Difference between Auto- and Cross-correlation function

[shayaan_musta]

Hello

I want to know what is the difference between Auto-Correlation function and Cross-Correlation?

I googled both but didn't find any answer which I could understand. I want you people to make me understand with quite easy language just like a spoon feeding.

And also tell me what information we get from these two?

 

[mathman]

Auto-correlation refers to correlations between two instances within a series (or two instances of a stochastic process). Cross-correlation is about correlation between instances of two different processes.

The information tells you how strong is the relationship.

 

[Khashishi]

Cross-correlation compares two (usually different) data series. Auto-correlation is the cross-correlation between one series and itself, so it's a special kind of cross-correlation.

 

[NascentOxygen]

And also tell me what information we get from these two?

The combination of correlation theory and noise (Gaussian or pseudo-random) was an area of study that I found captivating when I was a final year student. An autocorrelation of the output of an amplifier or a control system can reveal that system's impulse response. You can input your own noise signal, or perform this test using the small amount of noise that is naturally present at the input. In the latter case, you cause no disturbance to normal operation because you are carrying out the test without the need to input a specific signal.

Cross-correlation has endless possibilities. Suppose your job was to guard the strongroom of a bank. You could install a couple of microphones spaced well apart on the floor or walls. These microphones would pick up noise of all description, both from within the building and outside, including that of passing street traffic, and overhead aircraft. A cross-correlation of the signals from the two microphones would see most of the transitory noises smoothed over, just leaving identifiable steady spikes indicating airconditioner noise, office clocks ticking, etc. But should you notice the appearance of a new spike in the correllogram---a spike indicating a new and sustained source of sound---it could be the signature of someone tunneling nearby. Even though it might well be drowned out in amplitude by a host of other sounds, it gets revealed by the cross-correlation process.

The textbook we used was co-authored by Tom Ledwidge. https://books.google.com.au/books?id=zMtfAAAAMAAJ&focus=searchwithinvolume&q=autocorrelation

That book is not available for reading at google books, but I like this snippet:

:D

 

[pmacias]

Sure, I'd be happy to explain the difference between auto-correlation and cross-correlation functions. These are both statistical methods used to measure the relationship between two variables.

Auto-correlation measures the correlation between a variable and itself over a period of time. This is useful for detecting patterns and trends within a single variable. For example, if we wanted to see if there is a relationship between a company's sales from one month to the next, we could use auto-correlation to see if there is a pattern or trend in the data.

On the other hand, cross-correlation measures the correlation between two different variables over a period of time. This is useful for determining if there is a relationship between two variables that may be related to each other. For example, if we wanted to see if there is a relationship between a company's sales and advertising budget, we could use cross-correlation to see if there is a pattern or trend in the data.

Both auto-correlation and cross-correlation provide information about the strength and direction of the relationship between two variables. However, auto-correlation only looks at one variable, while cross-correlation looks at the relationship between two variables.

I hope this helps to clarify the difference between these two methods. Let me know if you have any other questions.