Question

The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system \( S \). The output is observed to be the continuous-time unit step signal \( u(t) \). Which one of the following statements is true?

• A. On applying any input signal to \( S \), the output signal is always unbounded.
• B. It is possible to find a bounded input signal which, when applied to \( S \), results in an unbounded output signal.
• C. Every bounded input signal to \( S \) results in a bounded output signal.
• D. On applying any input signal to \( S \), the output signal is always bounded.

Hint:

In LTI systems, the output may be bounded for a bounded input in many cases, but under certain conditions (such as resonance), the output can become unbounded even if the input is bounded.

Answer 1

The Correct Option is B

Step 1: The system \( S \) is linear and time-invariant. The response of the system to a unit impulse \( \delta(t) \) is the unit step signal \( u(t) \), which is known to be a bounded signal.
Step 2: The system \( S \) may exhibit a bounded output for some inputs (such as \( u(t) \)), but there are cases where a bounded input can lead to an unbounded output, especially if the system has an unstable behavior or certain resonance conditions.
Thus, the correct answer is that it is possible for a bounded input to result in an unbounded output.