I have no idea what your spectra look like, however removing truly periodic noise would likely be appropriate for a digital filter, specific a bandstop filter (for best results, specify the name-value pair 'ImpulseResponse','iir' in your bandstop call). The independent variable has to have regular intervals between the elements, however if it does not, first use the resample function to correct that, since the filters require it. After resampling (if necessary) use the fft function to determine the frequency of the periodic signal with enough precision to design the filter.
This is actually much more straightforward than it sounds. For a relatively recent exposition on all of this (although using a command-line filter design), see this Comment.
