Practice Example 3: Piecewise Convolution (13.11)

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6 sample questions

Question 1.
Define a piecewise function using f(t) = {1, 0 ≤ t ≤ 2}, g(t) = {t, t ≤ 2}. What is the convolution for t=1?
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Check the function definitions for limits.
Question 2.
What does g(t) represent in our example?
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It increases linearly.
3Question 3.
What is the convolution of two functions used for?
- To modify input
- To produce an output combining two functions
- To find echoes
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Remember the principle of convolution.
4Question 4.
For t ≤ 1, what is (f ∗ g)(t)?
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Evaluate the integral properly!
Question 5.
Given f(t) = {2, 0 ≤ t ≤ 3} and g(t) = {t, t ≤ 3}, compute (f ∗ g)(t) for t = 2.
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Make sure to correctly align the limits according to the piecewise definitions.
Question 6.
Design a piecewise function where f(t) = sin(t) for 0 ≤ t ≤ π; how does this affect convolution with g(t)?
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Visualize the changes in the sine function.

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