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502 Chapter 9 SAMPLING RATE CONVERSION
Hf1 = figure(’units’,’inches’,’position’,[1,1,6,4],...
’paperunits’,’inches’,’paperposition’,[0,0,6,4]);
subplot(2,2,1); Hs1 = stem(n,h,’filled’); set(Hs1,’markersize’,2);
axis([-1,length(n),-0.5,1.5]); ylabel(’Amplitude’); xlabel(’n’,’vertical’,’bottom’);
Title(’Impulse Response’,’fontsize’,TF);
subplot(2,2,3); plot(ww/pi,Hr,’m’,’linewidth’,1.0); axis([0,1,-1,6]);
set(gca,’xtick’,[0,wp/pi,ws/pi,1],’ytick’,[0,I]); grid; ylabel(’Amplitude’);
title(’Amplitude Response’,’fontsize’,TF); xlabel(’Frequency in \pi units’);
subplot(2,2,2); plot(w/pi,Hdb,’m’,’linewidth’,1.0); axis([0,1,-50,10]);
set(gca,’xtick’,[0,wp/pi,ws/pi,1],’ytick’,[-50,round(min_attn),0]); grid
ylabel(’Decibels’);
title(’Log-magnitude Response’,’fontsize’,TF);
subplot(2,2,4);
lw = length(w)-1; PB = [0:floor(wp/pi*lw)]; HrPB = Hr(PB+1)-I;
SB = [ceil(ws/pi*lw):lw]; HrSB = Hr(SB+1);
[AX,H1,H2] = plotyy(PB/lw,HrPB,SB/lw,HrSB);
delta1 = round(delta1*I*100)/100; delta2 = round(delta2*I*100)/100;
set(AX(1),’xtick’,[0,wp/pi,ws/pi,1],’ytick’,[-delta1,0,delta1],’Ycolor’,’g’);
set(AX(2),’xtick’,[0,wp/pi,ws/pi,1],’ytick’,[-delta2,0,delta2],’Ycolor’,’r’);
set(H1,’color’,’g’,’linewidth’,1); set(H2,’color’,’r’,’linewidth’,1);
title(’Scaled Ripples’,’fontsize’,TF); xlabel(’Frequency in \pi units’);
The responses of the designed FIR filter are given in Figure 9.20. Even
though this filter passes the original signal, it is possible that some of the neighboring
spectral energy may also leak through if the signal is of full bandwidth
of π radians. Hence we need better design specifications, which are discussed
further along in this section.
□
MATLAB Implementation To use the FIR filter for interpolation
purposes (such as the one designed in Example 9.8), MATLAB has provided
a general function, upfirdn, that can be used for interpolation
and decimation as well as for resampling purposes. Unlike other functions
discussed in this chapter, upfirdn incorporates the user-defined FIR filter
(which need not be linear phase) in the operation. When invoked as
y = upfirdn(x,h,I), the function upsamples the input data in the array
x by a factor of the integer I and then filters the upsampled signal data
with the impulse response sequence given in the array h to produce the
output array y, thus implementing the system in Figure 9.18.
□ EXAMPLE 9.9 Let x(n) =cos(0.5πn). Increase the input sampling rate by a factor of I =5,
using the filter designed in Example 9.8.
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