Study the autocorrelation function

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The discussion focuses on understanding the autocorrelation function (ACF) and its calculation for specific functions, particularly Hn(t). Participants share resources for studying ACF, including links to e-books and academic papers. A key point is the need to evaluate integrals involving Hn(t) and its derivatives to determine the ACF, with suggestions to apply the fundamental theorem of calculus. The conversation also touches on the orthogonality of different derivatives of H(t) and the relationship between covariance and correlation in the context of ACF. Overall, the thread emphasizes the mathematical techniques necessary for solving ACF problems and understanding their implications in signal processing.
  • #31
EnumaElish said:
My best understanding is this:
You are trying to find the autocorrelation coefficient of a signal. http://en.wikipedia.org/wiki/Autocorrelation#Signal_processing

You need to first determine the Rff(T) function.

Then you'd like to convert it into an AC coefficient as: r(T) = [Rff(T) - Meanf(T)^2]/Varf(T). http://en.wikipedia.org/wiki/Autocovariance (look under "Normalization")

Am I close?

yes, exactly! My points are to determine the mean and variance.
So, as I understand from your comments that if I will find the correlation coefficient then I can determine the mean and variance.
 
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  • #32
No. Typically you need to:
1. Calculate the mean
2. Calculate the variance
3. Calculate Rff
4. Put 1, 2, 3 together to calculate r (the corr. coeff.).

Is this helpful? If not, why not?
 
  • #33
EnumaElish said:
No. Typically you need to:
1. Calculate the mean
2. Calculate the variance
3. Calculate Rff
4. Put 1, 2, 3 together to calculate r (the corr. coeff.).

Is this helpful? If not, why not?

Yes, it’s fine. I agree.
But I think I should start with determining Rff(T) and after that the mean and variance.
Is that’s right?
 
  • #34
Any order would be fine.
 

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