Digital Signal Processing Reference
In-Depth Information
5
30
4
20
3
2
10
1
0
0
−4
−2
0
2
4
6
8
0
2
4
6
8
(a) Sequences Poised for Correlation
(b) Correlation Sequence
5
4
20
3
2
10
1
0
0
−4
−2
0
2
4
6
8
0
2
4
6
8
(c) Sequences Poised for Convolution
(d) Convolution Sequence
Figure 4.15:
(a) Signal sequence, samples 4-7, poised to be correlated with Impulse Response, samples
0-3; (b) Correlation sequence of sequences in (a); (c) Signal, (samples -4 to -1), properly flipped to be
convolved with Impulse Response, samples 0-3; (d) Convolution sequence of sequences in (c). The arrows
over the signal sequences show the direction samples are shifted for the computation.
Note that while the order of convolution makes no difference to the convolution sequence, i.e.,
∞
∞
y
[
k
]=
b
[
n
]
x
[
k
−
n
]=
x
[
n
]
b
[
k
−
n
]
(4.16)
n
=−∞
n
=−∞
the order of correlation does make a difference. In general,
∞
c
1
[
k
]=
b
[
n
]
x
[
n
+
k
]
n
=−∞
is a time-reversed version of
∞
c
2
[
]=
[
]
[
+
]
k
x
n
b
n
k
n
=−∞
In what case would
c
1
[
k
]
equal
c
2
[
k
]
?
