Databases Reference
In-Depth Information
h
x
k
k
1
2
M−1
k
1
2
3
4
N−1
k
F I GU R E 15 . 12
An example filter of length
M
and an input sequence of length
N
.
(a)
(b)
x
m
x
m
1234
N−1
1234 N−1
m
m
h
k−m
h
k−m
m
m
k−M+1
k−2 k−1 k
k−M+1
k−2 k−1 k
x
m
x
m
(d)
(c)
m
N− 1
m
1234
1 2 3
4
N−1
h
k−m
h
k−m
m
m
k−M+1
k−2 k−1 k
k−M+1 k−2 k−1 k
F I GU R E 15 . 13
A pictorial representation of the components in the convolution
sum for different values of k: (a) for k
<
0; (b) for 0
k M
+
1;
(c) for M
+
1
<
k N
−
1; and (d) for N
−
1
<
k
N
M
2.
+
−
is the length of the filter. We have increased the number of coefficients that need to be encoded.
Clearly this is not a desirable feature for a data compression system. The problem becomes
worse as we go through several levels of filtering operations, each resulting in an increase in
the number of coefficients.
