Question

Which of the following system is not stable with input \( x(n) \) and output \( y(n) \)?

• A. \( y(n) = 20 \sin(x(n)) + 10 \)
• B. \( y(n) = e^{x(n)} \)
• C. \( y(n) = \sum_{k=-\infty}^{n} x(k) \)
• D. \( y(n) = \sum_{k=-2}^{2} x(n - k) \)

Hint:

Exponential functions are often unstable unless specifically controlled.

Answer 1

The Correct Option is B

For a system to be stable, the output must be bounded for a bounded input. The system \( y(n) = e^{x(n)} \) is not stable because the exponential function grows rapidly with increasing \( x(n) \). Therefore, even for a bounded input, the output can become unbounded, violating the stability condition. Hence, the correct answer is option (2).