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Problems 301
P6.38 An IIR bandstop digital filter that satisfies the requirements:
0.95 ≤|H(e jω )|≤1.05, 0 ≤|ω| ≤0.25π
0 ≤|H(e jω )|≤0.01, 0.35π ≤|ω| ≤0.65π
0.95 ≤|H(e jω )|≤1.05, 0.75π ≤|ω| ≤π
can be obtained using the following MATLAB script:
wp = [0.25,0.75]; ws = [0.35,0.65]; delta1 = 0.05; delta2 = 0.01;
[Rp,As] = delta2db(delta1,delta2);
[N, wn] = cheb2ord(wp, ws, Rp, As);
[b,a] = cheby2(N,As,wn,’stop’);
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 log-magnitude response plot and the pole-zero plot
of the designed filter.
2. Assuming direct-form structure and a 12-bit representation for filter coefficients, provide
the log-magnitude response plot and the pole-zero plot of the designed filter. Use the
Qcoeff function.
3. Assuming cascade-form structure and a 12-bit representation for filter coefficients,
provide the log-magnitude response plot and the pole-zero plot of the designed filter. Use
the Qcoeff function.
P6.39 An IIR lowpass digital filter that satisfies the specifications:
passband edge: 0.4π, R p =0.5 dB
stopband edge: 0.6π, As =50dB
can be obtained using the following MATLAB script:
wp = 0.4; ws = 0.6; Rp = 0.5; As = 50;
[N, wn] = buttord(wp, ws, Rp, As);
[b,a] = butter(N,wn);
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 cascade-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.
P6.40 An IIR highpass digital filter that satisfies the specifications:
stopband edge: 0.4π, A s =60dB
passband edge: 0.6π, R p =0.5 dB
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