PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

410 Practical MATLAB® Applications for Engineers

FTxsym =simplify(FTx) ; % X(w)

FTh = fourier(exp(- 3*x)*sym(‘Heaviside(x)’)+

exp(3*x)*sym(‘Heaviside(-x)’));

FTy = FTx*FTh;

FTysym=simplify(FTy) ; %Y(w)

Disp(‘*****************************************************’)

disp(‘******* S y m b o l i c **** R e s u l t s*********’)

disp(‘ ‘)

disp(‘The Fourier Transf. of x(t) is:’)

disp(FTxsym)

pretty(FTxsym)

disp(‘The Fourier Transf. of h(t) is:’)

disp(FTh)

pretty(FTh)

disp(‘The Fourier Transf. of y(t) is:’)

disp(FTysym)

pretty(FTysym)

disp(‘*****************************************************’)

figure(4)

subplot(2,1,1)

ezplot(abs(FTxsym));

title(‘Symbolic plot of the Fourier Transf. of X(t) vs. w ‘)

ylabel(‘Magnitude’);xlabel(‘ frequency (in rad/sec)’);axis([-6 6 0 6])

subplot(2,1,2)

ezplot(abs(FTysym),[-6 6]);title(‘Symbolic plot of the Fourier Transf. of Y(t)

vs. w ‘)

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

axis([-6 6 0 5]);

The script fi le syst_anal is executed and the results are as follows (Figures 4.56 through

4.59):

>> syst _ anal

******************************************************

******* S y m b o l i c **** R e s u l t s*********

The Fourier Transf. of x(t) is:

-2*sin(pi*w)/w

sin(pi w)

-2 ---------

w

The Fourier Transf. of h(t) is:

1/(3+i*w)+1/(3-i*w)

1 1

------- + --------

3 + i w 3 - i w

The Fourier Transf. of y(t) is:

12*sin(pi*w)/w/(3+i*w)/(-3+i*w)

sin(pi w)

12 -----------------------

w (3 + i w) (-3 + i w)

*****************************************************