Question

A system defined by the difference equation $y(n) = x(-n)$ is:

• A. Casual but not stable
• B. Non-casual but stable
• C. Casual as well as stable
• D. Non-casual as well as not stable

Hint:

Remember, a system is non-casual if it depends on future values of the input. Stability means that the system will produce bounded outputs for bounded inputs.

Answer 1

The Correct Option is B

To analyze this system, we need to determine whether it is casual and stable.
- A casual system is one where the output at any time $n$ depends only on present and past values of the input. Since the difference equation defines $y(n)$ in terms of $x(-n)$ (a future value of the input), this system is non-casual.
- A stable system is one where bounded input always produces a bounded output. In this case, the system is stable because the output remains bounded as long as the input is bounded, despite being non-casual.
Therefore, the system is non-casual but stable.