Question 1: (25 marks) Compute the convolution f(t) = fi(t) + f(t) of the following two...

fo(t) = 52 (t) = c(t+1) – (t-1) r (H+1)-&r64) + r ct-1)-r(t-3) +ar(4-4) -r(+-5) Taking derivative of fact) < fico) fact) = 4(4+1)-24CH) + ci(t-1)-467-3+242(t-4) - 41(4-5) de [rctJJ= (Ct) fct) = fr (t) * f2Ct) f (t) = fo ct) * $2Ct) (Total convolution derivative) = [uct+1)-((t-1)] * [u(t+1)-2014) +4C6-1) -4(t-3)+24(6-4) -464-5)] o Ult) * Ct) = tult) = rct) uCt-8) * Ult-B) = r (+-2-B) f(t) = r(t+2)-2 r(t+1) +r(t)-r6t-2)+2 r(+3) - OCH4) - reg tarct-1) +r6t-2)

tr(444) - 20 rct-5) +r(4-6) Ercata) -ar(4+1) -ar(6-8) + 28 (1-3) tar(tt) ret) = tuilt) f(t) = (t+2) 45(4+2) - 2 (4+1) r(t+1) +2(+) 45CF-1) -2(t-2) 4(-2) +2(+-3) U(+-3) f(t) = f f ct) at 4ce) - 3 CH3) - Chu CH 1) và (-) 1.41 Ces) - (4-2)*vct-2) + 2 (431\ucts) Stuct)dt = {'UCE) t. 2 . f (t) = {t+2) 4(4+2) - Ctrljer (4+1) + CE-13°cice- -(4-2) "0c4-2) + (+-3)”uce-3)