Digital Signal Processing Reference
In-Depth Information
representation the input vector
s
(
n
) is filtered by the MIMO system
R
(
z
)to
produce the output vector
x
(
n
)
,
whose components are interleaved (unblocked)
to produce the scalar output
x
(
n
)
.
3.7.3 Receiving filter banks or analysis filter banks
Now consider the system shown in Fig. 3.23(a). In this system, there are
M
decimation filters with a common input
x
(
n
)
.
The decimation ratio
P
is in gen-
eral different from
M
(usually
P>M
in communication receivers and
P
M
in data compression analysis banks). Such a system is called an
analysis filter
bank
because it splits a signal
x
(
n
)into
M
components. In digital communica-
tion systems, such a filter bank is used as a
receiving filter bank
or receiver filter
bank, and this will be described in greater detail in Sec. 3.8. We now show how
this filter bank can be expressed in polyphase form.
≤
x
(
n
)
x
(
n
)
H
(
z
)
0
P
P
z
H
(
z
)
1
P
P
z
P
E
(
z
)
(a)
(b)
z
P
H
(
z
)
M
P
−
1
x
(
n
)
x
(
n
)
0
P
z
x
(
n
)
1
P
z
E
(
z
)
(c)
x
(
n
)
P
−1
z
P
Type-1 polyphase
components of
x
(
n
)
Figure 3.23
. (a) A receiving filter bank, also known as analysis filter bank, (b) Type-2
polyphase version, and (c) simplification with the use of the first noble identity.
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