Question

Q.5 (a) Show that a linear, time-invariant, discrete-time system is stable in the bounded- input bounded-output sense if, and only if the unit sample response of the system, h[n], is absolutely summable, that is, Alfa]]<00 | [n]| < do ***** (13 marks] (b) Consider a linear, time-invariant discrete-time system with unit sample response, hin), given by hin] = a[n] – đặn – 3 where [n] is the unit sample sequence. (1) Is the system stable in the bounded-input bounded-output sense? Justify your answer. (ii) Determine the unit step response of the system, s[n]. [7 marks]

Answer 1

n=-00 (a) for stable system, E lhems) <co Example, Let him] = {1, 2, 3,} → Ë 166]) = 14243=6200 him is stable L+ () = ? 4(0) ap 10) = + + 1+t+-- > him) is unstable for stable system & hindisoo

nooo ® hens = $(n)a sfm-3) (1) h(n=400,-1] In 62 ) = 1+1=2 <co » system is stable (1) Unit step response so) a hn* un] > sho=[s(n)= s(n-3)* um = sinds un- u[n=]