Question

Problem 2 Determine the signals having the following Fourier transforms. So, 0 < 1W < Wo (a) X(w) = { (a) A 10) | 1, wo < lw <a (b) X(w) = cos?w (hint: expand first X (w) in terms of ejw) (c) X(W) = { 1, wo – dw/25\w Swo + dw/2 10, elsewhere

Answer 1

the g fourien tramferm is Y()= 0 thc the raphical reprevata tiom of trantom Can be dsawn as X (w) T Tmverse founestranstom Can be the tormula foind iny the wo wo dw t "deo t(o. wo دار استگ ు wo [ => t wo jnt >ALt) te

Justjwot t Jt 27 jt TCast ust jsinust-CCoustSint) je Lt) = jt Tin t Sinwot tSin SntSinwot

nNew Ueing the formula Ivetce Hounics trantom 27 here Cesto X w) It Cos2 I+lotou 2 tavtof 2 2 7 X Cw)= Lt

Novo utng Y(w) inthe formula we haye e te )elug 27 .diw 4 jwtt)2jt) e e 2K e 27 f -e j() jur(t) eliat en(t) -1 jnt t te.e- (t) 1 n Lt) e -rt 2jt jist t - 1 jant t 2K 4jtt) + t

t 러ㄷ {r-나 Lt)=et t스나tt- t(e-) ). C2t) t Ct4)

-Swlwl t Sw else vohese is fantfem Ahe gaphial pescata ian Can he dnawn as woto Wo -wo-Suw -wot/2 wt Su jut dus 2A wo-lu2 C C) wotfwl 7 Lt)= t wo-SuL 2RL ut)t-jwt) e een-f)t

F7 21 S (-Sw)t njS(wott jt 21 Sn (wot Sn(uot fw)tS(wo-)t Sin C-Sm CRls (D)S( also 2 lo 2. S Ces (wt) t