# Auto Correlation vs Cross Correlation vs Convolution and their applications

I know from wikipedia that auto correlation in done on the same signal while cross correlation is done on different signals.But what does this actually imply in terms of application.I can always apply cross correlation on same signals and get same output. And in convolution one signal is reversed.Mathematically i understaand the formulas.

But what does these three mean in terms of applications?

• This question might be better on dsp.SE (you can ask the moderators to migrate the question to dsp.SE; click on the "flag" link below your question). Here I will simply say that the basic function is the crosscorrelation of signals $x$ and $y$. If we choose $y$ to be the same as $x$, then, rather that call the result the "crosscorrelation of $x$ and $x$" or the "crosscorrelation of $x$ with itself", we choose to simply say "the autocorrelation of $x$" which saves a few keystrokes/bytes and perhaps sounds a little more elegant and pleasing to the ear. – Dilip Sarwate Oct 1 '15 at 12:44
• I think that autocorrelation is exemplified by a predicting the future path of a particle given that we measure one of it's properties at some time. Whereas crosscorrelation is exemplified by Bell's Theorem/Experiment; how well to the statistics of two correlated but independent properties match given an underlying uncertainty. In convolution it seems you are looking backwards to satisfy cause and effect. This whole attitude would seem to imply that Bell's Theorem results distinguish autocorrelation from cross correlation? Anybody have an answer for that? – rrogers Oct 7 '15 at 12:23

I can tell you of at least three applications related to audio.

Auto-correlation can be used over a changing block (a collection of) many audio samples to find the pitch. Very useful for musical and speech related applications.

Cross-correlation is used all the time in hearing research as a model for what the left and ear and the right ear use to figure out a sound's location in space (this is called sound source localization). In the case of two microphones you would cross-correlate the left channel with the right channel.

Convolution is used in simulating reverberation. A room's impulse response can be determined from measurements and that impulse response can be convolved with any sound source to simulate the reverberant response (at the impulse response recording's exact location).

I know this answer isn't complete but maybe it can give you some idea that there is in fact a practical use for auto- and cross- correlation!

So in general, auto-correlation can be used to extract properties of a signal, cross-correlation can exploit the information between two related signals, and convolution can be used to modify the properties of an incoming signal based on some time, frequency, and phase response specified by the impulse response you're convolving the source with.

• why was this downvoted? – panthyon Oct 3 '15 at 21:03