Question

(d) [5] The input-output relation for DT system is described by following system equation y[n] = 31[] State if the system possesses the following properties: Linear BIBO-Stable Casual Memoryless Time-Invariance

Answer 1

ym]: eval Lineal ft! ->48) PgF) ->yglt) 2461 +27H) —> YiH) + 4 H) So fè ou les input y,( na e324() 29 (n) input 4.102: Bo ogro) 3(04m pagini) 24 (67) + Xolm) input ym) - e" 30(13062cm? # 4, 601+ yg in) So, System is not dinery

Moneyless: System is sedd to be memeyless it for artput, it is not sequired to store previous Input values Se yon esain Output depends on the input that is opplied at the time instant where we see the aitput So, System is memory less Causal :- = 16 cutput depends on paesent input and pastinputs but not future inputs So y(n): 3e 3an) autput only depends on present input Systern los Causal BIBO Stability : banded input should always give bounded cutput Curtput is exponential fronchon os input truly esegling the stability of the system depends 05 nature on (ie, absolute stability? I but is the input is branded then the artout is also bounded (ie, 300) So the System is BIB0 stable

ance Time Invariance If the autput is shifted by k then the gesetting is same as the artpit obtained if the input is shifted by K' then the system is time invanant 966)2 ne Baln) g(n-k) 2 3 x(n-k) > (output shifted Shifted input is applied to systeme bs O ocen -|_) - Sustem F yn me inva y662 2 e 30[n-K) sa so System is time Verant -
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