Taylor polynomials vs Prony exponentials -Part 1-

Both approximations are beautiful, let us enjoy the math.

Matlab code
https://gitlab.com/effective.sound.so...

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Timestamps
0:00 Intro
2:39 Exponential parameters
4:58 Identifying parameters - system of equations
6:22 Prony’s solution
11:55 Sampling the function
13:15 Avoiding sampling
14:37 Prony expansion
16:31 Simple pendulum
22:04 Pendulum with air resistance

References
The video mainly based on the following digital signal processing papers.

E. Azarov, M. Vashkevich and A. Petrovsky, "Instantaneous parameters estimation algorithm for noisy AM-FM oscillatory signals," 2014 22nd European Signal Processing Conference (EUSIPCO), 2014, pp. 989-993.

Azarov, E.S., Vashkevich, M.I., Petrovsky, A.A. Estimation of the instantaneous signal parameters using a modified Prony’s method. Aut. Control Comp. Sci. 49, 110–121 (2015). https://doi.org/10.3103/S014641161502...


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