
86-6 Signal Processing
where x
n
and y
n
are zero-mean, discrete-time signals dened in the interval n = 0, 1, 2, …, N − 1. For each
value of p, the cross correlation is computed by shiing y
n
by p∆t and calculating the average product in
Equation 86.10. If x
n
and y
n
are unrelated, the sum of positive and negative products will tend to zero.
Conversely, y
n
tends to follow x
n
, but with a time delay D, r
xy
(p) will show a peak at p = D/∆t. is prop-
erty
of the CCF is illustrated in Figure 86.3. As noted by Bergland [8], cross correlation can be viewed as
“one signal searching to nd itself in another signal.”
For
y
n
= x
n
, r
xx
(p) becomes the autocor ...