On Spectral Methods in Schumann Resonance Data Processing

Our experience in the processing of time series stems from the processing of magnetotelluric and geomagnetic pulsation data where conditions and aims are different from the processing of Schumann resonances. Nevertheless, several points are common in each of these fields. The major problem when processing time series is mostly the correct selection of the time/frequency resolutions. If one of them is increased, the other decreases. In the case of the Fourier transform, both resolutions are determined — in terms of a dynamic spectrum — by the time dimension of the time/frequency box within which the actual computations are made. In case of convolution filtering (especially if both components of complex vectors are computed), the selection is more versatile. The step in frequency can be freely selected, the independence, however, of the filtered series is only ensured if filters have sufficient length in time what means a corresponding time resolution. If time resolution is to be increased, then the frequency step most be increased (frequency resolution decreased) to get independent time series. Convolution filtering has the advantage that disturbed sections can be easily cut from the filtered series without disturbing other sections, thus the reduction of noise is more effective. Moreover “momentary” spectra can be found in any moment or section. Additionally, an impulsive event can also be resolved independently of possible other impulses in arbitrary position outside of the length of the filter. The same method of convolution filtering can also be used for the complex demodulation of time series, resulting in high precision frequency determination.