The Paley Wiener Theorem and the Inversion of the Laplace transform

Описание: How do you invert the Laplace transform without a table? This is done through the Paley Wiener Theorem and Fourier transforms. We go through the proof of the Paley Wiener Theorem in this video, which tells us that when we take the inverse transform of certain analytic functions, we get an L2 signal back. This is the converse of the results that we went over in the last video.

This video largely followed a PDF from Friedrich Littmann's homepage. I made a lot of modifications to get the result explicitly in terms of the Laplace transform, since the Paley Wiener theorem is most often communicated as a Fourier result. Littmann's pdf can be found here: https://www.ndsu.edu/pubweb/~littmann...

//Additional Reading
The Paley Wiener Theorems: https://www.ndsu.edu/pubweb/~littmann...

//Exercises


//Watch Next
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(The Other Pailey Wiener Theorem)    • Sampling theory and why I reject a lot of ...  
Undergraduate Intro to the Laplace Transform    • MAP2302 - Definition of the Laplace Transf...  
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0:00 Start
0:56 Where does this signal come from?
3:56 Cauchy's Theorem and Big Rectangles
6:20 FUBINATE!
8:17 What is this L2 Signal?
11:12 What's Next?