Question

solve for a and b

1. Plot each of the following functions and find its Fourier series representation, also determine the first three One zero harmonics (a) f(t) -1<t< T= 2 where T is the period. 0t<1 J (b) f(t) -t-1<t<0 T 4 where T is the poriod = 0t1 0-2<t<-1 T = 4 where T is the period (e) g(t) 1 -1<t<1 0 1<t<2 (d) g(t) = 1- t -1<t<1;T = 4 where T is the period

Answer 1

Feusier Series Patetominasies) poiedie fundtion t is lith a pesiod T- 2L Fousies Seis hefiesentation ot s n Cos (nTx + 2 +bn Sin (TX l2u Where f(x) dx L dx Cos L t)Sin n -L n0, 1,2,3..

f -1<t<0 : T: 2 46 T: 21= 2 ao t an Cas/n T t 2 nTt bn Sin (t) + tSu 1 dt 1 P(Af +CC ft) Gs (nrt) dt faneton no,1,2 y eWen ed4 function

t) Sin (hTt) dt -1 i) Sin (nTt) dt Sin (n Tt) dt bn=Gos (m rt) JI Cos (nT) Cot (n T) + MTT nTT C1-Gas (n)) 2 nT (ul)- 4 2 tolms Thiee mon-Zele TT 4. 3 TT g4 4. 5TT T 4Sin(Tt)+ Sin (3Trt). 4 Sin/5mt) 3 TT TT 5T (1-G) Sin (nrt).

0 1- / T= 4 b -2 2 Pelibd T 21 = 4 L= 2 unition ite foudies Sieties Sepielentation ill nst hake Sineseidal tems Sine ft) s an even / That is eh n1/2, 00 an Co (nt) ao + 2 11 2 2 2 4P ( -2

= 글2 AP +P (17 + 2 2 -1 ft) Gas dt $2 L 1 an= -2 l + 2 2 2 -2 1 + 2 2 4 Sin () Sta ATT ewen if n s an =o M2, 4, thvat 4 5 TT 4- 4- 1 a5 TT 3 T7 T4 -[N IN