# Fast convergence of smoothing of periodic noise

I have essentially periodic data from a simulation (not exactly periodic but is qualitatively fairly periodic), and I'd like to take an average or noise filter of some sort that I can get a well converged average/smoothed value. Ideally I'd like something that converges to a steady value as the square of the number of samples, but am unsure if this is possible. I'd like a filter that for approximately 10000 samples would be almost invariant with any further added points and the filtered value would be converged to approximately machine zero. Is there such a filter? I'd appreciate any help for either specific methods or families of methods I can look at.

Thanks

• Sounds like a good place for a DFT + zeroing high frequency coefficients (assuming you have uniformly sampling points), or maybe a Butterworth filter. But I think you'll get a better answer at the signal processing stack exchange. – user14717 Aug 21 '19 at 11:33
• I didn't know there was a signal processing exchange. I'll check it out! Thanks. – EMP Aug 22 '19 at 10:25