13.1.8 - Graphical Interpretation
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Practice Questions
Test your understanding with targeted questions
What is the mathematical representation of convolution?
💡 Hint: Think about the integration process and shifting one function.
State one property of convolution.
💡 Hint: Recall the basic properties discussed.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is defined as \( (f * g)(t) \)?
💡 Hint: Recall the definition of convolution.
True or False: Convolution is only applicable to continuous functions.
💡 Hint: Consider the types of functions that can be convolved.
2 more questions available
Challenge Problems
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Given \( f(t) = e^{-t} \) and \( g(t) = t^2 \), find \( (f * g)(t) \).
💡 Hint: Break down the integral into simpler parts to solve iteratively.
Demonstrate that convolution is a linear operation, proving that \( a(f * g)(t) = (af * g)(t) = (f * ag)(t) \) for any constant a.
💡 Hint: Manipulate the integral based on properties of multiplication and addition.
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