Practice Analytical Convolution: Direct Integration (2.1.3.4) - Time Domain Analysis of Continuous-Time Systems
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Analytical Convolution: Direct Integration

Practice - Analytical Convolution: Direct Integration

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the convolution of an exponential signal e^(-at) with itself?

💡 Hint: Consider the limits when both functions are valid.

Question 2 Easy

Define the unit step function and its significance in the convolution process.

💡 Hint: Think about the behavior of signals before and after time t = 0.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does convolution allow us to compute in LTI systems?

The frequency response
The output given the input and impulse response
The input given the output

💡 Hint: Think about how systems react to known impulses.

Question 2

True or False: Applying the convolution integral involves flipping one of the functions involved.

True
False

💡 Hint: This is part of the process you learned earlier.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given x(t) = cos(at)u(t) and h(t) = e^(-bt)u(t), compute the resulting convolution. What are the challenges you face in the process?

💡 Hint: Think about how you might approach integrating an oscillatory function.

Challenge 2 Hard

For the functions x(t) = u(t) - u(t-5) and h(t) = e^(-at)u(t), determine the output. Discuss any peculiarities in the result.

💡 Hint: Focus on how the step functions change the limits of active signal contribution.

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Reference links

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