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Highlights from
Digital Signal Processing Using MATLAB

Digital Signal Processing Using MATLAB

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21 Aug 2002 (Updated )

Companion Software

ex072500.m
% Chapter 7 Example 7.25

%           Highpass filter design using PM algorithm

%

ws = 0.6*pi; wp = 0.75*pi; Rp = 0.5; As = 50;

delta1 = (10^(Rp/20)-1)/(10^(Rp/20)+1);

delta2 = (1+delta1)*(10^(-As/20));

deltaH = max(delta1,delta2); deltaL = min(delta1,delta2);

weights = [1 delta2/delta1];

deltaf = (wp-ws)/(2*pi);

M = ceil((-20*log10(sqrt(delta1*delta2))-13)/(14.6*deltaf)+1);

% M must be odd

M = 2*floor(M/2)+1

f = [0 ws/pi wp/pi 1]

m = [0 0 1 1];

h = remez(M-1,f,m,weights);

[db,mag,pha,grd,w] = freqz_m(h,[1]);

delta_w = 2*pi/1000; wsi=ws/delta_w; wpi = wp/delta_w;

Asd = -max(db(1:1:wsi))

M = M+2;

h = remez(M-1,f,m,weights);

[db,mag,pha,grd,w] = freqz_m(h,[1]);

Asd = -max(db(1:1:wsi))

M

[Hr,omega,P,L] = ampl_res(h);

%

% Plots

figure(1); subplot(1,1,1)

subplot(2,2,1); stem([0:1:M-1],h); title('Actual Impulse Response')

axis([0 M-1 -0.4 0.4]); xlabel('n'); ylabel('h(n)')

set(gca,'XTickMode','manual','XTick',[0,M-1])

set(gca,'YTickMode','manual','YTick',[-0.4:0.2:0.4])

subplot(2,2,2);plot(w/pi,db);title('Magnitude Response in dB');

axis([0,1,-80,10]); xlabel('frequency in pi units'); ylabel('DECIBELS')

set(gca,'XTickMode','manual','XTick',f)

set(gca,'YTickMode','manual','YTick',[-50,0]);grid

set(gca,'YTickLabelMode','manual','YTickLabels',['50';' 0']);

subplot(2,2,3);plot(omega/pi,Hr);title('Amplitude Response');

axis([0 1 -0.1 1.1]); xlabel('frequency in pi units'); ylabel('Hr(w)')

set(gca,'XTickMode','manual','XTick',f)

set(gca,'YTickMode','manual','YTick',[0,1]);grid

subplot(2,2,4);

sbw = omega(1:1:wsi+1)/pi; sbe = Hr(1:1:wsi+1);

pbw = omega(wpi+1:501)/pi; pbe = Hr(wpi+1:501)-1;

plot(sbw,sbe,pbw,pbe);

axis([0,1,-deltaH,deltaH]);title('Error Response');

xlabel('frequency in pi units'); ylabel('Hr(w)')

set(gca,'XTickMode','manual','XTick',f)

set(gca,'YTickMode','manual','YTick',[-deltaH,-deltaL,0,deltaL,deltaH]);

set(gca,'XGrid','on')

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