Practice Evaluation Techniques For Convolution Integrals (13.8)

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6 sample questions

Question 1.
What is the equation for convolution?
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Think about how we express relationships between two functions.
Question 2.
What are the two main methods for evaluating convolution integrals discussed?
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Recall how each method approaches the problem.
3Question 3.
What is the convolution integral of two functions?
- 0
- (f * g)(t)
- (f ∗ g)(t) = ∫0^t f(τ) g(t−τ) dτ
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What is the basic formula for convolution?
4Question 4.
Using Laplace transforms gives what advantage?
- True
- False
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Think about the complexity of integration versus multiplication.
Question 5.
Evaluate the convolution of f(t) = e^(-t) and g(t) = sin(t) using both methods.
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Consider what integration techniques might be necessary.
Question 6.
Prove that using Laplace transforms reduces the time complexity for convolutions in certain systems.
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Focus on how both systems can be represented in frequency versus time domains.

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