The discussion revolves around the autocorrelation function, its properties, and methods for calculating it, particularly in the context of specific equations involving derivatives. Participants seek resources for study and engage in mathematical reasoning related to the definition and computation of the autocorrelation function.
Participants generally agree on the definition of the autocorrelation function and the methods to compute it, but there are multiple competing views regarding the application of these methods to specific cases, particularly concerning the derivatives of functions and the validity of certain integrals. The discussion remains unresolved on some aspects, particularly regarding the general case for arbitrary n.
Limitations include unresolved mathematical steps, particularly in deriving integrals for higher derivatives and the specific conditions under which the autocorrelation function is defined. There is also ambiguity regarding the application of the autocorrelation function to combinations of different derivatives.
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?
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?