Talk:Sinc function

message: There is nothing special to the sinc function resulting in f(x/a)/a approaching the delta. This is true for a very wide class of functions.  — Preceding unsigned comment added by 67.220.7.72 (talk) 03:04, 5 April 2012 (UTC)
thread_title:  Relationship to the Dirac delta distribution 

message: I have seen definitions of sinc where the removable singularity at x=0 is removed explicity, ie.,
: \mathrm{sinc}\ x  = \left\{\begin{matrix} 
{\sin{x}\over x} &\mathrm{if~~}  x\ne 0 \\
1 & \mathrm{otherwise} \end{matrix}\right.
However, I've also seen definitions where it is simply left as (sin x)/x. 
Which is best? Shall we mention both? Dysprosia 07:39, 8 Jan 2005 (UTC)
replies: text: vote for explicit removal plus comment that that makes the function analytic at 0.  --Zero 12:07, 1 Feb 2005 (UTC)

text: I agree, I inserted it Paul Reiser 15:03, 1 Feb 2005 (UTC)
replies: text:  I strongly disagree. Just read the definition of removable singularity (which is correct) and you'll see that this is not correct. I'm very much in favour of writing the correct definition (at least for the "mathematical" case, if engeneers would be offended), or at least write clearly and explicitely that the sinc function is defined to equal 1 in the point where this expression is not defined. Else it is NOT defined, and since it should be a classical function (and not only L² or distribution), one HAS to specify a value in 0. — MFH:Talk 11:58, 16 October 2008 (UTC)
thread_title:  Definition 

message: first of all, there appears to be something missing in the first paragraph.  "It is defined by:" what?!
certainly in some math and physics texts, i have seen the definition of sinc() as stated in this
: \mathrm{sinc}\ x  = \left\{\begin{matrix} 
{\sin{x}\over x} &\mathrm{if} & x\ne 0 \\
1 & \mathrm{otherwise} & \end{matrix}\right.
but in electrical engineering signal processing texts (this is where the sinc() function is used most often, as far as i can tell) the definition is adjusted a little:
: \mathrm{sinc}\ x  = \left\{\begin{matrix} 
{\sin{\pi x}\over {\pi x}} &\mathrm{if} & x\ne 0 \\
1 & \mathrm{otherwise} & \end{matrix}\right.
it is mentioned as the "normalized sinc" function in this article, but i have never seen that term used anywhere else.
this is typical of the difference in notation between math and physics texts and electrical engineering texts.  is it  i \  or   j = \sqrt {-1} \  ?  is it  \omega \   or  j 2 \pi f \  in the Fourier Transform?  is it  \sin (x)/x \  or   \sin (\pi x) / (\pi x) \  ?
i am bothered by the lack of self-consistent notation inside of wikipedia (the i vs. j thing doesn't bother me) but am not sure what can be done about it.  r b-j 17:07, 11 Mar 2005 (UTC)
replies: text: A google search on "sinc function" is helpful. It seems both are used. How do you suggest we fix the article? Regarding what to do, I think we just have to fix any inconsistencies whenever we run across them. Paul Reiser 17:38, 11 Mar 2005 (UTC)
replies: text:  believe me, i have googled it.  and it comes out both ways.  Wolfram likes it without the pi but there are many web pages on both sides of the definition.  what i think has happened is that some electrical engineering profs have long ago decided that the   \sin (\pi x) / (\pi x) \  definition was better, espcially in signal processing (since the sinc() function hits zero at all other sample times).  Many have also redefined the Fourier Transform from the definition here to one with   j 2 \pi f \  and no  1/( 2 \pi ) \  in the inverse transform.  This simplifies the duality property, power expressions, and Parseval's theorem.  It would be nice if it were completely consistent in Wikipedia and the simplest definitions, but i am afraid that historical and practical concerns are not identical. r b-j 05:47, 12 Mar 2005 (UTC)
thread_title: More on sinc definition

message: Since the article itself says: " Applications of the sinc function are found in digital signal processing, communication theory, control theory, and optics. " I can pretty much guarantee that, as the sinc() function is presently defined herein, that every appearance of sinc will have a π in it.  Since nearly every communications/signal_processing text defines the sinc() function as
: \mathrm{sinc}(x)  = \left\{\begin{matrix} 
{\frac{\sin(\pi x)}{\pi x}} &\mathrm{if} & x\ne 0 \\
1 & \mathrm{otherwise} & \end{matrix}\right.
why don't we change the definition to the normalized form, make mention that the historical definition and some mathematics texts will have it without the π and i am will to find all citations of this article and fix the reference to sinc() so that WP is consistent. Rbj 21:46, 30 April 2006 (UTC)
replies: text: Every appearance of sinc will have a π in it In your world. In my world (math and physics), I rarely see it defined with a π. We went through the same thing with the Fourier series stuff and the resolution was that if you want to understand the mathematics and prove theorems, learn the mathematicians notation. If you want to use it in a practical sense, learn the notation that suits that field. The article should attempt to address both users: Someone coming from a communications article should not have too much difficulty finding what they want, nor should someone coming from a mathematics or physics article. Its not easy. I'm sorry if I sound contentious, but it irks me when communications/signal_processing people start talking like they are the only real people in the known universe. Seriously, I realise the sinc-sub-pi notation for the communications people is a problem that needs to be fixed, but this kind of language isn't the right beginning.   PAR 00:46, 1 May 2006 (UTC)

text: It is a generous offer, and I happen to also inhabit Rbj's world, but unfortunately I think PAR is correct.  It's not a matter of contemporary vs. historical.  It's just two different conventions, overloading of the "word" sinc.  A textbook has the advantage of being able to choose one and ignore all others, and that is what we are accustomed to.  But Wikipedia does not have that luxury.  And anything we "resolve" today can be revisited ad infinitum (as we are doing right now).  That is why Wikipedia will never be high quality.  We could write the perfect article today, and it would erode over time.  We could make some aspect of Wikipedia totally consistent over all articles, and the inconsistencies and errors would creep back it, like weeds.  So all I am saying is that there is a limit to how much we should stress over this.  But each person must decide that for himself.  --Bob K 14:26, 2 May 2006 (UTC)
replies: text:  it's okay, i give up.  it's just that i clicked What links here and looked at some of the results.  Only Bessel function has an expression of  \frac{\sin(x)}{x} \  (without explicitly changing it to  \mathrm{sinc}(x) \ ).  even the Gamma function (the other ostensibly pure math article) uses the normalized  \mathrm{sinc}_N(x) \  and all of the other uses were communications/signal_processing or sampling/interpolation related and i know for sure that the normalized sinc is what is used in those context.  so i do not see evidence here at Wikipedia to support PAR's point. Rbj 16:24, 2 May 2006 (UTC)
replies: text: Nyquist–Shannon sampling theorem, for instance, has an explicit π in the argument of its sinc functions, so I believe that is the unnormalized variety.  But I think the only reason it was chosen is to conform with this article.  I.e., the normalized sinc would have a cleaner look.  Perhaps that is what you mean(?).  --Bob K 17:06, 2 May 2006 (UTC)
replies: text:  yes. that is what i mean.  until the definition is changed to include π in it, we have to put the π in everywhere else.  i, for the most part, refuse to use the present normalized sinc notation  \mathrm{sinc}_N(x) \  or  \mathrm{sinc}_\pi(x) \  or whatever.  i'll just put the π in the argument.  but it seems to me silly to do so because we want to leave it out of the  \mathrm{sinc}(x) = \frac{\sin(x)}{x} \  definition.  it makes much more sense, at least from the electrical engineering and DSP POV to do what the textbooks do and put the π in the definition.  i know this sounds EE and DSP centric, but i would like to see how often the sinc is used in applications in other contexts, and how many of those times there is no π in the argument (given the present definition). Rbj 19:15, 2 May 2006 (UTC)
replies: text: Me too.  --Bob K 01:13, 3 May 2006 (UTC)

text: Come to think of it, the Wikipedia standard for dealing with different concepts or definitions associated with the same [overloaded] title is to disambiguate.  Therefore Sinc function should actually be disambiguation page, pointing to Sinc function, unnormalized and to Sinc function, normalized.  Each article that references a sinc function would link directly to the appropriate definition.  --Bob K 17:06, 2 May 2006 (UTC)
replies: text:  i don't like that idea.  i'd rather keep it as it is and continue to put π in the argument of the sinc everywhere we use it. i want to reduce multiple definitions of the same thing.  i want more unification of meaning of terms. Rbj 19:15, 2 May 2006 (UTC)
replies: text: That is exactly what I have been doing, in the interest of global peace and harmony.  But the world is actually a messy place.  I am inclined to distinguish Wikipedia's role from that of a textbook.  Wikipedia's job is to organize a messy room (so people can find what they want), but not throw anything of value away.  A textbook, OTOH, achieves apparent unity by limiting its scope to just one corner of the organized room.  So I think your goal for Wikipedia is too ambitious.  To paraphrase PAR, unity within each discipline is more important than unity across the disciplines.  By reaching for the latter, we ensure that Wikipedia's EE-oriented articles will have different-looking mathematics than all the EE textbooks.  I was resigned to that fate until I realized that disambiguation is the organizational tool we need to avoid throwing away something of obvious value.  --Bob K 01:13, 3 May 2006 (UTC)
thread_title:  Revisit normalization and definition issue 

message: Rbj, you request that an admin do a move.  I'm an admin, and I'm happy to do a move with deletion if you like.  But is it ready to go?  Is there anything left at sinc function or sinc function (normalized) which needs to be merged back?   For example, the disambig page has a graph which is in neither particular page.  Is there any desire to keep that graph in the article?  What about the stuff about orthonormal bases that's in the normalized article but not the unnormalized article?  -lethe talk [ +] 06:23, 3 June 2006 (UTC)
replies: text: I've done the move. -lethe talk [ +] 06:47, 3 June 2006 (UTC)
replies: text:  i made a stab at merging the stuff.  more wordsmithing and editing will have to be done.  thanks for doing the move.  i would like to eventually kill the sinc function (normalized) and sinc function (unnormalized) pages, but i have to find the places where they are referenced and fix that before requesting AfD. r b-j 06:54, 3 June 2006 (UTC)
replies: text: Redirects are cheap, why bother?  -lethe talk [ +] 06:56, 3 June 2006 (UTC)
replies: text:  'cause i'm anal-retentive and i hate dangling loose ends. r b-j 06:59, 3 June 2006 (UTC)
replies: text:  Well, you can find all the articles which go through the redirects by Special:Whatlinkshere/Sinc function.  After you bypass all the redirects, I'll be happy to delete them for you.  By the way, I guess you've merged whatever content there was from sinc function (normalized), but not the picture from the disambig page.  If you want it, it's in the article history, which I've undeleted after the merge, in case you think it has a place in the article (I personally do not though). -lethe talk [ +] 07:05, 3 June 2006 (UTC)
thread_title:  move request to admins 

message: i'm pretty happy with the article they way it is and will just accept that the Optics guys will use sinc(x) differently than i would prefer.  i am now trying to make two new articles for Zero-order hold and First-order hold and to get rid of a poor rendition of the two in another article i'd like to see deleted.  i'm in a sorta "weed the garden" mode now. r b-j 02:18, 12 June 2006 (UTC)
thread_title:  yea!  PAR!  that  looks really nice! 

message: Anybody have any idea how to find the Fourier Transform of Sinc2(πax) using the Convolution Theorem? I cant find any refs that actually show examples of how to use the Conv Theorem in FTs.
Any thoughts?--Zereshk 21:53, 15 September 2006 (UTC)
replies: text: The transform of sinc times sinc is rect convolved with rect, which is the triangle function.  In the frequency domain, the triangle is scaled to go to zero at twice the frequency at which the sinc's spectrum goes to zero, which you can think of as a frequency doubling effect.  If you want equations, let us know. Dicklyon 23:57, 15 September 2006 (UTC)

text: Assuming you mean the unnormalized sinc function it's row 12  with  t \rightarrow x\,  and  a \rightarrow a\,   (not a \rightarrow \pi a\,)    --Bob K 05:02, 16 September 2006 (UTC)
thread_title: Question

message: I reverted the addition of the nice 3D picture of the 2D sinc as being off topic and not all that useful.  I cannot think of any use of the 2D sinc; can anyone? Dicklyon 04:56, 18 November 2006 (UTC)
replies: text: I assume that it applies to image filtering and filter design analogous to signal processing filters.  --Bob K 14:46, 18 November 2006 (UTC)
replies: text: Sounds like a plausible guess, but it is not so.  The impulse response of a circularly symmetric sharp lowpass filter is an Airy function, not a 2D since.  And the impulse response of a square sharp lowpass filter is a separable product of sincs, not a radial sinc. Dicklyon 16:46, 18 November 2006 (UTC)
thread_title:  2D Sinc? 

message: I never before saw Sa for sinc. In what context is it used? What does it stand for? If it is not used for the "math" version (sin x)/x, then maybe it could be removed at least there. I think w.r.t. its popularity, it occupies a much too much predominant postion on the page (at a first glance on the page one would think it is the main usage). I'd be in favour of removing it from the big displayed equation; anyway it's written on the 1st line that its "sometimes [denoted by] Sa(x)". — MFH:Talk 11:46, 16 October 2008 (UTC)
thread_title:  Sa ?? 

message: It appears that the example graph is incorrect.  The normalized (with pi) is shown crossing zero at integer (non-zero) points and the non-normalized appears to cross at multiples of pi.  —Preceding unsigned comment added by 134.50.53.42 (talk) 22:12, 15 October 2009 (UTC)
replies: text: Yes, sin(πx)/πx has zeroes at nonzero integer points. Why do you think it is incorrect? — Emil J. 10:22, 16 October 2009 (UTC)
thread_title:  graph incorrect 

message: If one didn't already know EmilJ's derivation for the limit of the (unnormalized) sinc at 0, how would one normally approach the problem of evaluating the simple expression:
:\lim_{x\to0}\frac{\sin(\pi x)}{\pi x}  ?
If one knew the trick of turning it into the derivative of another function, after recognizing that the numerator and denominator both evaluate to 0 at the point where you're taking the limit (the same recognition that traditionally triggers application of l'Hopital's rule), one would write, as EmilJ did
:\lim_{x\to0}\frac{\sin(\pi x)}{\pi x} = \lim_{x\to0}\frac{\sin(\pi x)-\sin(\pi 0)}{\pi(x-0)},
With a little rearrangement, this is easily recognized as the derivative of \frac{\sin(\pi x)}{\pi}.  For anyone with the most elementary skills at differentiation, this is clearly just cos(\pi x), which at x=0 is 1.  So, same answer as before, with just slightly more complicated path; but I think it illustrates that the method is based on being able to intuit what to do with the subtractions, and on the ability to recognize a limit expression as a derivative even when it's not in exactly the right form.  Is there any generality here, or is it just re-deriving l'Hopital's rule in a lucky case-specific way?
The way normal people (not you mathematicians) would do it is say:  "whoa, ratio 0/0, how am I going to do that?  Oh, I remember, they taught us about some French dude who had a rule that makes it work trivially...something about a hospital...oh, here it is...doh!" 
The sinc function is very often used as an example of where l'Hopital's rule is useful; for example, in the article l'Hôpital's rule; or in this book; or in this book; or in this book;  or in this book;  in general, many more books than I found before, because they don't call it "sinc". 
If there's a more straightforward way to evaluate such limits, I'd like to know it.  Dicklyon (talk) 01:52, 17 October 2009 (UTC)
replies: text: There is, in the sense that the limit is by a substitution that of sin(y)/y. Now why you know this is 1 is a matter of definitions, if it is not arguing in a circle. But we do know that limit. Charles Matthews (talk) 16:22, 17 October 2009 (UTC)
replies: text: OK, that's just stupid.  Replace one unsolved problem by another whose solution has not been well explained.  I agree that there are ways to find a path to the limit via such substitutions.  But that requires search, as opposed to the simple application of rule that is triggered by exactly this situation.  Did you look at any the books I linked?  Don't they all show the use of the l'Hopital's rule as the way to evaluate this limit?  Don't th e other methods described here all require some messing around to find the path of transformations to get to an answer?  That's the difference I'm talking about.  Dicklyon (talk) 18:40, 17 October 2009 (UTC)
replies: text: It seems that this discussion is no longer aimed at changing the article in any way, but at resolving this situation where two parties don't understand each other and don't know if they are talking past each other or what's going on. So far as I am concerned, that's fine. Here is how I feel about it, as a pure mathematician from a field where real numbers hardly occur at all: If you had asked me for this limit without giving me any hints or additional information, I would not have remembered l'Hôpital's rule. (Before EmilJ left a message at WT:WPM, this rule was hidden in a dusty corner of my brain.) Instead I would very likely have come up with the formula that I have given you above. (BTW: Sorry if the formula was nothing new for you, but at least it helped to clarify what we are talking about.) For a mathematician this is the natural way to do it; and part of our work in teaching university level maths is to make our students approach problems in the same way. If a significant portion of, say, second year mathematics students at a certain university would use l'Hôpital to compute this limit, this might be an indication that something went wrong in the course; that they don't think like mathematicians. For a mathematician doing a very small "backwards" step is no "messing around". We have to do it all the time and it becomes second nature. And many mathematicians find it harder to remember a theorem like l'Hôpital's rule than to remember vaguely that something like it exists and fill in the details by reinventing it. That's a result of our first year courses, in which the students must prove half a dozen theorems on their own every week. (Another result is that most people who drop out of a mathematics course do so in the first year, in contrast to most other subjects where people tend to drop out much later. At least that's the situation in Germany.) Hans Adler 01:05, 18 October 2009 (UTC)
replies: text: I agree with all that entirely.  I do a fair bit of math myself, though I'm primarily an engineer, so I know how to look around for the right transformations – or how to ask Mathematica to help me.  But for "the rest of us" as Steve Jobs used to say of the non-nerds, it's handy to just apply the rule that's triggered by the situation; of course, for those who don't remember the rule, or if it doesn't get triggered, that's not going help a bit!  Nonetheless, I was a bit miffed by all the people saying things like it's "completely pointless and brain-damaged"; or "no textbook would do it that way" when there's a ton of evidence that many do, and in fact use this particular limit as the canonical example; or saying "by definition" when they means it's possible to find a way...  Sigh... Dicklyon (talk) 03:59, 18 October 2009 (UTC)

text: Forgive me, but what I suggested is a two-line proof, consisting of an observation and then a look-up. I realise that the ad hominem arguments above have hardly added to the tone of the discussion, but they weren't from me. I answered your question and hardly deserve to be called "stupid" for that. Charles Matthews (talk) 10:51, 18 October 2009 (UTC)
replies: text: I'm not calling you stupid; the adjective applied to "that", which was a statement that the method involving a leap of recognition in the first step was "more straightforward" than simply applying the well-known rule. Dicklyon (talk) 15:18, 18 October 2009 (UTC)
replies: text: Shrug. "How would one normally approach the problem of evaluating the simple expression ... ?". That was the question. First, recognise that π has no business in there complicating the issue. Second, "simple expression" is then "well-known expression" for the slope of the graph of sin at 0. Sorry, it does depend on who "one" is. It does depend on being comfortable with the limit concept. On realising that if you know the derivative of sin then a fortiori you know this limit. As has been said before, there is nothing to justify dressing up the procedure of evaluating the limit in an algorithmic garb just to produce the same answer by a longer way round. Anyway, if you ask an honest question it goes down badly if you react that way to a competent answer. Charles Matthews (talk) 15:57, 18 October 2009 (UTC)
thread_title:  Computing (normalized) sinc(0) 

message: This article, like many others in the higher math domain, lack a root in reality.  Wikipeida is a general encyclopedia not a PhD in Mathematics encyclopedia.  Can an expert in the field please post why this is notable or relevant to those who are not math experts?  Otherwise I propose it be deleted. 74.115.216.130 (talk) 20:20, 28 June 2010 (UTC)
replies: text: I am sorry the article lacks a root in YOUR reality, but you are wrong, Wikipedia IS an encyclopedia for math experts. And science experts, and art experts, and history experts and every kind of expert you can think of. Its also a general encyclopedia. You start out at the simplest level. If you want to learn more about a subject, hopefully there will be a link to help you instead of a stop sign that says "sorry, if you want more information on this, you will begin to become an expert, and we can't have that". Wikipedia is not intended to bolster your self-esteem about the level of your education. There is not one "expert" contributor to Wikipedia who isn't totally baffled by some other "expert's" contribution. Instead of proposing to delete what you don't understand, why not contribute what you do understand, and just hit the back button for the ones that you don't. PAR (talk) 01:28, 29 June 2010 (UTC)
thread_title:  What is the Sinc function and why should I care? 

message: Sinc stands for something like 'cardinal sine' (see french article). Moemin05 (talk) 00:25, 11 February 2011 (UTC)
replies: text: Read the lead.  Dicklyon (talk) 04:34, 11 February 2011 (UTC)
thread_title:  Abbrevation for 'Cardinal Sine'? 

message: I've found intresting thing about generalized sinc function. If the function is given:
n*(sin(nx)/nx)
then function is limited by functions 1/x and -1/x. It is easy to see on function grapher  — Preceding unsigned comment added by 83.23.6.202 (talk) 19:05, 17 June 2011 (UTC)
thread_title:  Limit of function 

message: I added "(k integer)" to where "orthonormal base" is mentioned.
The orthonormality as well as values of all other scalar products (among functions
sinc(t−k) where k is not necessarily integer, this time) follows immediately from the following
nice property that you might want to include:
sinc * sinc = sinc. (* denotes convolution.) This in turn follows via Fourier transform from rect2=rect.
90.180.192.165 (talk) 00:30, 19 August 2011 (UTC)
replies: text: a graphic illustration would be nice (with sinc and sinc²)--46.115.99.134 (talk) 10:18, 8 September 2013 (UTC)
thread_title:  sinc * sinc = sinc 

message: The real definition of the Sinc function is \mathrm{sinc}(x) = \frac{\sin(x)}{x}\,\! if x ≠ 0 and Sinc 0 = 1. Blackbombchu (talk) 00:00, 2 December 2013 (UTC)
thread_title:  Incorrect definition of the Sinc function 

message: The name sinus cardinalis dates back by Edmund T. Whittaker in 1915, where he named the bandlimited or most simple function of a family of cotabular functions (sharing a function table, i.e., values at equally spaced sample points) the cardinal function of this family. One would have to check if he already named the basis functions or if that came later. See A History of interpolation.--LutzL (talk) 11:09, 4 December 2013 (UTC)
thread_title:  History of the name 

message: Since Sinc redirects here, it's very probable that some "audio freaks" will first search for sinc used in sound backends, but instead get a boatload of mathematical stuff they actually did not want to delve into so much. Of course, there is a link to the "Sinc filter", but it's on the very bottom, squeezed somewhere between antialiasing and lanczos stuff. However, there's already a "Redirect" template on top. In case you agree, could you give me a hand how to handle this best? (and remove the "Sinc filter" from the "See also" list in the process) -andy 2.242.236.31 (talk) 17:54, 11 October 2014 (UTC)
thread_title:  Put fork to Sinc ''filter'' on top of the article? 

message: The 'Infobox' that was introduced by the edit 2021 Nov 25, includes the heading "solution", and gives a year of 1952. That looks really dumb to me, as if that was the first year that the properties of sin(x)/x was first considered.
Does anyone else think that putting "Solution" = "1952" is wrong-headed?  — Preceding unsigned comment added by 70.20.25.26 (talk) 19:43, 29 March 2022 (UTC)
thread_title:  Infobox "Solution" year of 1952 

message: I agree that "year of solution" should be "year of definition" or any close item provided by the infobox.
I feel that the series for the extrema should be an asymptotic one; if so this should be stated.
151.29.137.229 (talk) 19:11, 10 October 2023 (UTC)
thread_title:  comment