Talk:Convolution

Conflict of motives: Does style consistency with post-graduate textbooks completely trump readability?

I made a revision. Someone reverted it for reasons that I disagree with. I am new to wikipedia. Where do I go to learn how to resolve "arguments" like this?

Per the initial revision I assert that "t" and "tau" are so similar looking that use of both, meaningfully, damages readability.

Responsive to the reversion comment:

I insist that it is inappropriate & undesirable to write wikipedia toward a target audience of people who are already comfortable enough with post graduate level engineering textbooks that _not_ deliberately using both "t" and "tau" makes something less legible.

I would further assert that any consistency in using "t" and "tau" in the same formulas is itself an affirmative flaw in said textbooks rather than something which wikipedia would be well advised to deliberately, explicitly, repeat.

Convolution: Revision history

curprev 03:17, 28 June 2021‎ 174.91.211.146 talk‎ 57,994 bytes −11‎ Undid revision 1029953540 by 2601:1C1:C100:F420:64D3:C217:8740:9837 (talk), to remain consistent with the notation used in most textbooks. In electrical engineering "u" usually means the unit step function, whereas t and tau are usually used to denote time-oriented variables. undo Tag: Undo

curprev 01:17, 23 June 2021‎ 2601:1c1:c100:f420:64d3:c217:8740:9837 talk‎ 58,005 bytes +11‎ →‎Readability improvement: Use of t & tau (which look similar) in the same equation is less readable than use of letter that look different. Hence, changed nearly all 'tau' to 'u'. undo Tag: Reverted

Full disclosure: I am not an argument resolution expert. That said, my answer is that you are at the consensus determination stage. And for that purpose, I vote for the current version, not for your changes. I'm not a WP policy wonk either, but I do know that there is a policy against wholesale changes (like yours) without an adequate (and successful) discussion here.

--Bob K (talk) 13:57, 3 July 2021 (UTC)

I'm a wikinewb, trying to work out notational and "cooperational" nuance. "Wholesale changes"? Yes, 58,005 bytes looks like a lot. But please look closer: I changed "\tau" to "u" many times. Is that really a "large enough" change to require discussion? That is a serious question. I had assumed "no". And am assuming that you looked at the size more than the specifics. Also, nearly everything I've read about dealing with situations "like" this talk about communicating to the reverter, who in this case did an anonymous drive by.

2601:1C1:C100:F420:2838:2866:A58E:9B94 (talk) 05:20, 7 July 2021 (UTC) Original change author.

Further explanation of original edit "23 June 2021‎ 2601:. . . ‎Readability improvement":

[BTW: Thank you Bob K.]

Imagine trying to learn analytic geometry but instead of calling the axes x, y, and z mathematicians were in the habit of calling them x1, xl, and xI. I deem pairing tau & t in an equation with only 2 variables to be equivalent. A person learning about convolutions "should not" be affirmatively disadvantaged by insistance on conformance with the choice of experts in the relevant field to make their work harder to read, especially for general audiences (who are the declared target audience of Wikipedia).

As for wiki wonkery I spent meaningful time trying to come up to speed.

It seems to me that my motives for making "my" change do indeed match wiki policy very well: I deem it easier to tell "t" and "u" apart than "t" and "\tau". That using tau in those contexts would be more familiar to _experts_ than to a general audience strikes me as hinting at an affirmative reason _not_ to use tau.

In contrast, I deem the revert to be "out of line" in several ways. 1. Reverting a change because one does not feel it was good/well-motivated/... enough does not strike me as a 'good reason' (per my read of WP:BRD). 2. Reverting a change to regain consistency with an insular convention which is alien and affirmatively problematic for Wikipedia's target audience strikes me as an affirmatively "bad" reason (per my read of WP:BRD). 3. "BRD is not a valid excuse for reverting good-faith efforts to improve a page simply because you don't like the changes." 4. "BRD is never a reason for reverting. Unless the reversion is supported by policies, guidelines or common sense, the reversion is not part of BRD cycle." 5. WP:BRD "A revert needs to present a path forward, either by expressing a concern with the content of the edit itself, or pointing to a previous discussion that did."

Bonus question: How much of this "further explanation" is superfluous/redundant/obvious-from-initial/irrelevant?

2601:1C1:C100:F420:2838:2866:A58E:9B94 (talk) 05:30, 7 July 2021 (UTC) Original change author

2601:1C1:C100:F420:2838:2866:A58E:9B94 (talk) 06:08, 7 July 2021 (UTC) Original tau -> u change author

Just use another variable. I agree tau and variable t may be mixed. Also it would have been better if your just used '[Link to change]' instead of this text wall. --Greatder (talk) 11:25, 7 July 2021 (UTC)

Thank you Greatder. Sorry for the text wall. 2601:1C1:C100:F420:C8A0:2CB7:1126:65B0 (talk) 05:21, 11 July 2021 (UTC) Original tau -> u change author

I did look at your edits, BTW, not just the byte count. $\tau$ and $t$ are variables on the same real line (i.e. of the same type). The comparison to x,y,and z is a false equivalence, IMO.

Legibility of the equations, specifically ease of distinguishing between 2 variables, is the point. Neither the role of those variables nor their mathematical characteristics are relevant to whether or not two glyphs are easy to distinguish.

I think we all know how you feel. Back in 2012 June, in the Fourier transform article, someone changed all the $\nu$ to $\xi ,$ representing frequency in units of cycles/sec when the independent variable x represents time.  $\nu$ was never my first choice (I prefer $f$), but at least it's clean/simple/less-intimidating, compared to $\xi .$ I reverted that wholesale change, and then someone reverted it back, citing the reason "A survey of the references shows that ξ is by far the more common convention in our sources than ν." If he really surveyed all those references, he's a lot more determined than I.

That's just one example. I could probably spend all day listing all the little things I would like to change. It's OK to test the waters, but if someone objects, it's usually best to just let it go. --Bob K (talk) 14:44, 7 July 2021 (UTC)

If it will help, here are a couple of downloadable examples of authors who use $t-\tau$:

Prandoni, Paolo; Vetterli, Martin (2008). Signal Processing for Communications (PDF) (1 ed.). Boca Raton,FL: CRC Press. ISBN 978-1-4200-7046-0.

Crochiere, R.E.; Rabiner, L.R. (1983). Multirate Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall. ISBN 0136051626.

--Bob K (talk) 22:18, 7 July 2021 (UTC)

It seems to me that the 3rd opinion from Greatder agrees that t & tau in the same equation can be confused. My understanding of the wikipedia process is that now my "tau" -> "u" changes may be restored (i.e. that the revert can be reverted). If anyone objects to said understanding, please say so soon.

Bob K: (a) I believe that I understand your points as well as that of the anonymous reverter. (I am still unclear if you did the revert. Did you?) (b) I believe that I have responded to those points. (c) I believe that, having called for & received an agreeing 3rd opinion, it is now appropriate for me to repeat my original changes. (d) If you disagree with any part of "c", please clarify how. Again: I'm new. If I will be wiki-misbehaving to revert your(?) revert then I want to know now.

It is extremely common to use the variable t for time, in functions of time. People would really laugh if you tried to use x or y. In cases where you need two variables with the time dimension, it is common to use t and tau. Now, convolution doesn't have to be done in the time domain, but it often is. If not, it is less obvious which two variables should be used. Gah4 (talk) 07:01, 11 July 2021 (UTC)

I am not the "anonymous reverter". OK? And yes, thanks to Gah4, I do disagree with your part (c). I provided you with two easily accessed references featuring $t-\tau ,$ and you have provided nothing but your own opinion to support replacing $\tau$ with $u.$

--Bob K (talk) 18:21, 11 July 2021 (UTC)

I don't know who wrote what, but I vote for $t-\tau ,$. Gah4 (talk) 04:13, 12 July 2021 (UTC)

To Gah4 - Sorry. I had understood "it is less obvious which two variables should be used." as agreement that tau is not indicated, partly since you had just remarked that convolution is not always in time domain. 2601:1C1:C100:F420:74A5:16C0:13DD:ED24 (talk) 17:56, 16 July 2021 (UTC) Original tau -> u change author

You and I and IP 174.91.211.146 and two downloadable references all prefer $t-\tau .$ Thanks for your help.

--Bob K (talk) 20:57, 12 July 2021 (UTC)

To Bob K - I was just guessing that you were original reverter. I had previously counted you as original reverter. Had not intended that as an assumption of bad faith: I figured someone might regard having made a drive by as not requiring acknowledgement. 2601:1C1:C100:F420:74A5:16C0:13DD:ED24 (talk) 17:56, 16 July 2021 (UTC) Original tau -> u change author

This keeps getting brought up: The 2 downloadable references (Vetterli & Crochiere) contributed by Bob K could only be relevant if they explicitly claimed that t & tau are the best way to present those equations for a general audience, including visually impaired audience members who might have difficulty distinguishing such similar glyphs. Instead those 2 references merely provide evidence that experts do use that particular jargon. However whether experts use that jargon has never been in question here and does not inform whether non-experts (such as wikireaders who are not fluent in calculus or the Greek alphabet) might find t & tau together in an equation confusing.

Final count is 3/2 for anonymously reverted version (keeping tau instead of u).

Now that this is done, do I remove this entire segment of the talk page? If not, how long to leave it up?

2601:1C1:C100:F420:74A5:16C0:13DD:ED24 (talk) 17:56, 16 July 2021 (UTC) Original tau -> u change author

I have no objection if you want to delete this conversation. What usually happens is conversations are just left in place. And if the talk page gets "too full" in someone's opinion, they archive some or all of it. I don't know how those decisions are made or who makes them. Maybe they are administrators.

--Bob K (talk) 20:57, 17 July 2021 (UTC)

Good to know. Thanks Bob K. 2601:1C1:C100:F420:C855:3E58:1C4E:EAF4 (talk) 19:34, 22 August 2021 (UTC) Original tau -> u change author

There is an automated system when a discussion isn't changing for long enough. But I don't know at all how it works. Gah4 (talk) 08:32, 18 July 2021 (UTC)

On an unrelated note, what do you folks think of my latest wiki-interjection? https://en.wikipedia.org/enwiki/w/index.php?title=Talk:Water_bridge&action=edit&section=2 2601:1C1:C100:F420:C855:3E58:1C4E:EAF4 (talk) 19:34, 22 August 2021 (UTC) Original tau -> u change author

This is not an appropriate place for your Unrelated notes. That's what I think.

--Bob K (talk) 22:47, 22 August 2021 (UTC)

I suppose some fonts have less readable glyphs for Greek letters. This reminds me of a story, which I knew only second hand from a reliable source, about someone who had a math TA from Greece, and complained about using his native alphabet in class. As we know, Greek letters are commonly used in math. For those not following the news, they are now used for naming Covid-19 variations, and also for tropical storms after they run out of names following the Roman alphabet. Hopefully people who are visually impaired have tools to help read text, and those tools can recognize Greek letters. Now, I would not recommend using both Α and A in the same equation. (For those who can't tell, one of those is a capital Alpha, and the other is an ordinary A.) By the way, Greek letters, and other Unicode letters are legal for variable names in Java. I did once have a math class that used (χ,η,ζ) along with (x,y,z) as two different 3D coordinate systems, and that was writing on a blackboard. One could use f(χ-x) for convolution in the spatial domain, and f(χ-x,η-y,ζ-z) for convolution in 3D space. (Does the article cover it in 3D?) Gah4 (talk) 21:19, 16 July 2021 (UTC)

Convolutions of the type defined above

In explaining convolution using FFT, the article says Convolutions of the type defined above. Presumably that means non-circular, but as it comes right after the explanation of circular convolution, that isn't so obvious. Gah4 (talk) 21:26, 16 July 2021 (UTC)

Definition of convolution

The current definition on the page is:

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f and g) that produces a third function that expresses how the shape of one is modified by the other.

I think this is a bad definition since the idea of a convolution has nothing to do with function "shape", even from an intuitive perspective. And function "shape" is not a precisely defined concept to begin with. I think my definition which just explains that the operation can represent different things depending on context is much better. For example, the functions might be PDFs in which case convolution is related to adding two independeng RVs. Or the context might be signal processing which is a totally different application and context. Or it could be convolution of a function by a dirac delta, in which case the result is simply the function evaluated at a single point and really has nothing to do with shape. DMH43 (talk) 15:27, 26 December 2023 (UTC)

Code for circular convolution (added 20-May-2024)

• It is unusual to see actual computer code in an article. I suspect there is a policy about that.
• Thank you for the /* reverse the signal */ code comment, but why only one comment?
• I think it needs an explanation of why one would want to use this program. What is your motivation?
• In my experience, the usual motivation for circular convolution is to exploit the efficiency of the formula:

$x_{_{N}}*y\ =\ \scriptstyle {\rm {DFT}}^{-1}\displaystyle \left[\scriptstyle {\rm {DFT}}\displaystyle \{x\}\cdot \scriptstyle {\rm {DFT}}\displaystyle \{y\}\right],$

implemented with a Fast Fourier transform algorithm. (see Eq.4c at Convolution_theorem#Periodic_convolution)

And only the non-circular part of the output sequence is actually retained.

Bob K (talk) 13:10, 21 May 2024 (UTC)

An article like this should not have code. It doesn't help with an understanding of the concepts except for a very few readers. Those special cases can use Google to find code. Johnuniq (talk) 01:38, 22 May 2024 (UTC)

Add time reversal property

I'm having difficulties trying to find the time reversal property, and people got it wrong too. If

$y(t)=x(t)*h(t)$

then

$y(-t)=x(-t)*h(-t)$

This is the property.

If you look for the property you can find like in this presentation "Signal and Image Analysis, University of Illinois" (PDF)., that they got it wrong, stating that

$y(-t)=x(t)*h(-t)=x(-t)*h(t)$

I would like to propose to add the property so there is no more doubt in this topic. Bouchet07 (talk) 11:27, 25 May 2024 (UTC)

Looks good to me:

$y(t)\ {\stackrel {\mathcal {F}}{\Longleftrightarrow }}\ \ Y(f)=X(f)H(f)$

$y(-t)\ {\stackrel {\mathcal {F}}{\Longleftrightarrow }}\ \ Y(-f)=X(-f)H(-f)$

${\begin{aligned}y(-t)={\mathcal {F}}^{-1}{\bigg \{}Y(-f){\bigg \}}&={\mathcal {F}}^{-1}{\bigg \{}X(-f)H(-f){\bigg \}}\\&={\mathcal {F}}^{-1}{\bigg \{}X(-f){\bigg \}}*{\mathcal {F}}^{-1}{\bigg \{}H(-f){\bigg \}}\\&=x(-t)*h(-t)\end{aligned}}$

--Bob K (talk) 21:31, 26 May 2024 (UTC)