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GATE 2015 EE (EE2) – Question 44

Signals and Systems · Linear time invariant and causal systems · 2 marks · Multiple choice

For BIBO-stable LTI systems, which statement is true?

  1. The impulse response is integrable but need not be absolutely integrable.
  2. The impulse response must have finite support.
  3. The step response must be absolutely integrable.
  4. The step response is bounded.

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Show answer and explanation

Correct answer: (D) The step response is bounded.

Explanation

The unit step is a bounded input. By the definition of bounded-input bounded-output stability, its output must be bounded. Hence **D**. For ordinary continuous-time convolution systems the impulse response is absolutely integrable, but it may have infinite duration; the step response can approach a nonzero constant and need not be absolutely integrable.

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