In order to estimate the Butterworth bandpass filter parameters (the order and cutoff), 2 types of time series are considered to find the best compromise between a typical time series with high-frequency noise, and another where a single GLE event occured. We want the order and cutoff to closely approximate the hourly mean in both cases, while still significantly improving the signal-to-noise ratio.
BW filter = 1 / SQRT( 1 + [ F / Fc ]^2N ), F is the frequency, Fc the cutoff frequency, and N the order.
The filtered time series y'(t) = FFT( FFT(y(t), -1) * filter, 1 )
Six stations are used, 2 of which have a high rigidity, the other 4 have very low rigidity:
|20 Jan 2005 GLE|