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Optimal Equiripple Design Technique 371
>> Asd = -max(db(1:1:wsi))
Asd = 49.5918
>> N = N+2;
>> h = firpm(N,f,m,weights);
>> [db,mag,pha,grd,w] = freqz_m(h,[1]);
>> Asd = -max(db(1:1:wsi))
>> Asd = 50.2253
>> M = N+1
M = 29
Note also that we increased the value of N by two tomaintain its even value.
The optimum M was found to be 29. The time- and the frequency-domain plots
of the designed filter are shown in Figure 7.37.
□
□ EXAMPLE 7.26 In this example we will design a “staircase” filter, which has 3 bands with
different ideal responses and different tolerances in each band. The design specifications
are
Band-1: 0 ≤ ω ≤ 0.3π, Ideal gain = 1, Tolerance δ 1 =0.01
Band-2: 0.4π ≤ ω ≤ 0.7π, Ideal gain = 0.5, Tolerance δ 2 =0.005
Band-3: 0.8π ≤ ω ≤ π, Ideal gain = 0, Tolerance δ 3 =0.001
0.4
Actual Impulse Response
0
Magnitude Response in dB
0.2
h(n)
0
−0.2
Decibels
50
−0.4
0 28
n
Amplitude Response
1
0 0.6 0.75 1
frequency in π units
Error Response
0.0288
Hr(w)
Hr(w)
0.0033
−0.0033 0
0
0 0.6 0.75 1
frequency in π units
−0.0288
0 0.6 0.75 1
frequency in π units
FIGURE 7.37 Plots for equiripple highpass FIR filter in Example 7.25
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