References for the bandpass and highpass filters in CDO
Added by Lyndon Mark Olaguera over 7 years ago
Hi all,
I am using the bandpass command in CDO. I would like to properly document this method. Where can I find the reference of the equations in these functions especially the bandpass and higpass filters?
Many Thanks
Replies (2)
RE: References for the bandpass and highpass filters in CDO - Added by Ralf Mueller over 7 years ago
did you check the docu ?
RE: References for the bandpass and highpass filters in CDO - Added by Uwe Schulzweida over 7 years ago
Hi,
the bandpass filter implementation in cdo uses a standard top-hat filter response function, i.e.
1; if f_1 < f < f_2
H(f) = 0; else.Where the frequency window [f1,f2] passes the filter. Frequency smaller than f_1 or larger than f_2 are suppressed.
Technically,- the timeseries x_i(t) at every grid point is transformed to Fourierspace, i.e. S_i(f) = FFT)
- the FFT S_i(f) is multiplied by H(f) to filter the data: S’_i(f) = H(f) S_i(f)
- S’_i(f) is transformed back x_{filtered}(t) = INVERSE_FFT(S’_i(f)).
For reference, you can check any textbook on Spectral analysis of time series, for instance
Von Storch, H and Zwiers, F: Statistical Analysis in Climate Research, Cambridge University Press 2003 (474pp.) [for an applied climatological point of view]
Buttkus, B: Spectral Analysis and Filter Theory in Applied Geophysics, Springer 2000 (667pp.) [for a more rigid mathematical approach]
Best Regards,
Cedrick