PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 345

>> F4 = i*pi*(Heaviside(-w)-Heaviside(w));

>> f4 = ifourier(F4,w,t)

f4 =

-i*pi*(-Heaviside(-t)+Heaviside(t))*Dirac(t)

>> F5 = 1/(1+i*w);

>> f5 = ifourier(F5,w,t)

f5 =

1/(1+i*t)*Dirac(t)

>> F6 = 1/(1+i*w)^2;

>> f6 = ifourier(F6,w,t)

f6 =

1/(1+i*t)^2*Dirac(t)

>> F7 = 2/(1+w^2);

>> f7 = ifourier(F7,w,t)

f7 =

2/(1+t^2)*Dirac(t)

>> F8 =exp(i*w)*(pi*Dirac(w)-i/w)-exp(-i*w)*(pi*Dirac(w)-i/w);

>> f8 = ifourier(F8,w,t)

f8 =

-(pi*Dirac(t)*t-i)*(-exp(i*t)+exp(-i*t))*Dirac(t)/t

>> simplify(f8)

ans =

2*Dirac(t)

>> F9 = pi*Dirac(w)-i/w F9;

>> f9 = ifourier(F9,w,t)

f9 =

(pi*Dirac(t)*t-i)*Dirac(t)/t

>> simplify(f9)

ans =

-i*Dirac(t)/t

R.4.74 Another popular transform, employed in system analysis, as well as in the solution

of initial value DEs is the LT.

Let a real signal (or function) be given by f(t). Then the LT of f(t) is given by

Fs()
 f te dt()st









∫