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The impulse response of a linear LTI system is given as g (t) = e(-t)The transfer function of the system is equal to:
  • a)
    1/s
  • b)
    1/s(s+1)
  • c)
    1/(s+1)
  • d)
    s/(s+1)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The impulse response of a linear LTI system is given as g (t) = e(-t)T...
Answer: c
Explanation: Impulse response is just the Laplace transform of the transfer function and the response is just the Laplace transform of the forward path block.
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The impulse response of a linear LTI system is given as g (t) = e(-t)T...
Impulse Response and Transfer Function

The impulse response of a linear time-invariant (LTI) system describes the output of the system when an impulse input is applied. It is denoted by g(t). The transfer function of the system, denoted by H(s), relates the Laplace transform of the input to the Laplace transform of the output.

Given Impulse Response

The given impulse response is g(t) = e^(-t). This means that when an impulse input is applied to the system, the output is the exponential decay of the impulse over time.

Determining the Transfer Function

To find the transfer function of the system, we need to take the Laplace transform of the impulse response. The Laplace transform of e^(-t) is 1/(s+1).

Therefore, the transfer function of the system is H(s) = 1/(s+1).

Answer

The correct answer is option 'C': 1/(s+1).

This means that the transfer function of the system is 1/(s+1), which relates the Laplace transform of the input to the Laplace transform of the output.
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