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510 Chapter 9 SAMPLING RATE CONVERSION
ylabel(’Amplitude’,’vertical’,’cap’);
title(’Amplitude Response’,’fontsize’,TF,’vertical’,’baseline’);
xlabel(’Frequency in \pi units’,’vertical’,’middle’);
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’,’vertical’,’cap’);
xlabel(’Frequency in \pi units’,’vertical’,’middle’);
title(’Log-magnitude Response’,’fontsize’,TF,’vertical’,’baseline’);
subplot(2,2,4);
lw = length(w)-1; PB = [0:floor(wp/pi*lw)]; HrPB = Hr(PB+1)-1;
SB = [ceil(ws/pi*lw):lw]; HrSB = Hr(SB+1);
[AX,H1,H2] = plotyy(PB/lw,HrPB,SB/lw,HrSB);
delta1 = round(delta1*1000)/1000; delta2 = round(delta2*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(’Unweighted Ripples’,’fontsize’,TF,’vertical’,’baseline’);
ylabel(’Amplitude’,’vertical’,’cap’)
xlabel(’Frequency in \pi units’,’vertical’,’middle’);
The responses of the designed FIR filter are given in Figure 9.25. This filter
passes the signal spectrum over the passband [0,π/2] without any distortion.
However, since the transition width is not very narrow, it is possible that some
of the signal over the transition band may alias into the band of interest. Also
the 30 db attenuation may allow a small fraction of the signal spectrum from the
stopband into the passband after downsampling. Therefore, we need a better
approach for filter specifications, as discussed further along in this section. □
MATLAB Implementation As discussed, the upfirdn function can
also be used for implementing the user-designed FIR filter in the decimation
operation. When invoked as y = upfirdn(x,h,1,D), the function
filters the signal data in the array x with the impulse response given in
the array h and then downsamples the filtered data by the integer factor
D to produce the output array y, thus implementing the system in
Figure 9.24.
□ EXAMPLE 9.12 Using the filter designed in Example 9.11 decimate sinusoidal signals x 1(n)=
cos(πn/8) and x 2(n)= cos(πn/2) with frequencies within the passband of the
filter. Verify the performance of the FIR filter and the results of the decimation.
Solution
The following MATLAB script provides the details.
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