Question

3) Determine whether the systems : a) y En] = 0.5 a[n] + 2.5 u [n-2], lor nyo. b) y In J -_0.25% (n-1) + 0.5u[n+1)-0.47 {n-1} lor nyo causal. are

Answer 1

Causal System Definition ::

In control theory, a causal system (also known as a physical or non-anticipative system) is a system where the output depends on past and current inputs but not future inputs i.e., the output y(t0) depends on only the input x(t0) for values of t < t0.

Solutions ::

(a) y[n] = 0.5*u[n] + 2.5*u[n-2] , n >= 0

Ans :: Given y[n] is only depends on present and previous Inputs Signals . So this is a causal system

(b) y[n] = 0.25*u[n] + 0.5*u[n+1] - 0.4*y[n-1] , n>=0

Ans :: Given y[n] is depends not only on present and previous Inputs Signals but also with future input signals . So this is a non-causal system