Databases Reference
In-Depth Information
(a)
We begin with the low-pass filter. Assume that the impulse response of the filter is
given by
k
=
3
{
h
1
,
k
}
k
=
0
. Further assume that
h
1
,
k
=
h
1
,
j
∀
j
,
k
{
h
i
,
j
}
that satisfies Equation (
91
).
(b)
Plot the magnitude of the transfer function
H
1
(
Find a set of values for
)
.
(c)
Using Equation (
23
), find the high-pass filter coefficients
z
{
h
2
,
k
}
.
(d)
Find the magnitude of the transfer function
H
2
(
z
)
.
3.
Consider the input sequence
(
−
n
1
)
n
=
0
,
1
,
2
,...
x
n
=
0 otherwise
(a)
Find the output sequence
y
n
if the filter impulse response is
1
√
2
n
=
0
,
1
h
n
=
0
otherwise
w
n
if the impulse response of the filter is
(b)
Find the output sequence
⎧
⎨
1
√
2
n
=
0
1
√
2
h
n
=
−
n
=
1
⎩
0
otherwise
(c)
Looking at the sequences
y
n
and
w
n
, what can you say about the sequence
x
n
?
4.
Consider the input sequence
1
n
=
0
,
1
,
2
,...
x
n
=
0 otherwise
(a)
Find the output sequence
y
n
if the filter impulse response is
1
√
2
n
=
0
,
1
h
n
=
0
otherwise
(b)
Find the output sequence
w
n
if the impulse response of the filter is
⎧
⎨
1
√
2
n
=
0
1
√
2
h
n
=
−
n
=
1
⎩
0
otherwise
(c)
Looking at the sequences
y
n
and
w
n
, what can you say about the sequence
x
n
?
