Question

Find the trigonometric Fourier series (FS) and the exponential FS of the following: x(t) TT Ana -3т -2n -TT 2TT d) x(t) πι -no -TT 0 TE 2TT exponential FS f(t) = En=-- Cnejnwot Where (n = +S40+" f(t)e-inwot dt trigonometric 30 f(t)=a, + a, cos(no),t)+b, sin(no,t n-1 ao 1 T. 2 to a. So f(t)dt -5° f(t)cos(no),1)dt Sº f(t)sin(no,t)dt oy b 2 T

Answer 1

o AA 가 Time Period T 2 W스 주: 쯔 Trigno media fourier senel (t) - + 3 4. Gos (not) + bm sin (huot) 의 4 2 는 ." Att) date Ht) t OLALA LgR 2T 10 * S. Alto dot ★ t at +o dt] 른 증 2 x2 2 IT 2 2. ㅈ 4. To an a 오 1 f(t) Cosnwot .dt, ہ

an - aż Sie Jak fit) cosnt at { wor? al + [ 66* trobente ķ T + Cosnt 52 - # [ +- (+ sinnt + [ 1-1, mix [(-34°+ c -1] h2 227 [tion an no even na odd n2x on = To - 2 27 {Wo = 1 -Ik t sinnt dt So f143 sinnwot.dt Sott f1t) sin nt dt À So [t. *[-(-3)*x +o -(-X" wint *|- **) sinnt :) ne c 2

an - aż Sie Jak fit) cosnt at { wor? al + [ 66* trobente ķ T + Cosnt 52 - # [ +- (+ sinnt + [ 1-1, mix [(-34°+ c -1] h2 227 [tion an no even na odd n2x on = To - 2 27 {Wo = 1 -Ik t sinnt dt So f143 sinnwot.dt Sott f1t) sin nt dt À So [t. *[-(-3)*x +o -(-X" wint *|- **) sinnt :) ne c 2

bon c + (+1) na odd na even sh nieven H16) - kit + - Stinnt nal na odd & Waewa E + H(t) cosnt + to sint) + E hal na

Exponenal T Cna + S fit) e inwot dt t jnt dt (wo WO/ 2A -int I 20 ( e-int (*)n) 2 ]]. 7 . ** -in Ha [ 01 (4 t 12 h2 Cn l' • j (-1)? an 90 xo 지다 int Ź (-1" (*) e f(t) = りこ-20 T -2% t 2Ã To - 2 T 2 ot = 20 21 20

० ८ १८ 11)2 { tk 7 ८+ ८.1 trignomenic senie- १० f(t) dh T f(t) at 21 M 7 dt T (4 (1) * [[+4+ ++ + x *] * [T + axn - x2] . 2R - *_372 32 30 4 an +9 cos not dt. M 2 9 dt ar (4) tes htd Sat Cosnt at X 4 + Toshtat K

sinnt tot) + losht b2 As +ㅈ. Sinnt HN 기 al n [(-1)-1] to Я 0 an he e Veh 르 LE M2 odd bn = f(t) sinnut at (0) tsinnt att samt at " 2T ★ - (-age) + sinet rasn't با K Lynn reyn 유 十 Ik 확 he even. H(t) 도 1 bT 3 +E 4 2) sinnut na odd 0 게 11 = 2 ㅈ } 2 머리 ร 2 cosnt + I sint 2T

je 06: لا مسا ہے -ارا لا در 2 (دز) (. y ہ لا ج - )اال { ( - : که در مورد ترد ] Y dt لا ۱) ? (? - ه ر م (4) - jn wat P