10/08 - Mechanics of Convolution & Fourier Transform
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Mechanics of the Convolution
Remember from the game:
We will also denote the convolution as
|The order of integration switched due to changing from|
- In this case, we are doing the FSMI to
- If isn't involved, then you can plug n chug with the integral. The u(t) will change the limits, which can be impractical to evaulate if you have more than 2.
- ? Does it matter which one you FSMI?
Convolution: A visual approach
- Flip: Flip one about the dependant axis
- Shift: The initial flipped function is at . Shift this function for the multiply & integrate
- Multiply: Multiply the two functions
- Add/Integrate: You may need to make multiple equations for different intersections