supplemental code tutorial.jl for my thesis https://tsukuba.repo.nii.ac.jp/records/2000757.
we demonstrate our nonlinear method of time-frequency analysis with a Julia code.
our method is a kind of mode decomposition with general complex functions.
our Julia code works as follows:
time series for analysis. (12 samples)
obtained results.
no.1 backgound noise, no.2&3 frequency of sinusoidal term frq=0.1, no.4 constant term amp=0.01
you will find following values with runnning our code.
please compare our results with the "theoretical limit of time-frequency resolution" of conventional methods.
related works:
``The "theoretical limit of time-frequency resolution in Fourier analysis" is thought to originate in certain mathematical and/or physical limitations. This, however, is not true. The actual origin arises from the numerical (technical) method deployed to reduce computation time. ...''
“Maximum Entropy Method without False Peaks with Exact Numerical Equation”, J. Phys.: Conf. Ser., vol. 1438, 012031 (6pp), 2020
``The standard numerical maximum entropy method (MEM) still uses the Yule-Walker equation which contains rough approximation by Walker. The commonly used numerical equation contains additional modifications to reduce calculation cost. Nowadays, we have powerful computers and there is no reason to use the modified equation. ...''
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