Question

Question 2:

(a) Derive the Trigonometric Fourier Series coefficients for the following periodic signal: ?(?) = |? ??? ?0?|

Hint: you may use the tringnometric form the F.S. representation.

(b) Compute the power contained in the DC component and the first 4 harmonics.

Answer 1

the solution of part a:

cosine is considered to be period with an evaluation period for analysis form -pi to pi

ze (t) = ln Cos (wot) checking for even orodd X(-+) = la cos (-Cot) - la coswot) = 24) : so it is an even fonction - Cos variation taking from it to it for analysis fraces (A Cos(60)| - A cos(toot) ; 05. lot att/ :.- - A COS(wot) ;.1/2c.coot sto

Calculation of Rota ao = f S xct) deert 207 + [ sua casa edest - facesat dent] * A [ 5'a (608792 [sin(0] = [ (1-0) – (0-0) : a = 24

Calculation of an: C S211) cos nwot decot 9 [ So manas datuwd der faslatot ng = are 7 2 A[cos (tn),t) + Cos (v«n)Wet)dot -SA lies onidant) + 7 F1z3 cos (0-n) Got) Jedinte ICOS A COBB -- [les (A+B) + COCA-B) TIE sin (i+n) Cot Sin (1-n) + sin(-n) +/"2 "2 Sin (1+ n Liitn et, Sin (l-nub Li+ni+sin In LD 2. 9 (cenoza, sneam) - (0- (shetra 74, sono Sini tn 12 12 SA sin(n) 1/2 sio (1+r) in sin(n Sin Oro Sin (I+) = 0 Sin (1-0)T=0 2A I sin (40) 1/2 + sin (1-0) 1/2 1- 99 (sh (m. We , salva vis Bin (19) W = sin( W24974) > Cos na

- ZA cas que consum? - HA (as our) "(*) an = the of (eraspt at n=1) an at nas put nal in an 0,3 ( s'estose) - sa este det? x 1+ Cos 27 2 4*(a finestreno dne a jengo land] *** [{ [na e shany."- Eustatius any] **{E=0)-o] - [(mos)- (9-)) * Å (9 -1 + 1] -0. aio

brzo fourier Sales » a. t & an cosne + 3 bn cosma n Cosnat osna 0 X(+) - PA s S 4A Cos (NTT/2) Coscoot) TT i-n2).

the solution for part b:

power of the signal

P= 18(4)? dt

dc component power

power for Dc component 2 TT Pag can 1961 out - they r *(602)

harmonic component power

power of harmonics Par 514 se comuna *#14 em 1 | lesbianast best at a century as vos con l'educt? 0 E UR

12 last 4 (14 los es)] * * { na celoten) (53 (1054) dent] * * { consomma[ (Side 15 as ant base] **{* ) 1 ( n + 4 column] 2coot dwat - Paixo as a,=0

substituting in the above-derived equation

Pa2 = 0.09A²

Pa3 = 0

Pa4 = 0.0036A²

Pa5 = 0