13.1 - Convolution Theorem
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Practice Questions
Test your understanding with targeted questions
What is the definition of convolution?
💡 Hint: Look for the integral definition.
State one property of convolution.
💡 Hint: Think about the order of functions.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the formula for convolution of two functions?
💡 Hint: Review the definition provided in this section.
Is the Convolution theorem commutative?
💡 Hint: Think about as addition works.
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Challenge Problems
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Given \( f(t) = e^{-3t} \) and \( g(t) = t^2 \), find \( (f * g)(t) \).
💡 Hint: Consider using substitution for \\( t - \\tau \\).
Calculate the Laplace Transform of the convolution of two functions, where drivers are \( f(t) = u(t) \) and \( g(t) = u(t - 3) \) and verify the Convolution Theorem.
💡 Hint: Remember the properties of the Heaviside unit step function.
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