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Pseudo Wigner-Ville Distribution for discrete and finite real sampled signals

Alejandro R. Urzúa (2020)

This repository contains the research on the application of Pseudo Wigner-Ville Distribution, hereafter PWVD, for the analysis of real sampled signals who are discrete ($N$-time points) and finite ($N<\infin$, bounded).

This research started as of 2012 when I was working on my bachelor's thesis implementing PWVD for the analysis of vibrational machine signals. Since then, the algorithms and analysis go stacked. Now, on lated 2020, I want to take again the subject and work it out.

(Possible) Roadmap:

  1. Translate the Fortran and Mathematica codes to Julia

  2. Optimize for $N$ values greater that $8192$. (Who is the maximum data points achieved with some reasonable performance with the Fortran code. Mathematica can manage up to $4096$ data points, but in a ridiculous long time.)

  3. Implement some other discrete filters and smooth-windows for the final representation. (Currently, Hamming filter and Gaussian smoothing window are implemented.)

  4. Extend the analysis for datasets with $N$ unrestricted to $2^n$. (Condition imposed by the discrete and finite Fast Fourier Transform.)

  5. Some other unreal goals goes here

Theory goes here