Re: Scaling factor in inverse fourier transform

On Apr 10, 5:06 am, "Titi Anggono" <titi.angg...@xxxxxxxxx> wrote:
Hi all,

I tried to calculate the autocorrelation from FFT using C. As far as I
know the input for the inverse FT is the power spectrum density of the
data X(t)
PSD = (Xreal(f)^2 + Ximag(f)^2) / N, N is the length of the real
number
After calculating the inverse FT, I scaled the result with 1/N but the
result is not 1 (less than 1).

I wonder if I made mistake with the scaling factor or something else.
Looking forward with your help.

Titi

There's nothing wrong with having an autocorrelation sequence with
values greater than one. It is defined by:

r[k] = E(x[n]*conj(x[n-k]))

for a wide-sense stationary signal x[n]. This can obviously be greater
than one, no issue there. As far as scaling factors go, as long as
between your FFT and IFFT you have a total factor of 1/N, you're fine.
You could have no scaling factor on the FFT and a 1/N on the IFFT, or
you could put 1/sqrt(N) on both. They will give you different
intermediate results, but you'll get the same values if you do an FFT-
IFFT operation on a dataset.

Jason

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