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284 Chapter 6 IMPLEMENTATION OF DISCRETE-TIME FILTERS
% 8-bit word-length quantization
N2 = 7; [bahat,L2,B2] = QCoeff([b;a],N2);
TITLE2 = sprintf(’%i-bits (1+%i+%i)’,N2+1,L2,B2);
bhat2 = bahat(1,:); ahat2 = bahat(2,:);
Hhat2 = freqz(bhat2,ahat2,w); magHhat2 = abs(Hhat2);
magHhat2db = 20*log10(magHhat2); zhat2 = roots(bhat2);
% Plots
Hf_1 = figure(’paperunits’,’inches’,’paperposition’,[0,0,6,5]);
% Comparison of Log-Magnitude Responses: 16 bits
subplot(2,2,1); plot(w/pi,magHdb,’g’,’linewidth’,1.5); axis([0,1,-80,5]);
hold on; plot(w/pi,magHhat1db,’r’,’linewidth’,1); hold off;
xlabel(’Digital Frequency in \pi units’,’fontsize’,10);
ylabel(’Decibels’,’fontsize’,10);
title([’Log-Mag plot: ’,TITLE1],’fontsize’,10,’fontweight’,’bold’);
% Comparison of Pole-Zero Plots: 16 bits
subplot(2,2,3); [HZ,HP,Hl] = zplane([b],[a]); axis([-2,2,-2,2]); hold on;
set(HZ,’color’,’g’,’linewidth’,1,’markersize’,4);
set(HP,’color’,’g’,’linewidth’,1,’markersize’,4);
plot(real(zhat1),imag(zhat1),’r+’,’linewidth’,1);
title([’PZ Plot: ’,TITLE1],’fontsize’,10,’fontweight’,’bold’);
hold off;
% Comparison of Log-Magnitude Responses: 8 bits
subplot(2,2,2); plot(w/pi,magHdb,’g’,’linewidth’,1.5); axis([0,1,-80,5]);
hold on; plot(w/pi,magHhat2db,’r’,’linewidth’,1); hold off;
xlabel(’Digital Frequency in \pi units’,’fontsize’,10);
ylabel(’Decibels’,’fontsize’,10);
title([’Log-Mag plot: ’,TITLE2],’fontsize’,10,’fontweight’,’bold’);
% Comparison of Pole-Zero Plots: 8 bits
subplot(2,2,4); [HZ,HP,Hl] = zplane([b],[a]); axis([-2,2,-2,2]); hold on;
set(HZ,’color’,’g’,’linewidth’,1,’markersize’,4);
set(HP,’color’,’g’,’linewidth’,1,’markersize’,4);
plot(real(zhat2),imag(zhat2),’r+’,’linewidth’,1);
title([’PZ Plot: ’,TITLE2],’fontsize’,10,’fontweight’,’bold’);
hold off;
The log-magnitude responses and zero-pole locations of the resulting filters are
plotted in Figure 6.34 along with those of the original filter. When 16 bits
are used, the resulting filter is virtually indistinguishable from the original one.
However, when 8 bits are used, the filter behavior is severely distorted. The filter
is still stable, but it does not satisfy the design specifications.
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