resolution problem IS the same as the Heisenberg uncertainty principle, but i have read enough over there to know that they are not actually the exact same thing.  a sound/voltage/whatever wave can have instantaneous frequency, for instance.  Can someone who understands in depth please explain this? Omegatron 17:05, Feb 24, 2004 (UTC)
(as in these paragraphs on the HUP talk page): 
"
:That's not true. It is not the same theorem. Standard QM uncertaintaty relations are derived from a theorem about operators on a hilbert space. These are not things that occur in classical wave mechanics. This idea about frequency and intervals is what underscores the time-energy relations, which is precisly why I cautioned against talking about them in the same language as standard QM relations. -- Matthew 
::There is a theorem relating the "uncertainty" in a function and the uncertainty in its Fourier transform. In standard wave mechanics, the Fourier transform is a Hilbert space automorphism which translates between the position observable x and the momentum observable -i d/dx. So the Fourier theorem can actually be used to prove the space-momentum uncertainty relation. --AxelBoldt
"
Omegatron 17:13, Feb 24, 2004 (UTC)
On Heisenberg - perhaps not just one mathematical formulation that says it. There is a version that says 'you can't localise a function and its Fourier transform in a way that is better than with Gaussians'. The reason that all these versions are really the same, in essence, is hidden in some group representation theory (as I'd explain it). But I think it's fine to allude to this question in passing - the reasons no one can get round the issue are surely the same in both cases.
Charles Matthews 17:46, 26 Feb 2004 (UTC)
replies: text: I'm aware that they're analogous, but are they really the same principle, or just similar in concept? — Omegatron 14:49, 7 November 2006 (UTC)
replies: text: In quantum mechanics the fourier transform is often used to convert between a position-based representation and a momentum-based one.   This trick can be used to derive the momentum-position uncertainty principle from the property of the STFT.  Also, the standard treatment of the uncertainty principle really is a derivation of this property of the STFT from the Cauchy-Schwartz inequality.  Because of this, I think they are essentially the same principle 69.234.75.107 20:58, 29 December 2006 (UTC)

text: The resolution of a time-frequency representation is constrained by Heisenberg's uncertainty principle. The wavelet transform allows different properties to be traded and, consequently, choosing to use low-uncertainty wavelets is of fundamental importance. See [http:// www.ffconsultancy.com/free/thesis.pdf my PhD thesis] and references therein for details. Jon Harrop 11:46, 16 April 2007 (UTC)
thread_title:  Heisenberg uncertainty principle? 

message: When referring to the imaginary unit, can we please change the j to an i?  Only electrical engineers use j, and the justification there (beyond "tradition!") is silly, since current (I) is talked about much more than current density (i).  --Aaron Denney 22:49, 5 March 2007 (UTC)
thread_title:  notation 

message: the wikilink to resolution to point to a more exact page. Resolution (logic) makes sense to me but I could be wrong.  STHayden [ Talk ] 02:30, 22 August 2006 (UTC)
thread_title:  resolution 

message: What happened to it!? Root4(one) 16:08, 27 March 2007 (UTC)
replies: text: It was requested, but it never had one. — Omegatron 17:41, 27 March 2007 (UTC)
thread_title:  Missing "Archived" Peer Review 

message: There was a lot of information about the reassignment method on this page. I've moved it onto its own page because it does not belong here (it is equally applicable to other linear TFRs, e.g. CWT). Jon Harrop 12:04, 16 April 2007 (UTC)
thread_title:  Reassignment method 

message: The term "compactly supported" has nothing to do with how narrow a window is. Any finite width window is compactly supported. compact is a technical term from topology, not a description of size. I'm not updating the main text because signal processing isn't my field, but I know enough to spot this error.  —Preceding unsigned comment added by Sigfpe (talk • contribs) 01:12, 20 March 2009 (UTC)
thread_title:  Compactly Supported 

message: The overlap and what it does to the time-resolution vs. frequency resolution issue could maybe be explained more?
As I understand it, overlapping windows in a sense increase the sampling rate and in this way does nice things for both frequency and time-domain - but this sounds a bit too good to be true?  —Preceding unsigned comment added by Klokbaske (talk • contribs) 13:30, 7 January 2010 (UTC)
thread_title:  Overlap 

message: I don't think the example is very helpful because the time resolution with the longest window actually detects the transitions just as well as the shorter windows because the windowing aligns perfectly with the transitions in the input signal. To get a feel for the time vs. frequency tradeoffs you need to have a signal which changes over time or a signal with some transients in it.  —Preceding unsigned comment added by 129.101.156.108 (talk) 19:29, 24 March 2011 (UTC)
thread_title:  Example 

message: The article says "the function to be transformed is multiplied by a window function which is nonzero for only a short period of time" but then Gaussian bell is given as an example of a window function. A Gaussian bell is nonzero on the whole real line, so maybe the sentence should be rephrased to something like "the function to be transformed is multiplied by a window function which is zero (or very close to zero) except for only a short period of time"? Jaan Vajakas (talk) 15:47, 24 July 2013 (UTC)
replies: text: I linked to Window function#Gaussian window, which has a comment about making the window finite. Glrx (talk) 20:39, 25 July 2013 (UTC)
thread_title:  Nonzero for only a short period of time 

message: Shouldn't there be the window function w(x) involved in the inverse STFT reconstruction formula ? See for example for answer here : http://math.stackexchange.com/questions/568204/inverse-of-short-time-fourier-transform  — Preceding unsigned comment added by 86.75.253.162 (talk) 14:21, 24 November 2013 (UTC)
thread_title:  Inverse STFT 

message: What's this, a Wikipedia math article written (and helpfully illustrated) in a way that students of science or engineering can understand and benefit from? Clearly, this needs to be marked with a "Rewrite Required" template, until it is brought in line with the usual level of post-graduate academic math elitism/obscurantism of the math-related segment of English Wikipedia!
Kidding aside, kudos to the authors of this article.  — Preceding unsigned comment added by 85.180.76.23 (talk) 09:25, 7 March 2015 (UTC)
thread_title:  Too understandable 

message: The article states, in the "explanation" paragraph:
    These N/2 coefficients represent the frequencies 0 to fs/2 (Nyquist) and two consecutive coefficients are spaced apart by fs/N Hz.
It seems to me there is an off-by-one problem in this statement:
- there are N/2 coefficient, let me number them 0 to N/2-1, and use the letter i for the coefficient index.
- there are N/2 coefficient, there are N/2 frequencies those coefficients correspond to. I'll note them f(i), where i goes from 0 to N/2 - 1.
- the first coefficient, where i = 0, represents the frequency 0 Hz: f(i=0) = 0 Hz
- the coefficients are spaced apart by fs/N Hz. so f(i=1) = f(i=0) + fs/N, ..., f(i+1) = f(i) + fs/N
- by induction: f(i) = i *  fs/N
- the last possible value for i is N/2 - 1, so the last value for f(i) is f(N/2 - 1) =  (N/2 - 1) * fs/N = fs/2 - fs/N
so the N/2 coefficients CANNOT represent the frequencies 0 to fs/2, but only 0 to fs/2 - fs/N
OR
they may also represent the frequencies fs/N to fs/2
OR
they may also represent the frequencies 0 to fs/2, but then two consecutive coefficients are spaced apart by (fs/2) / (N/2 - 1) Hz, not (fs/2) / (N/2) Hz.
OR there are actually one more coefficient in the output, to reach N/2 + 1
I am not competent enough to understand which of these cases is correct.
Thanks
Jdmuys (talk) 12:41, 16 March 2016 (UTC)
thread_title:  Off-by-one error in Explanation paragraph 

message: A subtopic of the short-time Fourier transform, not notable enough for a standalone article Enterprisey (talk!) 04:23, 8 September 2018 (UTC)
thread_title:  Proposed merge with [[Rectangular mask short-time Fourier transform]] 

message: All of the images, words and proofs in this article was plagiarized nearly word for word from "Fourier Analysis: Decomposing a waveform into a Harmonic Function" by Kasik. It's disappointing to see wikipedia claim this work as their own. — Preceding unsigned comment added by TerpeneOtto (talk • contribs) 19:50, 29 March 2019 (UTC)
replies: text: It looks like "Fourier Analysis: Decomposing a waveform into a Harmonic Function" by Kasik was published in 2016 (paperback book 1st edition), but looking it that history of the Short-time Fourier transform page it was quite developed in 2015, and had its origin back in 2004. Are you sure that you have the plagiarism (I haven't checked the text of the book carefully) in the right direction? If so, please have a look at Wikipedia:Plagiarism to see the next step. Klbrain (talk) 21:16, 30 September 2019 (UTC)
replies: text: It's not plagiarism, but is from Wikipedia.  Starting on page 138 he extensively cites the many WP articles that he drew on for the book.  That's what WP is for (among other things). We should feel good that this WP article was so good he didn't bother to change it.  Dicklyon (talk) 23:54, 30 September 2019 (UTC)
replies: text: All fine and dandy to me if Wikipedia was cited. Thanks for checking this! Klbrain (talk) 19:36, 1 October 2019 (UTC)
thread_title:  Plagiarism