Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
inverse F.T
assume
$ X(\omega) = 7\pi\delta(\omega-3\pi)+\delta(\omega+5\pi)-\delta(\omega-7\pi)\! $
answer
$ x(t)= \frac{1}{2\pi}\int_{-\infty}^{\infty}7\pi\delta(\omega-3\pi)+\delta(\omega+5\pi) - \delta(\omega-7\pi)e^{jwt}dw $
$ =\frac{1}{2\pi}[2\pi^{j3\pi t} + e^{-j5\pi t}- e^{j7\pi t}] $
$ =e^{j3\pi} + \frac{1}{2\pi}[e^{-j5\pi t}-e^{j7\pi t}] $
