Question

Find the Fourier Transform of the following signals: (a) x(t) = Sin (t). Cos (5 t) (b) x(t) = Sin (t + /3). Cos(5t-5)

Answer 1

164 - Sint 1954 2ct = [esint.cosst) : [sin st = singo] - sinkt_Simha Dia tafinition, xlove. Sometimes Samas ele competing saxw Sicherheit fie inghe Sot a we know by Duality & TF275 (w) lielos <!s 27.5Cw-w)..but rest -jut 6 wt dt til jut jut ae dt. at t - Je edt ut jut e dt 469) e inf (e4) - for Leing a poing 2 p Pleint 4 Kw) - [cm-6) -56wto) + eg (scu -1) - scw+y] [xcm) = (60.6) -(w+6) + (60w-4)-co-tw] 10 + T74) cos (St-Tr] X(H = sin(t+1) cos(st-173), (sin(Ct) sin (-44 +214) • Yasin (ct) - Sin (at-20%) =(simbt + { Sin 4+ + cost! 7

=> + (since) - Globalisie). (56-63) - 66 ms] IF [ sinust to] - I sin (ast to) e tut dit og jezt tjo jwt - jo fut ol 2 J F (sncwot-ro] - Cav (56w-a) - zlo (217 66 o [eo scaww) - zido scuores)

no- 1. ñaly 1 - -34 4 4 to 7 37 37 ..... - m(H). S 8(49; -12 <tsty lo; else where period = 1 Anggular Fundamental freq.(w.)=217 By the definition of fourier Series H = Geskust where 6+ + f2c4 dt - sl scen.de - 64 10 24 .: C = $ $24.event and a 4 "sch, jestling y Teschidt = top % 1"* see de a Ck = 4 & KEZ 12C4 - 3 11 ).clkast T KED

X.CH) = sint cos(su) + (sin 6t - Sm4t] | 2.4 - -; (2014)th, eshit , last) + te, le 17 to x By Fournier Series R CH = B C ei kaste - Here If we consider = 2 = These are 2nd & 3rd Hermonts - Wool & These are 4th & 6th Harmonics on comparing and ck-f-yuj ;k :6 Yuy ; K=6 | -lajiksy ...XC) - Cējot) + 1 Cebut) in Lejut) + Cetset) 16 Fourier series of act). representation By Applying Fourier Transform =x6w) - ff tile jist. Ej64) - L, Cebuta Juj] from the Question @ we desired just ] = [s[w-))- (66w=6) – 56w+6)]21 - 15 16-0)-s(w trus - Iscw-o) - (w+67) - g / 66w-- (ws ent] ) - S(w+6) - S/W-4)+s (w+u)]