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Problems 299
4. Explain why the magnitude |Ĥ1(ejω )| is “different” from the magnitude |Ĥ2(ejω )|.
P6.34 An IIR lowpass filter designed to meet the specifications of 0.5 dB ripple in the passband,
60 dB ripple in the stopband, a passband edge frequency ω p =0.25π, and a stopband edge
frequency ω s =0.3π is obtained using the following MATLAB script:
wp = 0.25*pi; ws = 0.3*pi; Rp = 0.5; As = 60;
[N, Wn] = ellipord(wp/pi, ws/pi, Rp, As);
[b,a] = ellip(N,Rp,As,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, plot the log-magnitude and phase responses of the designed
filter. Use two rows and one column of subplots.
2. Quantize the direct-form coefficients to 4 decimals (by rounding). Now plot the
log-magnitude and phase responses of the resulting filter. Use 2 rows and 1 column of
subplots.
3. Quantize the direct form coefficients to 3 decimals (by rounding). Now plot the
log-magnitude and phase responses of the resulting filter. Use 2 rows and 1 column of
subplots.
4. Comment on the plots in parts 1, 2, and 3.
P6.35 Consider the digital lowpass filter used in Problem P6.34.
1. Using infinite precision and cascade-form realization, plot the log-magnitude and phase
responses of the designed filter. Use two rows and one column of subplots.
2. Quantize the cascade-form coefficients to 4 decimals (by rounding). Now plot the
log-magnitude and phase responses of the resulting filter. Use two rows and one column
of subplots.
3. Quantize the cascade-form coefficients to 3 decimals (by rounding). Now plot the
log-magnitude and phase responses of the resulting filter. Use two rows and one column
of subplots.
4. Comment on the plots in the above three parts and compare them with the similar plots
in Problem P6.34.
P6.36 A length-32 linear-phase FIR bandpass filter that satisfies the requirements of 60 dB
stopband attenuation, lower stopband edge frequency ω s1 =0.2π, and upper stopband edge
frequency ω s2 =0.8π is obtained using the following MATLAB script.
ws1 = 0.2*pi; ws2 = 0.8*pi; As = 60;
M = 32; Df = 0.2115;
fp1 = ws1/pi+Df; fp2 = ws2/pi-Df;
h = firpm(M-1,[0,ws1/pi,fp1,fp2,ws2/pi,1],[0,0,1,1,0,0]);
The filter impulse response h(n) isinthe array h and can be considered to have infinite
precision.
1. Using infinite precision, plot the log-magnitude and amplitude responses of the designed
filter. Use 2 rows and 1 column of subplots.
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