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(w3)+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)
CRC_47760_CH004.indd 343
CRC_47760_CH004.indd 343
7/28/2008 12:25:56 PM
7/28/2008 12:25:56 PM