xt 3 rectt1 Use the integral that defines the Fourier transf

x(t)= 3 rect(t-1)

Use the integral that defines the Fourier transform to determine X(f) and X(omega) for: x(t)= 3 rect(t-1)

Solution

Fourier transform of rect(t) => sinc(w/2)

3rect(t) => 3sinc(w/2)

from time shifting property 3rect(t-1)=> e^jw sinc(w/2)

in frequency domain: FT => e^j2*pi*f sincf