Question

20 points) Consider the periodic signal z(t) shown in the Figure below: X(t) 3 2 N. 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

Given signal xlt) slope slope 2 - - 2 2 10 K T: 4 (A) a 4 Jee. frequny = we know Here is Here signal Repeats itself at interval of fundamental time Peniod T=4 see Indemental wo = zat= 27 The sad/see (B) foresies Series F(t)= ao E ancuenoot ton Sinnoot the given ware from symmetric etic about y-axis. xlt) = (E) It is even signal. so brzo x - xq = 42-44 (4-4) ay - 11 ft) at flt) at X-02-(y-2) 1464) Wenwot dt Q<t<4 2 ++2) dx + )"(++2)dt I (4-0) ΤΙΣ X2-X •T/2 o x = -4+2 (10) -t+2 an 0<t<2 #+2 do - X-2 :[{c+4) de [4*+24)* +(*424),*] X = t +2 ao 4 & L p +4 + 16 + 20 do - ["2] 3 - 40 4 4 an (-+*a) ce ng + ["(++z) que no te det 2 4 すん *+2) sinna + +t+2) sinna sinart det ht 2t ил 1 + + d 0 АК 2 sinnt/ t at ni

2 + + went/t (11/2) 6 NI sin ant - 4 sinna o ni2 sinnt=0 L (wwwx), t)," ] + (1072) L count + (Malz)? Serije (u zar - count] (-""} Hunk= (-1)" + cu o W12) Cuant = ! - 2 lunk + 1 (1412)? ㅗ Cuaukt (nal2² er 2 (-1)" (1512)² (nala)² **(1.)? [ - (-)"] 2 lan {"-60"] (na) 2 is so the fourier senier co ao cu F(t) = + E n=1 nat 2 100 + Ź 2 [1-64)"] FIE) = wel nA t han (nr)
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