Question

1300 30 November Sat Favorites Edit PDE Fa a Sign Annotate 98 T et mge Lin edact EE311F1819 Midterm Exam Reterans Deerendime Formu-YsO OPPENHEM Question 1 [25pts]: Let x[n] = 0.5 + (–-1)" and y[n] = sin (En+) be two periodic signals. a) [8pts] Determine the Fourier series coefficients and plot the magnitude of each coefficient for x[n]. b) [8pts] Determine the Fourier series coefficients and plot the magnitude of each coefficient for y[n]. e) 19pts] Let z[n] = x[n]y[n] be a periodic signal with fundamental period 10. Determine the Fourier series coefficients and plot the magnitude of each coefficient for z[n]. 2 of 5 I Stop Screen Mirroring Document Screenshot A Focus bant

Answer 1

ain)= 0.5+ EDn y cr) = sin n +) y (n) 0.5+ (-1)" We know, xl0) = 0.5+(-1)°= 1.5° 0.5 +(-1) -D. 5 X12) = 0.5 +(-1)* - 15 1.5 1.5 1.5 -0-5 -0-5 No = 2 ) It is pe riedic with Wo = 21 =T NO

We know jā Íin -jin 0.5 + jin -i 0.5 + î.be O.5 ė comparo it with, -juion jwon Co = 0.5 = 0.5 =C, |Cnl 0.50.5 0.5

yin) : Sin (f+u). yın) 0.5 e + 0.5 ē3n In! 0.5 0.5 c) z in) = xim)yın) [0.5+61] Sin (n+) חןו 0.5 Sin - 0,25 e 25 +0.25 e +0.25. '+Cz5 ( +0.25 e s! O25 e -13n +e:25 e +0-25 e +o.25 e t0.25 e +0.25 e No : 10 : 2x"15 : 2wo 315 : Sil/5 = Cy= 0-25 : C.2 0-25 -S -2 -3