Question

Find the inverse Fourier transform of sgn(ω).

Answer 1

Fourier Transform of Signcen function Sance) = Si, to 0-1 , t<o. Sgret) Sgnet) = ult) - u(-t). we know that: ult) <ET, + 1586). Ult) e simes + TT 8(-) ul-t) + + TT 5(w). 1:5(W) is even. F7 [gen] - [sing + Tren] - [ +Tsw) to com Slow) = $1W) sen Tişl+ - TT 846) Scanned CamScanner

Inverse fourier Transform of sgnew) Foerier Transform of Sgn (t) is 22 23 Applying the duality property F(t) + 204 (w). we get F(t) = 2/7 Sg" (-w). As Synow) is an odd franchion, Sgn (-6) = -8gncw) Hence - - Sgn (w) r - sgniw) Fourier transform of signum. Therefore the function inverse is 3004) - 1944) Tit: Scanned with CamScanner