Code covered by the BSD License

# MatLab Solutions: "Introduction to Digital Signal Processing: A Computer Laboratory Textbook".

### Ilias Konsoulas (view profile)

29 Oct 2012 (Updated )

These files are the MatLab solutions of exercises contained in the above DSP lab textbook.

ex545b.m
% Exercise 5.4.5.b.  Determining Poles and Zeros from the DTFT.
%	Pole & zeros & frequency response of the H2(z) digital filter - animation
%
% Note: This m-file contains large portions of code originally presented in the
% companion software of the comprehensive and well-written DSP textbook:
% "Digital Signal Processing: Concepts and Applications", 2nd Ed.
% by B.Mulgrew, Peter Grant and John Thompson, Palgrave-Macmillan (2003).
% It was modified as necessary for solving Exercises 5.4.1., 5.4.2. and 5.4.5.
clear; clc; close all; colordef black;

b = [1 1.9 0.8 -0.8 -0.7];
a = [1];

[zz,pp,k] = tf2zpk(b,a);

figure('Name','Exercise 5.4.5.b. Determining Poles and Zeros from the DTFT');
subplot(1,2,1);
zplane(b,a);
title(['                                                          ';
'H_2(z) = 1 + 1.9z^{-1} + 0.8z^{-2} - 0.8z^{-3} - 0.7z^{-4}';
'                                                          ';]);
ylim([-1.5 1.5]);
xlim([-2 1.5]);
hold on

pause;

th = -pi;
pt = exp( j*th);
xx = real(pt);
yy = imag(pt);
l1 = line('Xdata',xx,'Ydata',yy);
set(l1,'Color','w','Marker','o','EraseMode','xor');
l2 = line('Xdata', real ([ pt zz(1)] ),'Ydata',imag([ pt zz(1)]),'Color','b','LineStyle','-','EraseMode','xor');
l3 = line('Xdata', real ([ pt zz(2)] ),'Ydata',imag([ pt zz(2)]),'Color','b','LineStyle','-','EraseMode','xor');
l4 = line('Xdata', real ([ pt zz(3)] ),'Ydata',imag([ pt zz(3)]),'Color','b','LineStyle','-','EraseMode','xor');
l5 = line('Xdata', real ([ pt zz(4)] ),'Ydata',imag([ pt zz(4)]),'Color','b','LineStyle','-','EraseMode','xor');
l6 = line('Xdata', real ([ 0 pt ] ),'Ydata',imag([0 pt ]),'Color','r','LineStyle','-','EraseMode','xor');

M = 128;
w = -pi:pi/M:pi;
hh = freqz(b,a,w);

h = abs(hh);
ang = unwrap(angle(hh))/pi*180;
angmax = max(ang);
angmin = min(ang);

if max(h)~= Inf
maxh = max(h);
else
ind = find(h==Inf);
maxh = max([h(1:ind-1) h(ind+1:end)]);
end

if min(h) < 0
minh = min(h);
else
minh = 0;
end

subplot(2,2,2)
title('|H_2(j\omega)|');
xx = [ w(1) w(1) ];
yy = [ h(1) h(1) ];
ll1 = line ('Xdata',xx,'Ydata',yy,'Color','y','LineStyle','-','Erasemode','none');
ll2 = line ('Xdata',w(1),'Ydata',h(1),'Color','w','Marker','o','Erasemode','xor');
set(gca,'XTick',-pi:pi/4:pi);
set(gca,'XTickLabel',{'-pi','-3pi/4','-pi/2','-pi/4','0','pi/4','pi/2','3pi/4','pi' });
axis ([ -pi pi minh maxh ]);
grid
ylabel ('gain')
hold on

subplot(2,2,4)
title('\angleH_2(j\omega)');
xx = [ w(1) w(1) ];
yy = [ ang(1) ang(1) ];
lx1 = line ('Xdata',xx,'Ydata',yy,'Color','y','LineStyle','-','Erasemode','none');
lx2 = line ('Xdata',w(1),'Ydata',h(1),'Color','w','Marker','o','Erasemode','xor');
set(gca,'XTick',-pi:pi/4:pi);
set(gca,'XTickLabel',{'-pi','-3pi/4','-pi/2','-pi/4','0','pi/4','pi/2','3pi/4','pi' });
axis ([ -pi pi angmin angmax ]);
grid
ylabel ('phase (degrees)')
hold on

% pause

step = 2*pi/M;

for ii = 1:4:2*M+2;

th = -pi + (ii-1)*step/2;
pt = exp( j*th);
set(l1,'Xdata',real(pt),'Ydata',imag(pt));
set(l2,'Xdata', real ([ pt zz(1)] ),'Ydata',imag([ pt zz(1)]));
set(l3,'Xdata', real ([ pt zz(2)] ),'Ydata',imag([ pt zz(2)]));
set(l4,'Xdata', real ([ pt  zz(3)] ),'Ydata',imag([ pt zz(3)]));
set(l5,'Xdata', real ([ pt  zz(4)] ),'Ydata',imag([ pt zz(4)]));
set(l6,'Xdata', real ([0 pt ] ),'Ydata',imag([0 pt ]));

if ii==1,
xx = [ w(1) w(1) ];
yy = [ h(1) h(1) ];
else
xx = w(ii-1:ii);
yy = h(ii-1:ii);
end
set(ll1,'Xdata',w(1:ii),'Ydata',h(1:ii));
set(ll2,'Xdata',w(ii),'Ydata',h(ii));

if ii==1,
xx = [ w(1) w(1) ];
yy = [ ang(1) ang(1) ];
else
xx = w(ii-1:ii);
yy = ang(ii-1:ii);
end
set(lx1,'Xdata',w(1:ii),'Ydata',ang(1:ii));
set(lx2,'Xdata',w(ii),'Ydata',ang(ii));

pause(0.25)

end