Question

6) If a continuous-time periodic signal has the Fourier series coefficients ak, where k = 0, +1, +2, +3,..., derive the Fourier series coefficients bk of the following signals in terms of aki a) <(-t) b) x*(t) c) x(t – t.) where t, is a constant e) (t) dt In part e), assume that the average value of x(t) is zero.

Answer 1

Given (+) - Continuous -time periodic Signal which has fowies (oefficient ak whexek = 0,11,12,... @ x(-+) es blakfowsico Coefficient of 26-t). 2 t) ak By definition of Foudies Scoies, x(+) = I ate zare N=k to jnwot w اما لازم n =-40 ท- (1) ونماز al-th= N=-66 letn=-p. par 2-t)= { q evlp)wo(4) P=n = Egés a spust i p=-6 ) an einwol asi[an] alt) = acto a olkata alt) Gak nak © tatt tott FS[80]=43 * 2 core mandata + sameingebot Xcelon) what = Blanja Los o fat be]

© (Henan xatto be . alt) = Š ane inwot n 264-by = an einwock-to) - 2 lane inwote ] e nust =ts-'[an e inwoto ] n -10 alt try to an einusto Fox -que Tikuoto 2(t) tak delt de bk xH)= Žan enost des - Žan element aména). mint - Ź (bouw) an comhedens inwan) . n=-6 n=-20

© rhide Jx (7) di obie 2 Se oldt to an ho to kwook n=k Assuming average Value of X(t) =0. Hence aboo boso