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(A): If the impulse response of a network is available, the response to any arbitrary input can be derived.
(B): The laplace transform of unit impulse is unity.
(B): The laplace transform of unit impulse is unity.
- a)Both A and R are true and R is a correct explanation of A
- b)Both A and R are true but R is not a correct explanation of A
- c)A is true but R is false
- d)A is false but R is true
Correct answer is option 'A'. Can you explain this answer?
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(A): If the impulse response of a network is available, the response t...
Statement A: "If the impulse response of a network is available, the response to any arbitrary input can be derived." This statement is true. The impulse response of a network represents the output of the network when an impulse function (Dirac delta function) is applied as the input. The impulse response provides a complete characterization of the network's behavior. By convolving the impulse response with an arbitrary input signal, the response of the network to that input can be determined. This property is known as the superposition principle.
Statement R: "The Laplace transform of the unit impulse is unity." This statement is true. The Laplace transform of the unit impulse, also known as the Dirac delta function, is equal to 1. The Dirac delta function is defined such that its integral over the entire real line is equal to 1. When applying the Laplace transform to the Dirac delta function, it results in a constant function with a value of 1.
Since both statements A and R are true, and statement R provides a correct explanation for why the impulse response allows the derivation of the response to arbitrary inputs, the correct answer is A: Both A and R are true, and R is a correct explanation of A.
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(A): If the impulse response of a network is available, the response t...
Explanation:
Impulse Response of a Network
- The impulse response of a network provides a complete description of how the network responds to an impulse input.
- By convolving the impulse response with any arbitrary input signal, we can obtain the response of the network to that input.
Deriving Response from Impulse Response
- If the impulse response of a network is known, we can derive the response to any arbitrary input by convolving the input signal with the impulse response.
- This is a fundamental concept in signal processing and system analysis.
Laplace Transform of Unit Impulse
- The Laplace transform of a unit impulse is indeed unity.
- This property is often used in the Laplace domain to simplify calculations and analysis of systems.
Conclusion
- Therefore, both statements (A) and (B) are true.
- Statement (A) correctly explains that knowing the impulse response allows us to derive the response to any input signal, and statement (B) is also true in stating the Laplace transform of a unit impulse.
Impulse Response of a Network
- The impulse response of a network provides a complete description of how the network responds to an impulse input.
- By convolving the impulse response with any arbitrary input signal, we can obtain the response of the network to that input.
Deriving Response from Impulse Response
- If the impulse response of a network is known, we can derive the response to any arbitrary input by convolving the input signal with the impulse response.
- This is a fundamental concept in signal processing and system analysis.
Laplace Transform of Unit Impulse
- The Laplace transform of a unit impulse is indeed unity.
- This property is often used in the Laplace domain to simplify calculations and analysis of systems.
Conclusion
- Therefore, both statements (A) and (B) are true.
- Statement (A) correctly explains that knowing the impulse response allows us to derive the response to any input signal, and statement (B) is also true in stating the Laplace transform of a unit impulse.
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(A): If the impulse response of a network is available, the response to any arbitrary input can be derived.(B): The laplace transform of unit impulse is unity.a)Both A and R are true and R is a correct explanation of Ab)Both A and R are true but R is not a correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer?
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