UploadFile_6417

Round-off Effects in IIR Digital Filters 555
□ EXAMPLE 10.6 In this example simulate the results for the system given in Example 10.5 using
the Qfix function with B =3bits. In addition, also examine limit-cycle behavior
for the truncation operation in the multiplier and for the case when the system
is a lowpass filter with coefficient α =0.5.
Solution
The MATLAB scripts:
% Highpass filter, rounding operation in multiplier
a = -0.5; yn1 = 0; m = 0:10; y = [yn1, zeros(1,length(m))];
x = 0.875*impseq(m(1),m(1)-1,m(end));
for n = m+2
yn1 = y(n-1);
y(n) = QFix(a*yn1,3,’round’,’satur’) + x(n);
end
subplot(’position’,[0.08,0.2,0.24,0.6]);
plot([-1,20],[0,0],’w’); axis([-1,10,-1,1]); hold on;
Hs_1 = stem([-1,m],y,’filled’);set(Hs_1,’markersize’,3,’color’,[0,1,0]);
set(gca,’ytick’,[-1:0.25:1],’fontsize’,6); ylabel(’Amplitude’,’fontsize’,8);
title(’\alpha = -0.5, Rounding’,’fontsize’,10);
xlabel(’Sample index n’,’fontsize’,8);
% Lowpass filter, rounding operation in multiplier
a = 0.5; yn1 = 0; m = 0:10; y = [yn1, zeros(1,length(m))];
x = 0.875*impseq(m(1),m(1)-1,m(end));
for n = m+2
yn1 = y(n-1);
y(n) = QFix(a*yn1,3,’round’,’satur’) + x(n);
end
subplot(’position’,[0.42,0.2,0.24,0.6]);
plot([-1,20],[0,0],’w’); axis([-1,10,-1,1]); hold on;
Hs_1 = stem([-1,m],y,’filled’);set(Hs_1,’markersize’,3,’color’,[0,1,0]);
set(gca,’ytick’,[-1:0.25:1],’fontsize’,6); ylabel(’Amplitude’,’fontsize’,8);
title(’\alpha = 0.5, Rounding’,’fontsize’,10);
xlabel(’Sample index n’,’fontsize’,8);
% Highpass filter, Truncation operation in multiplier
a = -0.5; yn1 = 0; m = 0:10; y = [yn1, zeros(1,length(m))];
x = 0.875*impseq(m(1),m(1)-1,m(end));
for n = m+2
yn1 = y(n-1);
y(n) = QFix(a*yn1,3,’trunc’,’satur’) + x(n);
end
subplot(’position’,[0.76,0.2,0.24,0.6]);
plot([-1,20],[0,0],’w’); axis([-1,10,-1,1]); hold on;
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.