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352 Chapter 7 FIR FILTER DESIGN
Lowpass: M=60,T1=0.59, T2=0.109
Impulse Response
1
0.2
Hr(k)
0.59
h(n)
0.1
0.109
0
0 0.2 0.3 1
frequency in π units
Amplitude Response
1
0
−0.1
0 20 40 60
n
0
Magnitude Response
Hr(w)
0.59
Decibels
63
0.109
0
0 0.2 0.3 1
frequency in π units
0 0.2 0.3 1
frequency in π units
FIGURE 7.29 Lowpass filter design plots in Example 7.16
The time- and the frequency-domain plots are shown in Figure 7.29. The minimum
stopband attenuation is now at 63 dB, which is acceptable. □
□ EXAMPLE 7.17 Design the bandpass filter of Example 7.10 using the frequency sampling technique.
The design specifications are these:
lower stopband edge: ω 1s =0.2π,
A s =60dB
lower passband edge: ω 1p =0.35π, R p =1dB
upper passband edge: ω 2p =0.65π
upper stopband edge: ω 2s =0.8π
R p =1dB
A s =60dB
Solution
Let us choose M =40sothat we have two samples in the transition band.
Let the frequency samples in the lower transition band be T 1 and T 2. Then the
samples of the amplitude response are
H r (ω) =[0,...,0 ,T
} {{ } 1,T 2, 1,...,1 ,T
} {{ } 2,T 1, 0,...,0 ,T
} {{ } 1,T 2, 1,...,1 ,T
} {{ } 2,T 1, 0,...,0 ]
} {{ }
5
7
9
7
4
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