Question

The Fourier transform of f(t), F(W) is as follows: F(W) = F[f(t)] vendºsce-iat de Find the Fourier transform of f(t): 0 < \t] =1 = 1t| 10 t = 0,|t| > 1 (1) f(t) = {i (2) f(t) = {2 (t2 0 < t < 1 lo |t| > 1

Answer 1

ber Guven f(t)2 t It' 0 < t <1. 1 th 10, tao, Ityti F(w) = VAT S the weat - iwt -cwt. flt) سا Seleracing + V2T t. ( relentit + Pore than a de i'at Edt dt t VZT - iwt. - iwt 67 e V teorette seg at Joint le to I () - Hotel on to Celenting ] Pe 1 + costa] VIT i w -iw -1 1 VET i'w 2 لے

fleste f (t) - 122 oct & 1 1>1. : 1 F(w) f (t) è int quint t e dt. V2M 21 Klated to Wat + {fty't tud? in t) + @o ()'] 1 -i'w 2 2 (ما) ( it VI Van W -i'w -iw - iw 2 - ) ] 2. - le t e W 2 - iw V2n i'w - i'w e a 2 i W3 + + Cice'w) 125 W