13.1.5.3 - Distributive over addition
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Practice Questions
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Define convolution in your own words.
💡 Hint: Think about how two signals can influence one another over time.
What does the distributive property of convolution state?
💡 Hint: Consider the parts involved in the convolution and how they can be simplified.
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Interactive Quizzes
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What is the definition of convolution?
💡 Hint: Think of how two signals interact over time.
Does convolution distribute over addition?
💡 Hint: Recall the formula for the distributive property.
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Challenge Problems
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Given \( f(t) = t \) and \( g(t) = e^{-t} \), compute \( (f * g)(t) \) and verify the result using the Distributive Property.
💡 Hint: Before integrating, think about parts you can simplify.
Show that the output of a system described by the Laplace transform \( F(s) \cdot G(s) \) is equivalent to the convolution in time domain of the functions \( f(t) \) and \( g(t) \).
💡 Hint: Break down each transformation to reveal the convolution aspect clearly.
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