I am in the starting phase of a master thesis and are having some trouble finding a good starting point in the literature for my thesis. The aim of my thesis is to provide as good of an estimate as possible to an underlying constant signal, given measured data with periodic noise. My degree is in informatics, with a specialization in machine learning, so I don’t have a strong background in signal processing.
The naïve approach is to just take the average of the measured data, it’s clear that the main issue with this approach, is the effect of incomplete wavelengths. Of course if one could measure long series the periodic noise would average out, the goal of my thesis is rather to see how short it is possible to measure and still accurately estimate the underlying mean value. A more sophisticated approach is to apply a filter before averaging the signal, but most filters are designed for this purpose so it is not clear which filters would be best suited. Many filters does not alter the average at all, but what we need is to flatten out the waves such that the incomplete waves at the ends does not affect the signal. One approach is tapering the edges of the signal, but we haven’t found any literature on that approach.
we will look into how to model the periodic noise as sine waves and then subtracting the periodic noise from the measured data. This approach works very well if you know the frequencies of the periodic noise but seems harder to do if little is known about the periodic noise.
I have looked a bit into using the autocovariance to sample the signal such that each wave top is accompanied by a wave bottom. I had a bit of an unfounded hunch about Fourier analysis, but it seems our signal might not be of sufficient quality for this. In any case, I just need to find some literature tackling this problem, so I have some background on the solutions others have made before.
I would think this is a problem occurring with many different measurements, and that it would have been tackled by someone previously, but I seem to have a bit of trouble navigating the literature.