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}] $


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Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood