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2
H
10
(
z
)
z
-1
2
H
11
(
z
)
2
H
20
(
z
)
z
-1
2
H
21
(
z
)
F I GU R E 14 . 24
Polyphase representation of the analysis portion of a two-band
subband coder.
2
G
1
(
z
)
2
G
2
(
z
)
F I GU R E 14 . 25
The synthesis portion of a two-band subband coder.
Replacing
H
1
(
z
)
with its polyphase representation, we get
2
X
z
2
H
10
(
2
X
z
2
H
10
(
1
1
1
2
H
11
(
1
2
H
11
(
z
−
z
−
Y
1
(
z
)
=
z
)
+
z
)
+
−
z
)
−
z
)
(100)
1
z
2
1
2
z
−
z
2
(101)
2
X
z
2
2
X
2
X
z
2
2
X
1
1
2
z
−
1
1
=
H
10
(
)
+
−
+
H
11
(
)
−
−
z
z
Note that the first expression in square brackets is the output of a downsampler whose input is
X
, while the quantity in the second set of square brackets is the output of a downsampler
whose input is
z
−
1
X
(
z
)
. Therefore, we could implement this system as shown in Figure
14.24
.
Now let us consider the synthesis portion of the two-band system shown in Figure
14.25
.
As in the case of the analysis portion, we can write the transfer functions in terms of their
(
z
)
