There are signals whose Fourier transforms cannot be found directly by either the integral definition or the Laplace transform. For instance, the sinc signal

is one of them.

(a) Let X(Ω) = A[u(Ω + Ω₀) ˆ’ u(Ω €“ Ω₀] be a possible Fourier trans-form of x(t). Find the inverse Fourier transform of X(Ω) using the integral equation to determine the values of Aand Ω₀.

(b) How could you use the duality property of the Fourier transform to obtain X(Ω)? Explain.

Transcribed Image Text:

sin(t) x(t) =