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(Î©) = A[u(Î© + Î© 0 ) u(Î© Î© 0 ] be a possible Fourier trans-form of x(t). Find the inverse Fourier transform of X(Î©) using the integral equation to determine the values of Aand Î© 0 . (b) How could you use the duality property of the Fourier transform to obtain X(Î©)? Explain. sin(t) x(t) =

Question: 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

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(Î©) = A[u(Î© + Î©₀) ˆ’ u(Î© €“ Î©₀] be a possible Fourier trans-form of x(t). Find the inverse Fourier transform of X(Î©) using the integral equation to determine the values of Aand Î©₀.

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

sin(t) x(t) =

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