Try with the first differencing filter which keep only the high frequencies and throw up the periodicity. It will keep the fluctuations over the periodicity. What is the periodicity ? (hourly, daily, seasonally etc)

Thanks for your reply sir. Actually I have a porous media liquid infiltration data and the periodicity is in micro seconds as pore size is in microns. Presently I did fourier series data fit for my data. I am sorry I made a mistake in my question. Actually I wish to have time variable periodic fit eqn. But in one of my fit error at some instants is above 40 % although R-Squared value is 0.87 for the fit. I am using 8th terms in fourier series. Please suggest some way to minimise error.

Thanks & Regards,

Bharat

Dear collegue:

1) I suppose that you have a set of "N" points in an X-Y "plane", and in each point [xk;yk] a phenomena succed in an "occurrence time" tk. Also, the N values in the series tk results periodic in time, with period "T".

2) The average of the entire tk set can be realized by the "arithmetic mean" = SUM(tk) / N, and its standard deviation SIGMA = SQRT(VARIANCE) calculated from VARIANCE = - ()2 as usual. This average represents the complete set of N points, which can cover several periods T.

3) If you need averaging points belonging only to "one" period, first you need to identify a subset of "n" t-values within the period, and perform the averages summing over n-points instead of summing over N-points as in 2).

4) In both situations, the averaging can be performed if the data are evenly-spaced in time or not.

5) ¿Perhaps do you want to calculate an average "vector" ? If it is the case, the average "vector" is calculated as = [:], and a similar procedure as before can be used for the "variance-vector".

Good luck.

Leonardo NICOLA SIRI: [email protected]

Thanks for your reply Prof. Siri. I appreciate your detailed reply. I will try out your suggestion.

Thanks & Regards,

Bharat

If you have a trigger/key phasor for each period, then you may want to consider re-sampling the data synchronously with your period trigger, prior to averaging.