From kozick@charcoal.eg.bucknell.edu Thu Mar 27 21:19 EST 1997
Date: Thu, 27 Mar 1997 21:19:11 -0500
From: Kozick Rich  <kozick@charcoal.eg.bucknell.edu>
To: ligong@bucknell.edu, suqi@bucknell.edu, yuesun@bucknell.edu,
        fhaosng@bucknell.edu, piatt@bucknell.edu, tassone@bucknell.edu,
        grace@bucknell.edu, nclark@bucknell.edu, cdavies@bucknell.edu,
        morelli@bucknell.edu, dmorelli@sunlink.net, daviesfive@aol.com,
        kozick@bucknell.edu
Subject: Problem 4.16

Hi,

Here is a hint for Problem 4.16 for computing correlations with
the FFT:

If x1 and x2 are your two time signals, the you should be able to see
that the number of points in the cross-correlation is

N = length(x1) + length(x2) - 1;

When you do the cross-correlation, just use "xcorr" with no extra 
argument, i.e. do not say 'unbiased'.

Then, when you use the FFT, use N points, and:

1.  Omit the (1/N) in front of the ifft, since we did not use the
(1/N) on the direct correlation with xcorr.

2.  Use the "fftshift" command to process the ifft output before
displaying the results.  This causes the correlation to be displayed
with positive and negative values for the "lag" parameter.

If you do this, then the direct and FFT methods should produce
identical results.  Try to understand what is going on with each step
listed above.  Please ask questions in class if you are unclear!

Thanks and have fun.


Rich