Compute and plot the Fourier transforms a ft sinw0tt b gt

Compute and plot the Fourier transforms

a) f(t) = sin(w₀t)/t


b) g(t) = f(t) * cos(w₀t)

Solution

a) f(t) = sin(w0t)/t

fourier transform F(W) = X1(w)

where X1(w) = { 1 , |w| < W0

   { 0 otherwise

Plot of this is as shown in figure

B. g(t) = sin (w0t) /t * cos(w0t)

g(t) = X1(w) * X2(w)

on following convolution property

The plot will be as shown