[Help-gsl] Cross correlation using FFT

[Saurav Pathak]

Hi All,

I am trying to calculate the cross correlation of two time series
using FFT.  The effective part of the code is:


        z = gsl_fft_real_radix2_transform(&x[0], 1, x.size());
        z = gsl_fft_real_radix2_transform(&y[0], 1, y.size());

        vector<double> c(n);
        c[0] = x[0]*y[0];
        c[n/2] = x[n/2]*y[n/2];
        for (int i=1; i<n/2; ++i) {
            c[i] = x[i]*y[i] + x[n-i]*y[n-i];
            c[n-i] = x[n-i]*y[i] - x[i]*y[n-i];
        }

        z = gsl_fft_halfcomplex_radix2_inverse(&c[0], 1, c.size());
        

All is well, and I seem to be getting there except that the
correlations are not normalized properly.  For example, c[0] =
111.899 when x and y are identical series of random numbers
with a stadard normal distribution.  It should be 1.0.  
I have checked the result against ccf in R.

What am I missing here?  Thank you for your tips and comments
in advance.  
--
saurav