Question

Q2 (a) Given the signal x(t) and system h(t) as presented in Figure Q2(a). Determine the output y(t) using the graphical representation of convolution integral. (7 marks) x(1) h(t) 1 e-'u(t) e-2 (1) 0 Figure Q2(a) Q2 (b) Consider a system as shown in Figure Q2(b). t2 - 1 x(t) y(t) Advance by 1 second Х Figure Q2(b) Find the input-output relation between x(t) and y(t). (i) (1 mark) Examine whether the system is time variant or time invariant. (5 marks) (iii) Determine the linearity and causality of the system. (7 marks)

Answer 1

è tuct] -2.1 (a C UG 2.2.4) = het) 9 ct) = tice) NCH) Ly convolution. t 964) = hc+) ¥ x64) - Shee) 264-2782. oo heef and act) both are causal Signals h(+), 16+) =0 to so; - Convoldhoninreguat teduced to YCH) = hét)#26+) -ct-2) or t Sez dr. = $j 2 C2-12;-t atar.

e or. ēt ēt - + + fourtya y (+) ē е, e -7 et et_ 1] - lētiepty for +Eo This Jy (+) =ēt- et u(t) HP bo) 26t) I sec e. bo) Advance by 964) a) yc+) = 2C++0x148) ote due to delated infot g (tj I) = T [QCH+1)?__xchU] YCHT) = [2(t+1-T)-2 C++1-1) if the old is delayed by yet-T) = (4-1)*2(t+1=1)- 26421-5 T Sec toe get,

Date:. Thes 94, 7) = 264+1-T) (+-1). y C3-T) = 204+1-1) ((4-1) 2-1) 4C-T) # 9C, 1) System time variant since يا Ult four input act) Let olp is yit) Yict) H1(4+1)(+21) for in input K2 (+) 이P YQCP) = 22 C++1) C42-1). weighted sum of our ayı (t) tayz (+)=Y+) 43Ct) = e(+21) Cax, Ch+)+629 C++.]] Olp doe to weighted Som of inp 20% (+) + 642 () cis YA (+) So, 9464) = (42-) ( 991c+ ) 46CHI) | Uz [+) = 44 ) its Since alteco s482 four t=0 4 (0) = n(i) - tal YC!) = x (I) <) Since old depends future Value of input dence system is Thon caused on