Something interesting from class - HW2
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Max Woesner
Homework #2 - Something interesting from class
The Linear Time Invariant System Game can be used to help us understand the impulse response of a linear time invariant system.
Input | Linear Time Invariant System | Output | Reason |
Given | |||
Time Invariance | |||
Proportionality | |||
Superposition |
where for any and is the convolution integral.
We can expand the game further.
Input | Linear Time Invariant System | Output | Reason |
Given | |||
Time Invariance | |||
Proportionality | |||
Superposition | |||
Superposition |
Let , so and
Therefore
This tells us that is the eigenfunction and is the eigenvalue of all linear time invariant systems.
This amazing conclusion makes solving linear time invariant systems (the only systems we are really able to solve) so much simpler that we usually approximate real-world nonlinear problems as linear systems so we can solve them.