Digital Signal Processing Reference
In-Depth Information
1
0
−1
0
50
100
150
(a) Sample Number
1
0
−1
0
50
100
150
(b) Sample Number
10
0
−10
0
50
100
150
(c) Sample Number
Figure 4.12:
(a) First sequence, one period of a sinusoid over 32 samples; (b) Second sequence, four
cycles of a sinusoid having a 32-sample period; (c) Correlation sequence, consisting (in the steady state
portion) of a sinusoid of period 32 samples.
[
1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,1,1,1,-1,-1,-1,-1]
The high frequency information is at the Nyquist limit, and consists of the pattern [1,-1,1,-1].
Correlators such as [1,1] or [-1,-1] (i.e., DC) will eliminate the Nyquist limit frequency. Longer versions
also work ([ones(1,4)]) or its negative.
4.6
CORRELATION VIA CONVOLUTION
Previously we've noted that the output of an LTI system can be computed by use of the convolution
formula
∞
y
[
k
]=
x
[
n
]
h
[
k
−
n
]
n
=−∞
