How to compute the Fourier Transformation of a triple correlation involving three variables
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Hi all,
I have three time series measured all simultaneously at a sampling frequency of 10 Hz for 30 minutes. So each of the time series contains 18000 points. Let me call these three time series as A,B and C.
Now I want to compute the triple correlation of these three in the frequency domain via taking the Fourier transform.
So basically I am interested at the Fourier transformation of mean(A'.*B'.*C') where A'=A-mean(A), B'=B-mean(B) and C'=C-mean(C)
Now lets call the individual Fourier transforms of A,B and C as F(A),F(B) and F(C).
If I had required co-variance between A and B, I could have easily computed that by taking Real(F(A).*(conj(F(B))) , where conj is the complex conjugate of F(B).
By extending the same logic, can I also express the triple correlation as defined above like this in the Fourier space
Real(F(A).*(conj(F(B)).*conj(F(C))) ?????
I would be very grateful if the experts here, can help me out with this and provide the solution.
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