Practice Definition Of Convolution (13.1.2) - Convolution Theorem - Mathematics - iii (Differential Calculus) - Vol 1

Practice: Definition of Convolution

Lesson 13.1.2Convolution Theorem

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9 questions

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6 sample questions

Question 1.
Define convolution in your own words.
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Think about how we can mix two different functions.
Question 2.
What does the notation $(f \ast g)(t)$ represent?
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Look at how we express the product of functions in convolution.
3Question 3.
What is the definition of convolution?
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Think about integrating the product of two time-based functions.
4Question 4.
The Commutative property states that $(f \ast g)(t)$ equals which of the following?
- (g \\ast f)(t)
- (f \\ast g)(t)
- (f + g)(t)
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Consider if changing the order matters during addition.
Question 5.
Using the functions $f(t) = sin(t)$ and $g(t) = e^{-t}$ , compute the convolution $(f \ast g)(t)$ . Show all steps.
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Use the identity of sine and consider integration by parts.
Question 6.
Illustrate the behavior of convolution through a graphical representation of $(f \ast g)(t)$ for $f(t) = t$ and $g(t) = u(t)$ over [0, 5].
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Draw graphs and look at how the areas combine. Use numerical integration if needed.

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