Jan, I don't know how much is required to get at the primary spectral components.

This paper applies the technique to the same kind of geophysical time-series data
https://www.researchgate.net/publication/318821331_Tidal_Analysis_Using_Time-Frequency_Signal_Processing_and_Information_Clustering

The multitaper method does reduce the noise background so therefore might lift out some of the weaker spectral lines. However it doesn't do much with respect to the strongest.
![](https://imagizer.imageshack.com/img922/1386/mSHsSq.gif)

This appears to be the most impressive approach I have come across
"Application of stabilized AR-z spectrum in harmonic analysis for geophysics"
https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018JB015890


Perhaps I should be using MM to recover the time-series? The plain Fourier series works well for me so I don't know what else it will add at this level. For example, I already know that the signal is heavily aliased, but this is due to a physical aliasing not related to sampling aliasing. The spectral leakage caused by having signals of 27.2122, 27.312, 27.554 so closely separated may not be a factor if the time series is long enough. In any case, the physical aliasing separates these as 2.37, 2.715, and 3.91, which are much more widely separated. I think that is what is causing all the confusion in the first place -- the fact that no one is aware that nonlinear physical aliasing is occurring. Maybe get that point across first and then we can use more advanced spectral techniques. I don't think I am missing anything but who knows.