Summary: A new method is presented of computer processing of amplitude-time records. The method is based on a two-component spectral analysis, suitable for investigating a planar stationary oscillatory event. The method is applied to the study of the fine structure of short-period geomagnetic pulsations. Apart from a semi-quantitative representation of the directional distribution of the pulsation event in the plane of oscillation, the proposed method enables one to obtain quantitative information on the frequency components, representing the pulsation -- the distribution of the overall energy in the spectrum of the pulsation, the ellipticity of the polarization ellipses, the orientation of the major axes of the ellipses, and the sense of rotation of the disturbance vector. In studying the fine structure of the pulsations of the geomagnetic field it is usual to start with the analysis of the spectra of the records in two, or three perpendicular components of the field (X, Y, Z) separately [1, 2]. In these components only the projections of the pulsation event are studied. Their selection is related to the geometry of the magnetosphere and, thus, to the geometry of propagation of HM waves, however, it does not provide a sufficiently representative image of the spatial formation of the disturbance under any conditions. Only by processing the spectra simultaneously in all independent components can one obtain new information, e.g., the polarization characteristics (the ellipticity of the polarization ellipse of the oscillation, etc.) for the frequencies, corresponding to the main peaks in the spectra, in [3]. Processing by computer makes it possible to go into greater detail in treating the spectra. In the present paper the authors describe a new method of spectral analysis, suitable for investigating the planar stationary oscillatory event. Drawing on the spectra of a signal in two mutually perpendicular components, the spectrum of the projection into any chosen direction is computed. On applying this method concretely to the study of the fine structure of geomagnetic pulsations, one can obtain, in the first place, a spatial image of the frequency content of the pulsation (frequency-direction display). It is also possible to obtain a whole series of data on the polarization characteristics of the oscillation in frequencies, corresponding to selected spectral peaks (the frequency components of the pulsation).