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Problems 383
P7.34 Design a minimum order linear-phase FIR filter, using the Parks-McClellan algorithm, to
satisfy the requirements given in Figure P7.1.
1. Provide a plot of the amplitude response with grid-lines and axis labeling as shown in
Figure P7.1.
2. Generate the following signals
x 1(n) =cos(0.25πn), x 2(n) =cos(0.5πn), x 3(n) =cos(0.75πn); 0 ≤ n ≤ 100.
Process these signals through this filter to obtain the corresponding output signals
y 1(n), y 2(n), and y 3(n). Provide stem plots of all input and output signals in one figure.
P7.35 Design a minimum-order linear-phase FIR filter, using the Parks-McClellan algorithm, to
satisfy the requirements given in Figure P7.3. Provide a plot of the amplitude response with
grid-lines and axis labeling as shown in Figure P7.3.
P7.36 The specifications on the amplitude response of an FIR filter are given in Figure P7.4.
1. Using a window design approach and a fixed window function, design a minimum-length
linear-phase FIR filter to satisfy the given requirements. Provide a plot of the amplitude
response with grid-lines as shown in Figure P7.4.
2. Using a window design approach and the Kaiser window function, design a
minimum-length linear-phase FIR filter to satisfy the given requirements. Provide a plot
of the amplitude response with grid-lines as shown in Figure P7.4.
3. Using a frequency-sampling design approach and with no more than two samples in the
transition bands, design a minimum-length linear-phase FIR filter to satisfy the given
requirements. Provide a plot of the amplitude response with grid-lines as shown in
Figure P7.4.
4. Using the Parks-McClellan design approach, design a minimum-length linear-phase FIR
filter to satisfy the given requirements. Provide a plot of the amplitude response with
grid-lines as shown in Figure P7.4.
Hr(ω) (Not to Scale)
3.3
2.7
2.2
1.8
1.1
0.9
0.05
−0.05
0 0.2 0.25 0.45 0.55 0.7 0.75 1
ω
π
FIGURE P7.3 Filter Specifications for Problem P7.35
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