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The impulse response of a linear time invariant system is a unit step function. The transfer function of this system would be
- a)1
- b)1/s2
- c)s
- d)1/s
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The impulse response of a linear time invariant system is a unit step ...
Impulse response,
c(t) = u(t)
We now that,
(impulse response) - Transfer function = 
∴
c(t) = u(t)
We now that,
(impulse response) - Transfer function = ∴
Most Upvoted Answer
The impulse response of a linear time invariant system is a unit step ...
Explanation:
Impulse Response:
- The impulse response of a system is the output of the system when an impulse function is given as input.
- In this case, the impulse response is a unit step function, which means that the output of the system is a step function when an impulse is applied.
Transfer Function:
- The transfer function of a system is the Laplace transform of the system's impulse response.
- Since the impulse response is a unit step function, its Laplace transform would be 1/s, where s is the Laplace variable.
Relation between Impulse Response and Transfer Function:
- The transfer function H(s) is the ratio of the output Y(s) to the input X(s) in the Laplace domain.
- Therefore, if the impulse response is h(t), the transfer function H(s) is given by H(s) = L{h(t)}, where L{} denotes the Laplace transform.
Conclusion:
- Given that the impulse response is a unit step function, the transfer function of the system would be 1/s. This is because the Laplace transform of a unit step function is 1/s.
- Hence, the correct answer is option 'D': 1/s.
Impulse Response:
- The impulse response of a system is the output of the system when an impulse function is given as input.
- In this case, the impulse response is a unit step function, which means that the output of the system is a step function when an impulse is applied.
Transfer Function:
- The transfer function of a system is the Laplace transform of the system's impulse response.
- Since the impulse response is a unit step function, its Laplace transform would be 1/s, where s is the Laplace variable.
Relation between Impulse Response and Transfer Function:
- The transfer function H(s) is the ratio of the output Y(s) to the input X(s) in the Laplace domain.
- Therefore, if the impulse response is h(t), the transfer function H(s) is given by H(s) = L{h(t)}, where L{} denotes the Laplace transform.
Conclusion:
- Given that the impulse response is a unit step function, the transfer function of the system would be 1/s. This is because the Laplace transform of a unit step function is 1/s.
- Hence, the correct answer is option 'D': 1/s.
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