PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 409

xw =2*pi*sin(w*pi)./(w*pi);

% FT of x(t) from Table 4.1,transf.#3

% H(w) = 6/(w^2+9);

% FT of h(t) from Table 4.1,transf.#13

a = [6];

b = [1 0 9];

Hw = freqs(a,b,w);

magxw = abs(xw);

magHw = abs(Hw);

yw = magxw.*magHw;

figure(1)

subplot(3,1,1);plot(w,magxw);

ylabel(‘Magnitude’);axis([-6 6 0 8]);

title(‘ X(w) vs.w’);xlabel(‘frequency w(rad/sec)’);

subplot(3,1,2);plot(w,magHw);axis([-6 6 0 8]);

ylabel(‘Magnitude’);

title(‘ H(w) vs.w’);xlabel(‘frequency w(rad/sec)’);

magyw=magxw.*magHw;

subplot(3,1,3)

plot(w,magyw);axis([-6 6 0 5]);

ylabel(‘Magnitude’);

title(‘ Y(w) vs.w’);xlabel(‘frequency w(rad/sec)’);

figure(2)

plot(w,magHw);

title(‘ H(w) vs. w (showing impulses)’);

ylabel(‘Magnitude’);xlabel(‘fequency w (rad/sec)’)

magyw=magxw.*magHw;

%time domain analysis

figure(3)

t=-5:.1:5;

xt=[zeros(1,20) ones(1,61) zeros(1,20)];

ht=exp(-3.*abs(t));

hut=[zeros(1,50) ones(1,51)];htt=ht.*hut;

conxh=conv(xt,ht);

tt=-10:.1:10;

subplot(3,1,1)

plot(t,xt);axis([-5 5 0 1.5])

title(‘x(t) vs. t’);

ylabel(‘Amplitude’);xlabel(‘time (in sec)’)

subplot(3,1,2)

plot(t,ht);

title(‘h(t) vs. t’);

axis([-2 2 0 1.5])

ylabel(‘Amplitude’);xlabel(‘time (in sec)’);

subplot(3,1,3)

plot(tt,conxh);

title(‘y(t) vs. t’);

ylabel(‘Amplitude’);

xlabel(‘time (in sec)’)

% Symbolic evaluations

syms x;

FTx = fourier(sym(‘Heaviside(x-pi)’)-sym(‘Heaviside(x+pi)’));