Causality in Signals

Causality in signals means that the output of a system should depend only on the present and past values of the input signal, not on future values. A causal system is a system that satisfies this condition.

y(t) = x(t-2) x(2-t)

In this case, the output signal y(t) depends on both present and future values of the input signal x(t), which violates the causality condition.

Therefore, the correct answer is option 'C' - Non-causal.

Explanation:

To understand why the given signal is non-causal, let's break down the signal equation into two parts and analyze them separately.

Part 1: y(t) = x(t-2)

This part of the signal equation means that the output signal y(t) at present time 't' depends on the input signal x(t-2) at a past time 't-2'. This satisfies the causality condition since the output signal depends only on past values of the input signal.

Part 2: y(t) = x(2-t)

This part of the signal equation means that the output signal y(t) at present time 't' depends on the input signal x(2-t) at a future time '2-t'. This violates the causality condition since the output signal depends on future values of the input signal.

Overall, the signal equation y(t) = x(t-2) x(2-t) is a combination of two parts, one causal and the other non-causal. Therefore, the signal as a whole is non-causal.

Conclusion:

In summary, a signal is causal if the output at any time depends only on the input up to that time. The given signal y(t) = x(t-2) x(2-t) is non-causal since it violates this condition by depending on future values of the input signal.