Fourier and Laplace 343
F1 =
pi*Dirac(w-3)+pi*Dirac(w+3)>> F2 = fourier(cos(3*t+pi/4)) % part (b)F2 =
1/2*2^(1/2)*pi*Dirac(w-3)+1/2*i*2^(1/2)*pi*Dirac(w-
3)+1/2*2^(1/2)*pi*Dirac(w+3)1/2*i*2^(1/2)*pi*Dirac(w+3)>> factor(F2)ans =
1/2*2^(1/2)*pi*(Dirac(w-3)+i*Dirac(w-3)+Dirac(w+3)- i*Dirac(w+3))>> F3 = fourier(sin(3*t)) % part (c)F3 =
-i*pi*Dirac(w-3)+i*pi*Dirac(w+3)>> F4 = fourier(1/t) % part (d)F4 =
i*pi*(Heaviside(-w)-Heaviside(w))>> F5 = fourier(exp(-t)*sym(‘Heaviside(t)’),t,w) % part (e)F5 =
1/(1+i*w)>> pretty(F5)1
-------
1 + i w>> F6 = fourier(t*exp(-t)*sym(‘Heaviside(t)’),t,w) % part (f)F6 =
1/(1+i*w)^2>> F7 = fourier(exp(-abs(t)),t,w) % part (g)F7 =
2/(1+w^2)>> F8 = fourier(sym(‘Heaviside(t+1)’)
-sym(‘Heaviside(t- 1)’),t,w) % part (h)