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FIR Filter Designs for Sampling Rate Conversion 515
% Filter Design
[delta1,delta2] = db2delta(Rp,As);
[N,F,A,weights] = firpmord([wp,ws]/pi,[1,0],[delta1,delta2],2); N = ceil(N/2)*2;
h = firpm(N,F,A,weights); delay = N/2; % Delay imparted by the filter
Hf1 = figure(’units’,’inches’,’position’,[1,1,6,4],...
’paperunits’,’inches’,’paperposition’,[0,0,6,4]);
% Input signal x(n) = cos(2*pi*n/16)
n = [0:256]; x = cos(pi*n/8);
n1 = n(1:33); x1 = x(33:65); % for plotting purposes
subplot(2,2,1); Hs1 = stem(n1,x1,’filled’); set(Hs1,’markersize’,2,’color’,’g’);
set(gca,’xtick’,[0:8:32],’ytick’,[-1,0,1]);
axis([-2,34,-1.2,1.2]); ylabel(’Amplitude’,’vertical’,’cap’);
xlabel(’n’,’vertical’,’middle’);
Title(’Input Signal: x(n) = cos(\pin/8)’,’fontsize’,TF,’vertical’,’baseline’);
% Decimation of x(n): D = 2
y = upfirdn(x,h,1,D);
m = delay+1:1:128/D+delay+1; y1 = y(m); m = 0:16; y1 = y1(14:30);
subplot(2,2,3); Hs2 = stem(m,y1,’filled’); set(Hs2,’markersize’,2,’color’,’m’);
axis([-1,17,-1.2,1.2]); set(gca,’xtick’,[0:8:32]/D,’ytick’,[-1,0,1]);
title(’Output signal y(n): D=2’,’fontsize’,TF,’vertical’,’baseline’);
xlabel(’m’,’vertical’,’middle’); ylabel(’Amplitude’,’vertical’,’cap’);
% Filter Design Plots
[Hr,w,a,L] = Hr_Type1(h); Hr_min = min(Hr); w_min = find(Hr == Hr_min);
H = abs(freqz(h,1,w)); Hdb = 20*log10(H/max(H)); min_attn = Hdb(w_min);
subplot(2,2,2); plot(w/pi,Hr,’m’,’linewidth’,1.0); axis([0,1,-0.1,1.1]);
set(gca,’xtick’,[0,wp/pi,ws/pi,1],’ytick’,[0,1]); grid;
ylabel(’Amplitude’,’vertical’,’cap’);
title(’Amplitude Response’,’fontsize’,TF,’vertical’,’baseline’);
xlabel(’Frequency in \pi units’,’vertical’,’middle’);
subplot(2,2,4); plot(w/pi,Hdb,’m’,’linewidth’,1.0); axis([0,1,-60,10]);
set(gca,’xtick’,[0,wp/pi,ws/pi,1],’ytick’,[-60,round(min_attn),0]); grid
ylabel(’Decibels’,’vertical’,’cap’);
xlabel(’Frequency in \pi units’,’vertical’,’middle’);
title(’Log-magnitude Response’,’fontsize’,TF,’vertical’,’baseline’);
The signal stem plots and the filter responses are shown in Figure 9.27. The
designed filter achieves an attenuation of 51 dB, and the decimated signal is
correct.
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