Question

Which of the following is a causal system?

(a) y(n) = 3x(n) – 2x(n-1)

(b) y(n) = 3x(n) + 2x(n+1)

(c) y(n) = 3x(n+1) + 2x(n-1)

(d) y(n) = 3x(n+1) + 2x(n-1) + x(n)

I had been asked this question by my school principal while I was bunking the class.

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

Answer 1

Correct option is (a) y(n) = 3x(n) – 2x(n-1)

For explanation: We know that, for a causal system, output must depend on present and past but not on future.

For y (n) = 3x (n) + 2x (n+1), we can observe that output depends on future because of the term x (n+1). Hence, not a causal system.

For y (n) = 3x (n+1) + 2x (n-1), we can observe that output depends on future because of the term x (n+1). Hence not a causal system.

For y (n) = 3x (n+1) + 2x (n-1) + x (n), we can observe that output depends on future because of the term x (n+1). Hence not a causal system.

For y (n) = 3x (n) – 2x (n-1), we can observe that output depends on present and past but not on the future. Hence, it is a causal system.