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.