Talk:Cross-correlation

message: The article mentions f^* in many equations but doesn't define it. What's f^*? —Ben FrantzDale 20:07, 19 December 2006 (UTC)
replies: text: A superscript asterisk indicates the complex conjugate. --Abdull 21:06, 20 May 2007 (UTC)
thread_title:  f*? 

message: I don't see yet why f(t)\star g(t) = f^*(-t)*g(t). Let's simplify things to f(t) and g(t) being real functions, therefore f(t)\star g(t) = f(-t)*g(t).
As f(t) * g(t) = \int_{a}^{b} f(\tau) g(t - \tau)\, d\tau, what does f(-t)*g(t) look like expressed in integral form?
Besides, if convolution is commutative and cross-correlation is not commutative why can you say f(t)\star g(t) = f^*(-t)*g(t) at all? --Abdull 21:23, 20 May 2007 (UTC)
thread_title:  Cross-correlation and convolution 

message: The definition used on convolution page is inconsistent with that used here such that the first property of the cross-correlation is unclear with respect to how to derive it starting from the definition of convolution currently being used. Would it be such a bad thing to show the entire derivation here, i.e. just fill in the 2-3 steps between the correlation of f and g and the convolution of f*(-t) and g?  Alternatively, one could define the convolution in terms of the covariance since it would not require a definition that's not listed on the page and would create consistency.
--Kdmckale (talk) 13:17, 18 October 2015 (UTC)
thread_title:  Confusion with definition on convolution page 

message: The article curently does not describe what the appropriate integration limits are. Can someone who knows the answer please add them? Ngchen 14:58, 7 October 2007 (UTC)
thread_title:  appropriate integration limits 

message: I think that the usage and terminology in "signal processing" and in "statistics" are so different that a split into articles specific to each is required.
Melcombe (talk) 11:47, 26 March 2008 (UTC)
thread_title:  Possible split 

message: Can someone please add some words about cross-correlating in the frequency domain, a basic description, its advantages (computing economy), disadvantages (only circular correlation unless periods are lengthened and high-pass is used), etc.
Can someone also add a few words about multidimensional correlation and how it reduces to sets of linear correlation?
Fleem (talk) 11:13, 26 September 2008 (UTC)
replies: text: Another thing that might be included here or in a disambiguation page is the computing definition of the term. Here is a brief def : A cross-correlator is a generic name for a process that compares usually two input streams and usually produces 'summing' or 'difference' streams. All streams will follow their own defined rules and 'summing' and 'difference' are generic labels rather than mathematical terms. The centre of the definition is that it is about feature comparison. Common examples might include text searching algorithms in word processors or database analysis, or various levels in image processing. Lucien86 (talk) 16:22, 13 May 2009 (UTC)
thread_title:  Things to add (but not by me) 

message: For some reason when working with cross-correlations, the notation for the time-lag "t" and time variable "tau" are switched from the usual convention--little "t" as time and "tau" as a temporal shift.  I think the definition could be substantially improved if the the time lag is stated explicitly as "t", as is done in "Numerical Recipes in C", 2nd Ed, on page 498, Eq 12.0.10.  I will not change the page, however, because I am not in the habit of changing pages before I get feedback from others.
Bjf624 (talk) 17:07, 18 February 2009 (UTC)
thread_title:  Confusing Definition 

message: Is there any accepted definition of when a cross correlation can be rated as "good". Assuming any given normalized cross-correlation, a correlation coefficient of 1/-1 points to identical functions / inverted identical functions while the coefficient being 0 clearly defines a "non-correlation" (or orthogonal correlation). But what about the values inbetween? Is 0.8 a good correlation, or would 0.9 do the job? Is there a general classification of coefficients in terms of correlation quality? Or does that very much depend on the subject of application? I understand that the whole approach of cross-correlation is a statiscal one. Hence there may even be research into that field, describing correlation quality (cross-correlation coefficients) by statistical values such as standard deviation? Could someone knowledgeable maybe give some references and include information in the article? Thank you! --194.246.46.15 (talk) 16:13, 1 July 2009 (UTC)
replies: text: No. Sometimes an apple is just an apple. --Drizzd (talk) 11:55, 4 July 2009 (UTC)

text: Yes, there is more that could be said about that. It depends a lot on your signal-to-noise ratio and on the frequency of your expected signal. If you have zero noise, then 1 means perfect alignment and anything else is imperfect alignment. If you have band-limited (no infinite spatial frequencies) then values near 1.0 mean near-perfect alignment. SNR means you can never expect 1.0 for perfect alignment, and the worse the SNR, the lower the maximum expected correlation value. So yes, the value means something but no it isn't directly interpretable. e.g., a maximum correlation of 0.99 doesn't mean there is a 99% chance that that is the correct correlation. You have to think about what could cause less-than perfect correlation values. —Ben FrantzDale (talk) 19:42, 6 July 2009 (UTC)

text: Intermediate values of correlation have an interpretation in terms of how well one series can be predicted from another  in the sense that one minus the square of the correlation says what proportion of the variance of one series would be left as an error variance if a simple shift and scale is applied optimally from one series to the other. But in signal processing you could hope to do better than than this by using an optimally filtered version of one series to predict the other. Ideas about prewhitening both series could come in here. But even a small amount of correlation could be important depending on what is being predicted ... even a small improvement in predictive power might be important.Otherwise iy may be worth looking at other related articles such as correlation function and correlation. Melcombe (talk) 16:03, 7 July 2009 (UTC)
thread_title:  Help please 

message: The formula given for the normalised cross-correlation is wrong/misleading.  The normalisation varies over the convolution, and is calculated based on the current template position.  Refer to Lewis's paper (http://scribblethink.org/Work/nvisionInterface/nip.pdf) for more information. --StefanVanDerWalt (talk) 09:50, 6 December 2009 (UTC)
thread_title:  Incorrect formulation of normalised cross-correlation 

message: I would suggest that all useful properties such as distributivity etc. are listed in an way analogous to how it is done in the convolution article. Furthermore, the notation with "h(-)" as used in the properties section was new to me. I didn't find a definition anywhere. Cheers, Jo. —Preceding unsigned comment added by 129.132.71.148 (talk) 07:40, 6 April 2010 (UTC)
thread_title:  Known properties of cross-correlation should be added 

message: >> If either f or g is Hermitean, then f*g=f*g.
At first glance, this seems to be a trivial identity which holds for _any_ f and g.
At a closer look, you notice the difference between the fivefold and the sixfold asterisk.
I think this can easily lead to confusion. Should we use a different notation?
DrBaumeister (talk) 01:31, 24 April 2011 (UTC)
thread_title:  different asterisks 

message: >> If either f or g is Hermitian, then:  f\star g = f*g.
The same statement can also be found in the Hermitian page.
Is that true? I think only if f is Hermitian then f\star g = f*g.Can anyone show the proof of f\star g = f*g if g is Hermitian?  -Clarafly (talk) 07:23, 17 June 2012 (UTC)
replies: text: I agree that this statement is incorrect. Counterexample: f anything not Hermitian, g is the Dirac impulse. Then f \star g = f^*(-t) * g(t) = f^*(-t) and f(t) * g(t) = f(t). --Drizzd (talk) 13:59, 17 June 2012 (UTC)
thread_title:  Hermitian properties 

message: The "Visual comparison" picture is a great idea, but the lines that represents f*g, f♦g and f♦f (where I'm using "♦" for correlation since I can't find a star symbol) are offset.  Assuming f(t) and g(t) use the same time scale, f*g should be shifted right and f♦g and f♦f should be shifted left.  To be a bit more precise, and for the sake of simplicity assuming f(t) and g(t) are nonzero between t=0 and t=1 (i.e., defining t=0 at the leading edges of f and g, and t=1 at the falling edge of f and where g(t) goes to zero again), f*g is zero for t<0 and maximum when t=1; whereas f♦g and f♦f are zero for t>1 and maximum when t=0.  It's also really easy to read the wrong thing into the graphs of the overlapping functions, but on the other hand there's a lot of intuitive value in it as well, so I'm not sure I would change that.  But if there's a way to change the picture to shift the black lines, it would be a lot clearer.  — Preceding unsigned comment added by Gdlong (talk • contribs) 20:56, 15 November 2013 (UTC)
thread_title:  Visual comparison graphs are offset 

message: "This problem arises because some moments can go to zero and this can incorrectly suggest that there is little correlation between two signals when in fact the two signals are strongly related by nonlinear dynamics."
If the moments go to zero, and the correlation becomes zero, then it isn't incorrect to suggest that there is little correlation between two signals. The writer seems to be confusing "correlation" with "connection" or some other word that means a relationship exists. The problem arises, because correlation is a measurement of linear dependence, so it makes sense for nonlinear dependencies to circumvent the measurement. A Wikipedia article itself describes this for random variables (and stochastic processes are simply a series of random variables, so it applies just as well): http://en.wikipedia.org/wiki/Correlation_and_dependence  — Preceding unsigned comment added by 71.80.79.67 (talk) 09:40, 6 February 2014 (UTC)
thread_title:  Problem with Nonlinear Section 

message: "there will always be a peak at a lag of zero unless the signal is a trivial zero signal."
Peak here means "highest point in the signal", so even for the trivial zero signal, there is still a peak at a lag of 0 (equal to 0).  — Preceding unsigned comment added by 96.38.109.155 (talk) 13:11, 14 March 2014 (UTC)
thread_title:  Zero Lag Peak Statement is Slightly Incorrect 

message: The article for convolutions has an extremely helpful section for understand what the convolution function does: https://en.wikipedia.org/wiki/Convolution#Derivations
It unpacks the terms in the function, the steps in the algorithm, and animates it.
Someone should do the same for this article!
Richard☺Decal (talk) 04:32, 26 February 2015 (UTC)
thread_title:  Visual explanation needed 

message: (1) The definition given in the section entitled "Time-delay analysis" is different from both of the definitions given in the introduction. Yet it is a good, mature definition, and deserves to be mentioned in the introduction.
The "signal processing" definition in the introduction refers only to a time-lagged single inner product, not a random variable. On the other hand, the "probability and statistics" definition in the introduction does not have the structure of a time series or time-dependent signal; in particular it has no concept of "time lag". 
(2) I also have trouble seeing how the time-lagged inner product of the introduction is useful for signals. Don't signals last forever, so they are not in L^2,  so the convolution integral would be ill-defined or infinite?
:I feel that is explained by "It is commonly used for searching a long signal for a shorter, known feature."  An example is a matched filter for detecting the arrival of radar pulse returns.  It cross-correlates the streaming signal with the finite-length pulse shape, producing peaks at the points that pulses occur.
:--Bob K (talk) 13:31, 20 November 2016 (UTC)
thread_title:  Missing or misleading content in the introduction 

message: That minus sign before the f* in the first property is just flat out wrong.  — Preceding unsigned comment added by 188.174.57.61 (talk) 13:58, 14 August 2017 (UTC)
thread_title:  Bad property 

message: The animated .gif on this page (link here) is quite large at 7.13MB. 
It uses 20 fps for 40s (800 frames total). I suggest reducing the frame rate to get the .gif under 2 MB.
Would anyone have an objection to this? I cannot contact the original uploader to this .gif but it has CC 4.0 license
Davidjessop (talk) 00:16, 24 February 2019 (UTC)
replies: text: No objection.  Frankly, I don't find it helpful.  You can delete it completely, as far as I'm concerned.  --Bob K (talk) 05:04, 24 February 2019 (UTC)
thread_title:  Reduction in animated .gif size 

message: There is discussion in talk:convolution about the notation of the operators for convolution and cross-correlation. It seems that this article uses five and six pointed asterisks to distinguish them. Is there a reference for these being the WP:COMMONNAME  (well, except that they aren't names) for them?  After about 2 seconds, I forget which one is which.  Gah4 (talk) 21:39, 7 June 2019 (UTC)
thread_title:  asterisks