How to determine the dominant length scale for smoothing in a spatial measurement signal?

Hello,

I have a velocity signal along vertical direction in a flow (attached). It is uniformly sampled data with a spacing of 0.2 cm between each point (from y = 1 cm to y = 204.8 cm). I need to understand how I can smooth this signal, specifically what scales should I filter out? My idea was to use a FFT based analysis to understand what scales are dominant in the signal and then filter the ones that cause noise.

How can I do this? Am I thinking in the right direction?

Any help would be appreciated.

TA