10.10 - Convolution Integral and System Linearity
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Practice Questions
Test your understanding with targeted questions
Define the convolution integral in your own words.
💡 Hint: Think about how functions can be combined in mathematics.
What is an impulse response function?
💡 Hint: Consider the response of a system to a sudden force.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the convolution integral compute in an LTI system?
💡 Hint: Consider what we are trying to determine about the system.
True or False: The principle of superposition applies to all systems, including non-linear.
💡 Hint: Review linear vs. non-linear characteristics.
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Challenge Problems
Push your limits with advanced challenges
Describe the process of applying the Duhamel integral to analyze a building’s response to an earthquake, including mathematical formulation.
💡 Hint: Focus on the relationship between the ground motion and the system's impulse response.
Given a non-linear system with a specific input, explain why the convolution integral cannot be directly applied and suggest an alternative approach.
💡 Hint: Think of what characterizes non-linear systems and alternative mathematical solutions.
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