File talk:Comparison convolution correlation.svg

Convolution = Cross-correlation?

it seeems like the convolution example uses a different triangle shaped window from the top row to the lower rows... can anyone correct it?

The difference is intentional; in convolution, g(t) is horizontally flipped. That's what distinguishes it from cross-correlation. cmɢʟee ☎✉ 23:23, 17 July 2012 (UTC)[reply]

The cross-correlation $f\star g$ is incorrect. According to the definition in the article, it should be reversed, making it look exactly like the convolution (this is consistent with the statement in the Properties section that "If f is Hermitian, then $f\star g=f*g.$ "). It looks like this diagram was made using a different convention from that in the article. --TSchwenn (talk) 23:56, 29 September 2012 (UTC)[reply]

I've done a bit of checking and still think that the graphic is correct.

For convolution, Fig 13-5 in ^[1] has similar f, g and f * g.

I couldn't find proper source for cross-correlation, but this video shows MATLAB giving the same result.

This video summarises the differences. cmɢʟee⎆τaʟκ 01:22, 19 September 2014 (UTC)[reply]

^ Steven W. Smith. "The Scientist and Engineer's Guide to Digital Signal Processing — Chapter 13: Continuous Signal Processing". Retrieved 19 September 2014. {{cite web}}: line feed character in |title= at position 38 (help)

I found a proper source(s) for cross-correlation. For real-valued functions, it is defined as:

(f\star g)(\tau )\ {\stackrel {\mathrm {def} }{=}}\int _{-\infty }^{\infty }f(t)\ g(t+\tau )\,dt.

^[1]^[2]^[3]^[4]

It follows that when the $f$ function is symmetrical (as in the figure we're talking about), convolution and cross-correlation are identical. The figure is wrong.

^ Bracewell, R. "Pentagram Notation for Cross Correlation." The Fourier Transform and Its Applications. New York: McGraw-Hill, pp. 46 and 243, 1965.
^ Papoulis, A. The Fourier Integral and Its Applications. New York: McGraw-Hill, pp. 244-245 and 252-253, 1962.
^ Weisstein, Eric W. "Cross-Correlation." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Cross-Correlation.html
^ https://en.wikipedia.org/wiki/Cross-correlation

--Bob K (talk) 22:00, 19 November 2016 (UTC)[reply]

Hi Bob K, You've convinced me with the sources and File:Comparison_convolution_james.png. I've updated the graphic and hope it's all right now. Cheers, cmɢʟee⎆τaʟκ 19:10, 20 November 2016 (UTC)[reply]

P.S. Apologies for doubting editors who pointed out my mistake previously.

Asymmetric function to illustrate autocorrelation

IMO it would be more informative if some non-symmetric function (for example g function instead of square f) were used tu illustrate autocorrelation. Marioosz (talk) 17:41, 17 January 2013 (UTC)[reply]

Done cmɢʟee⎆τaʟκ 02:03, 19 September 2014 (UTC)[reply]

[1] Steven W. Smith. "The Scientist and Engineer's Guide to Digital Signal Processing — Chapter 13: Continuous Signal Processing". Retrieved 19 September 2014. {{cite web}}: line feed character in |title= at position 38 (help)

[2] Bracewell, R. "Pentagram Notation for Cross Correlation." The Fourier Transform and Its Applications. New York: McGraw-Hill, pp. 46 and 243, 1965.

[3] Papoulis, A. The Fourier Integral and Its Applications. New York: McGraw-Hill, pp. 244-245 and 252-253, 1962.

[4] Weisstein, Eric W. "Cross-Correlation." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Cross-Correlation.html

[5] ttps://en.wikipedia.org/wiki/Cross-correlation

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