Practice Associative (13.1.5.2) - Convolution Theorem - Mathematics - iii (Differential Calculus) - Vol 1

Practice: Associative

Lesson 13.1.5.2Convolution Theorem

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6 sample questions

Question 1.
What is the definition of convolution?
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Think about how two functions are combined in the integral.
Question 2.
State one property of convolution.
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Recall the properties that allow rearranging or regrouping functions.
3Question 3.
What does the Convolution Theorem state?
- The product of two functions is always zero.
- The inverse Laplace transform of the product of two functions is their convolution.
- Convolution operates on discrete functions only.
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Think about how transformations relate in the Laplace domain.
4Question 4.
True or False: Convolution is always commutative.
- True
- False
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Recall properties discussed earlier in class.
Question 5.
Given $f(t) = e^{-t}$ and $g(t) = u(t)$ , derive $(f * g)(t)$ using the definition of convolution.
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Substituting u(t-\\tau) might simplify your calculation.
Question 6.
Prove that convolution is commutative, meaning show $(f * g)(t) = (g * f)(t)$ .
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Start from the definitions and apply the properties of the integral.

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