Digital Signal Processing Reference
In-Depth Information
X(e
j
w
)
1.0
X(e
j
w
)
1.0
0.05
−
0.5
p
−
0.4
p
0.4
p
0.5
p
p
200 300
500
f
w
(
a
)
(
b
)
Figure 5.29
Problem 5.27.
5.27
Find the Fourier series coefficients for the frequency response of the low-
pass digital filter as shown in Figure 5.29a, in which the Nyquist frequency
is 500 Hz.
5.28
Find the Fourier series coefficients for
5
<n<
5 for the frequency
response of the lowpass filter shown in Figure 5.29b.
5.29
Find the coefficients of the unit impulse response for 0
−
64, using
the MATLAB function
fir2
after sampling the frequency response of
the lowpass filter shown in Figure 5.29b. Compare the result with that
obtained in Problem 5.28.
≤
n
≤
MATLAB Problems
5.30
Design a lowpass FIR filter of length 21, with
ω
p
=
0
.
2
π
and
ω
s
=
0
.
5
π
,
using the spline function of order
p
=
2
,
4 for the transition band. Plot
the magnitude response of these filters on the same plot. Compare their
characteristics.
5.31
Design a lowpass FIR filter of length 41 with
ω
p
=
0
.
3
π
and
ω
s
=
0
.
5
π
,
=
2
,
4 for the transition band. Show
the magnitude responses of these filters on the same plot. Compare their
characteristics.
5.32
Design a lowpass FIR filter of length 41 with
ω
p
using the spline function of order
p
=
0
.
4
π
and
ω
s
=
0
.
5
π
,
=
2
,
4 for the transition band. Give
the magnitude responses of these filters on the same plot. Compare their
characteristics.
5.33
Design a lowpass FIR filter with a passband cutoff frequency
ω
c
using the spline function of order
p
=
0
.
25
π
and a magnitude of 2 dB, a stopband frequency
ω
s
=
0
.
4
π
,
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