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:
“Maximum Entropy Method without False Peaks with Exact Numerical Equation”, J. Phys.: Conf. Ser., vol. 1438, 012031 (6pp), 2020 https://iopscience.iop.org/article/10.1088/1742-6596/1438/1/012031
"Refreshing idea on Fourier analysis," Proc. IEEE CSPA 2025 https://arxiv.org/abs/2501.03514
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