Digital Signal Processing Reference
In-Depth Information
h
(
k
)
x
(
k
)
k
→
k
→
F
O
L
D
I
N
G
h
(
k
−
)
k
→
S
H
I
F
T
I
N
G
y
(0)
=1×
(−1)
+
(−1)
×
1+
0
=
0
h
(1−
k
)
y
(1)
=
0
+1×(−1)
+
(−1)×1
=
0
k
→
h
(2
−
k
)
y
(2)
=
0
+
(−1)
×
(−1)
+
1
×
1
=
2
k
→
Fig. B.2
Convolution operation between two sequences
B.1.1 Basic Properties of Convolution
B.1.1.1 Commutative Law
)
∗
x
2
(
)
∗
x
1
(
x
1
(
t
t
)
=
x
2
(
t
t
)
(B.5)
Proof
From the basic definition of convolution in discrete domain referring
Eq.(
B.4
), we can also express convolution in continuous domain as
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