Test the following systems for causality Y1 13xn xn 2 Y2

Test the following systems for causality. Y_1 = 1/3(x[n] + x[n -2]) Y_2 = 1/3(x[n + 1] + x[n] + x[n -1])

Solution

A causal system is the system whose output at any time depends only on the present and past values of the input but not the future inputs.

i) Y1 = 1/3 (x[n] + x[n-1] + x[n-2])

From the definition of causal system, this sytem have only present ( x[n] ), and past ( x[n-1], x[n-2] ) inputs and does not have future inputs. So, this system is causal.

ii) Y2 = 1/3 (x[n+1] + x[n] + x[n-1])

This system has future input (x[n+1]) along with the past (x[n-1]) and present (x[n] inputs. So, it is not a causal system.