Question

Which of the following is a dynamic system?

(a) y(n) = y(n-1) + y(n+1)

(b) y(n) = y(n-1)

(c) y(n) = x(n)

(d) y(n) + y(n+1) + y(n+3) = 0

I had been asked this question in my homework.

This key question is from Fourier Series and LTI Systems topic in division Fourier Series of Signals and Systems

Answer 1

The correct choice is (a) y(n) = y(n-1) + y(n+1)

Explanation: We know that for a dynamic system, the present output of the system should depend only on the past output and the future output.

For y (n) = y (n-1), we can observe that output depends only on the past but not on the future. Hence it is not a dynamic system.

For y (n) = x (n), we can observe that output depends on the present. Hence it is not a dynamic system.

For y (n) + y (n+1) + y (n+3) = 0, we can observe that output is a constant. Hence it is not a dynamic system.

For y (n) = y (n-1) + y (n+1), we can observe that output depends only on past and future outputs. Hence it is a dynamic system.