Question

4) Fill out the following table just by Yes/No. if you answer is in another paper redraw the table on your answer sheet. System\characteristic Linear Time invariant Memoryless causal stable y(t) = 8x(t -3) + X(t)? y(t) = txt) y = 5x(-t) y(t) = dx(t))/dt (D + 1)x(t) = 2x(t)

Answer 1

sy,CH) - 881(7-3) tacts Ya (t) = 802(t-3) traces ay, ifs + by its = sanit-g) + basit. ta xics + braces Sun weighted of output Suro Not a weighted of input the weighted sum of outputs not produced due to weighted sum of inpurs. Thus, the system is non-linear. Hatt ato fact-to-3) + Xo Ct-to) is=xct-to) = 8ct-to-3fhot-to) e the delayed outpul is equal to ourpul due to delayed input. Thus, the system is Time Invariant. The present output depends on past valas the of inpul Thus, the system is memoly. Nof memory less → Car

output output does not does not present depend on future t the inlues thus, the system is causal ₃ let X(t) = ucts Bounded inpur yat : Suct-3) tucts in un Bounded Bounded = Bounded Hence, Bounded the Bounded output: Thus, input the produced the sustem is Stable 6 yets = tacts . predefined furiction Thes, the sustem is non-linear şey Cus = t-to) xlf-fo) YCHacts=-to) - i mitato) Time variant. since both are not equal Mendly less. Since no past & future valus. causal Let 2CH= UCHS

tules y (t) = - rets un bounded the thas sustem is instable. ② ycts a sx.(-4). [ ancats & brat) ay, cts toys ass = in a • time variant. Since yetlt=t-to & yets x B= x 4-to). Memoly system i At t= -1 y(-) = Sxci) Future veley. non caused system. inpur causal xers = ucts) since Bounded produces bounded output. ych - sunt

gets = dxu ay ist. Abys us = 4 2 linear [ar, cts + 6d243} linear. Time invariant.. Memory since & integral all differentia functions consists of memory. . The present depinde only outpul inpure Thus, the susten on is present causa yo - dче с: «ау = 4сь ) Bounded E SIM unbornded. #be unstable. (6+1)y (= sarts , б )С94 см + 5 ) Linear . = 2усн De Time Invariant memory suffen since differential ean canal stable it is n!