Databases Reference
In-Depth Information
Ideal
low-pass
filter
Ideal
low-pass
filter
x
n
y
1,
n
2
Encoder 1
Decoder 1
2
z
-1
z
-1
Ideal
high-pass
filter
Ideal
high-pass
filter
y
2,
n
x
n
Encoder 2
Decoder 2
2
2
F I GU R E 14 . 11
Decomposition into two bands using ideal filters.
X
(
e
j
ω
)
π/2
π
ω
F I GU R E 14 . 12
Spectrum of the source output.
Y
1
(
e
j
ω
)
Y
2
(
e
j
ω
)
π/2
ω
π/2
πω
F I GU R E 14 . 13
Spectrum of the outputs of the ideal filters.
the frequency profile shown in Figure
14.12
. For this sequence the output of the ideal filters
will have the shape shown in Figure
14.13
.
Let's represent the downsampled sequence as
{
w
i
,
n
}
. The Z-transform
W
1
(
z
)
of the down-
sampled sequence
w
1
,
n
is
w
1
,
n
z
−
n
W
1
(
z
)
=
(24)
The downsampling operation means that
w
1
,
n
=
(25)
y
1
,
2
n
