In particular, I'm not sure how to choose the parameters of the filter, to best extract out the original signal. I presume that σσ in the Mathematica documentation is the σσ above? I have tried a large number of combinations of the parameters in the filter, but none seem any good at extracting out the original signal.
I have a fear that the amount of noise I am adding means that it is basically going to be impossible to reconstruct the original signal. The histogram of new data looks basically gaussian, so I fear the noise is just swamping the signal.
Does anyone have any ideas here? The thing I am most interested in extracting is the PDF of XX, so if there are any methods that bypass the need to get XX, then I'd also be interested in hearing them. Sorry, I am a complete novice in signal processing.
Data Analysis Video