Question

4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2 N VAA 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.

Answer 1

X(t) 2 2 6 T 2T wo 2177 T = 4 woo Nli 2 Wo = 1 Tourier series coefficient are ao, bag an 20 = Sectar 4 (othea under triangle) TJ Trn x 42 x 4x2 a

bna 2 / ja(t) sinnost at -2 alt) is enen function sin wat is odd function a(t) sinnwot becomes odd function so area under ood function is o Idence bn=0

anz * f zce) a(t) Konwot at 2) 2 tt -2htro 0くとく2 xce) 2-t 2 anz 24 jQ+z.com,t + 5(2-1) cosnost a 2 an= I seu Seconwot & iconwo Hart 2 cosawot-toone of the 2 S-tcosmoot " Izcomove a commentare = { [0 + (rsinnwot + conwer (mus) (I sinnwot tronwort) ) nwe mus)" = { [°* chamos com mais cos (-99) (1 wo)² Icos (nn) - 1 (nwo) (nwalt

2 - 2 cose no W wo nowo 4(1- co no) an M² T2 n = 2,4,6, o an = for 's's't an & for 거류로 no aot + E ancosnwot ton sinnwort X(H) = n=1 ancosnwor .ao X(t) z + Σ A= even (aix 1 + 8 connot M²72 1 + Σ 2 (7) 2 & con It n=even nu