Digital Signal Processing Reference
In-Depth Information
X
(e
j
w
)
1.0
−
0.5
p
−
0.3
p
0
0.3
p
0.5
p
p
w
(
a
)
X
(e
j
w
)
1.0
0.2
−
0.4
p
−
0.2
p
0
0.2
p
0.4
p
p
w
(
b
)
Figure 5.26
Problem 5.23.
x
2
(n)
where
x
2
(n)
is as shown
in Figure 5.25b. Plot
y
2
(n)
and derive its frequency response (DTFT)
Y
2
(e
jω
)
.
5.20
What is the frequency response of the filter attained by cascading the two
filters described by Figure 5.27a,b?
5.21
Plot the spectrum of the product
y(n)
5.19
Find the convolution sum
y
2
(n)
=
x
2
(n)
∗
=
x
1
(n)x
2
(n)
where
x
1
(n)
=
10 cos
cos
(
0
.
25
πn)
.
5.22
If the signal
y(n)
given in Problem 5.21 is the input to the filter shown
in Figure 5.27b what is the output signal?
5.23
Derive the expressions for the Fourier series coefficients (for
(
0
.
5
πn)
and
x
2
(n)
=
−∞
<
∞
) for the DTFT of an LTI DT system as shown in Figure 5.26a,b.
5.24
Derive the expressions for the Fourier series coefficients for
−∞
n<
<n<
∞
for the frequency response of the LTI-DT system as shown in
Figure 5.27a,b, respectively.
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