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.