Question

A system is given by:      

yt=5xt+1-3

Is the system BIBO stable? Justify

Is the system memoryless? Explain

Is the system causal? Explain

Is the system time invariant? Justify

Is the system linear? Justify

What is the impulse response h(t) of the system?

Is the system internally stable? If you could not figure out h(t) from part f, use the h(t) from the problem below.

ht=5e-tut-u(t-4)

Answer 1

bol: → Jet) 52(t+1-3 (a) BIBO Stability: – det act) = 4(6) bolended input ylt) 5 () 33:46 H€) (54C+0-3] act) YCt? 1 -3 1 Foom figure the amplitude of yct) is finite Hence the The at system is system is B.130 slable (b) Memory. out feet any time y(to) depends upon futiere value of imput X(tot!). Hence memoryless. (C) Causality:- The outfect at any tine depends upon future Vale of input. do system is not callsal. (d) Time inwarlant : act) → y(t) Let there is time shifting input X,(£) + 2(t-to) 4, (+) (6) +52 (t+1)-3 Y(th 55241t-to+1)-3 Now fut tz tto in ylt) 40t-to) => 52(t-to +1-3 = filt) Haben Custom is time iniquit

Fes linearity : Let x 20,(+) => ax(+) 41(t) = 5a 2(t+1)-3 32(t) = b 20 €) 21t) — 56X6H1 -3 Let 33 () = alt) + 620(+) (t) + 533(4+1) -3 port) as 5(ax(t+1) +back+0]–3 Sax(4+1 +5b2(t+1-3 adly, (t) + 82 (+) Hence system is not linear Y(t) = 5 act+1)-3 YLB) = 5x68):ë' -3 HLt) = 5e-turt-U( 6-4) -48 52 8 (f) HC8) 1 е 82 s H68) ► 528-1-siels 82 الم o becaus it has two poles on origin. Hence system is internally stable