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302 Chapter 6 IMPLEMENTATION OF DISCRETE-TIME FILTERS
can be obtained using the following MATLAB script:
wp = 0.6; ws = 0.4; Rp = 0.5; As = 60;
[N,wn] = ellipord(wp, ws, Rp, As);
[b,a] = ellip(N,Rp,As,wn,’high’);
The filter coefficients b k and a k are in the arrays b and a, respectively, and can be
considered to have infinite precision.
1. Using infinite precision, provide the magnitude response plot and the pole-zero plot of
the designed filter.
2. Assuming direct-form structure and a 10-bit representation for filter coefficients, provide
the magnitude response plot and the pole-zero plot of the designed filter. Use the Qcoeff
function.
3. Assuming parallel-form structure and a 10-bit representation for filter coefficients,
provide the magnitude response plot and the pole-zero plot of the designed filter. Use
the Qcoeff function.
P6.41 A bandstop linear-phase FIR filter that satisfies the specifications:
lower stopband edge: 0.4π
upper stopband edge: 0.6π
lower passband edge: 0.3π
upper passband edge: 0.7π
can be obtained using the following MATLAB script:
A s =50dB
R p =0.2 dB
wp1 = 0.3; ws1 = 0.4; ws2 = 0.6; wp2 = 0.7; Rp = 0.2; As = 50;
[delta1,delta2] = db2delta(Rp,As);
b = firpm(44,[0,wp1,ws1,ws2,wp2,1],[1,1,0,0,1,1],...
[delta2/delta1,1,delta2/delta1]);
The filter impulse response h(n) isinthe array b and can be considered to have infinite
precision.
P6.42 A bandpass linear-phase FIR filter that satisfies the specifications:
0 ≤ |H(e jω )| ≤ 0.01, 0 ≤ ω ≤ 0.25π
0.95 ≤ |H(e jω )| ≤ 1.05, 0.35π ≤ ω ≤ 0.65π
0 ≤ |H(e jω )| ≤ 0.01, 0.75π ≤ ω ≤ π
can be obtained using the following MATLAB script:
ws1 = 0.25; wp1 = 0.35; wp2 = 0.65; ws2 = 0.75;
delta1 = 0.05; delta2 = 0.01;
b = firpm(40,[0,ws1,wp1,wp2,ws2,1],[0,0,1,1,0,0],...
[1,delta2/delta1,1]);
The filter impulse response h(n) isinthe array b and can be considered to have infinite
precision.
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