Question

2. Determine the FS coefficients for each of the following DT periodic signals. (a) x[n] = sin(2 /3) cos(in/2) (b) x[n] periodic with period 4 and x[n] = 1 - sin n for 0 <n<3. (e) a[n) periodic with period 12 and [n] = 1 - sin for 0 <n<11.

Answer 1

@ Given x(n)=s*(210) (03CTD). aC) = \fo (attu)nsigleym-)) = 13 ( sto ()] al) = ks 940 Now Here wo- 40 a(n) = E ak Skwon EN XC) = E aK eSKT)" - KEN from & a = /y; Ang= -1/45 a == /us; a = - 1/43 Hence the fourier series Coefficients are lak= (1/4s too K=1,7 To o otherwise for k=-1-7

1 (6) Given a (n) = 1- Sin th for 02063 time period= 4. fourier Series coefficients are ak-se ame SR (29) posolog). =kſtov*(-$ 4) F4 (1304 *(1-5o 34 )e Samk = ', [lt (1-on Je (-i)e SK + remis de 3014] = \a{1+ft+yale" (amb content = Ky 14(1- Val ). ok ( ak = (1+2 6+1)*(1 +] CO3(TIL)] Hence the fourier series Coefficients are. ak = Plank (1-16) cos oc) 71

DAT (C). X = ls for soci time pestod = 12 fowie Coefficiersts are ak i ne frau de % fin so (pp)]e familien 4 (C-02-ft-story Consor Sirvek +(1-sºn3m)=39438 + (-stort) - Fr X4K * (l-senso a task + (hse, byr) eSTxok +(1-sar) e 3989k + (l-skan) e trek +(-Sin 9 ) e myk +Cl-sim nje Srx rok 1 + (1-son 14] ITAK * (ja soy +G+) es (nt je + Jelt kt fi-+) 29tk #07 (47 km

te , $123p) Eesme omegryting talok = {1+ (w tyle 94 +(-4745 1 1/2" 4" J+(44) Esote Love] [ +210k ak = %[1+21 Cas(78) *a ( 1443 (15)] 1 + 2018 (pnyc) +2 (1++) C08 (STC) [ta(4) Hose the fourier series Coefficients are ak= , Si+2(1-) cos(uk)+211-7) 03 (5?) ? 12.08 (c)+2{1+.)cor suk) tarde