Well the data is already recorded, so at this point I am looking at digital solutions. Analog solutions could prove useful for next time though.
I have a relatively short signal sitting on a relatively long (and noisy) window, with the 50kHz (actually more like 45 to 60 kHz) being the part of the noise that interferes the most with my signal. I care about the noise during and right before or after my signal.
Something like a notch filter seems to create too many aberrations to be useful (admittedly I haven't tried all possible implementations). I've tried identifying the phase of the ~50kHz and substracting a sinusoid with same amplitude, but the phase is only stable for some 400 μs before some transient behaviour changes it in some random way, as far as I can see.
For the time being, the best solution I've found is to "flatten" the 50kHz peak in frequency space; it does reduce the contribution of that noise without affecting my signal, just not quite enough.
Worst part of this is that trying to read the research on the topic is very frustrating, because for some reason signal processing comes associated with different terminology depending on the area it is being applied to.
Any idea what a denoiser does, exactly?