Question

Question (1) Find the Trigonometrie Fourier Series (FS) for the signals shown in Figure 1 and Figure 2. M -6rt 41 -2 4r Figure 1 Figure 2 Question (2) (a) Find the power of x(t) = 5 + 10 cos (100t + 3) (b) Express signal x1(t) in terms of signal x(t) and its time-shifter, time-scaled, or time reversed versions. Figure 3

Answer 1

0 Figure 0 signal is enpre fse d as slope = Y(2T) - You) 21-0 21 0 4ct) - t oute27 and it is prevodec with perlod 21 =) To = 20 · W5 = 27. 1 20.= s sadisec] 203 € Suctsdt * To Set 2T la.= 0.51 2. = 0.5 To 2 | 4 (1) tesquot de 27 + cont de 21 J PT

amis 000ben Tan -0) zo 21 bn = = J 464) sen nast ot 2T 2 st stant at The post (t (-casat) – ( -stant . - Senj + (-296).0 + entry boz to nto info SO 2T yet) Sin cnwolt dt geta bo Tatno - To lycu) codt [bo zo]

903 this to stude] - jun u jesmojis a Jeon) iu'+(+39-43.) * 24 ore) = (2-0) =[ { +1-] (osnoot de 10 to ans esment de) - ja aswangu ni u jasenya a jes etar) Sinn (os-nu-los (2 ) I-SPn(-noustrony 20 113 (132 nt

yet) = .. lot E ancosnwot te bo sin noot .nal no Y(t) = 1 + Ž Sinnt n=1 Tin conseder figuren for -22t2 464)= -o t +2 -1-1-2) 8 (t) = 6+2 for lctco Yt) = 1 For oct22 )=- ylt) t2 - alte- -Ictco oct 22 =0 elge -32t2-2 and 24613 and it is periodic with period To = 3-6-3) | To=6] wo: 20 - 27 Two = II rad /sec)

* *[jout + Jenyer a fer a Jesort) 129 + 0-49 – (2-0) = + (Å +1 -2] Tao = 1 / n = toll yas cos nint de) - op je esenangan pinga u jeshagan) Sin-n) COS-NI-COS (2 Int1/3) n7713 4/7

clo Sina 1/3) nl (t) Sennst dt juny songs are comgret a jesting and Con + 13th T1/3 DV cost - Cosnt/3. Sir ton 3 - + los 3 los nTV3 (n Tyzz 1113 nn (OS2NT 2 ( n to 17/3) TV/3) 5/7

pocoby of x2 power of DC = A² power of pertodec segnal = ₃ s (acts) at power of sinusord = [Am cos(cost +)] Given signal 911)= 5 + lolos (100t + ) Senu sord power of x(t) = 52 + (10) - 25 + 100 = 25 + 50 power of act) = 75 Watts YU) 6 Giren xH) Tart) I time revesal niet) > 6/7

I alt+1) Time shefting of ul-t) Cright shift by one unet EM46-1)) → tyttu Time shifting of 110 (left shift by one unit) El(t+1) t - on sde ing above 2 time sheffing signals we Conculude that, by adding these WC can get Xi(t) rict) then 2,(t) = n(t+1+x-t+1