Applying MATLAB in the design of digital filters for selecting Pc5 geomagnetic pulsations

The paper considers a design procedure of an optimal nonrecursive bandpass digital filter with a finite impulse response (FIR-filter) using the MATLAB Filter Design tool and the method of best uniform (Chebyshev) approximation. The filter helps solving the problem of extracting Pc5 geomagnetic pulsations from a data set of geomagnetic field measurements. This type of pulsations was chosen due to the availability of 1-second data in a widely spaced network of ground-based geomagnetic observatories with standardized ground-based geophysical equipment. After proper processing, these data can be used in a detailed analysis of: the disturbance properties in the Earth's magnetic field in the range of long-period pulsations; the nature of the interaction of waves and particles in the magnetosphere. The results of this analysis can be used, for example, in calculating a space weather forecast, which makes this work relevant. The problem of selecting Pc5 ripples is solved by passing the original data set through a band-pass FIR filter with the required characteristics depending on the range of the Pc5 ripple period – 150÷600 seconds. Hereof it follows the limits of the bandwidth equal to 1.7÷6.7 mHz. The choice of a non-recursive band-pass FIR filter is due to the possibility of providing a linear phase-frequency characteristic that excludes phase distortions at the output of the FIR filter; stability by definition of this type of filters. The first condition also ensures that there are no requirements for the phase response of the FIR filter. The operability of the obtained digital filter is demonstrated on the example of processing a real set of measurement data of the geomagnetic field state obtained from the Lycksele geomagnetic observatory (Sweden, Geological Survey of Sweden, international IAGA code LYC), which is a part of the INTERMAGNET international network. The necessary information about this observatory is available on the Internet: https://www.intermagnet.org. Bandpass FIR filter design and calculations were carried out in MATLAB R2022b.