Registration of the wave processes in atmosphere/ionosphere is linked with the difficulty of recognizing of the wave disturbances against the background of powerful low-frequency trends of atmospheric/ionospheric parameters. The generally accepted approach for selection of a wave under such conditions is exclusion of a trend from original data series. Different groups of the authors use various methods of trend approximation that causes different wave profiles at the output. Especially noticeable differences appear in the spectral domain, in which, depending on the method of trend fitting, various spectral components of the wave process are amplified or suppressed.

                        The goal of present work was to develop a correct method for decomposing signal on a trend and wave process for the case when the trend and the wave are separated in the frequency domain (which is typical, in particular, for acoustic and gravity waves in the Earth's thermosphere). Used research methods were the digital signal processing and spectral analysis.

                        Physical approaches and mathematical methods for data processing were developed. Verification of methods was performed on the model data sets. The problem of estimation of the error inserted to wave characteristic by data decomposition procedure was formulated and solved for the first time. For this purpose the error analysis was transferred from the spatial-temporal domain to the spectral one. On atmospheric acoustic and gravity waves scales the error of the wave spectrum resolution is 1–5 %. This error arises from the basic principles of frequency estimation on finite data interval and could not be eliminated due to “more thorough” data processing. The nature of difficulty of signal decomposition on trend and wave was revealed; it is caused by the trend spectrum spreading that is an artifact of digital signal processing. The solution of the problem of wave disturbance selection was realized using dual data filtering. At the first stage a rough exclusion of the trend was done. This stage aimed on the elimination of trend and wave spectrum overlapping upon the condition that algorithm of trend exclusion doesn’t distort the frequency range of the useful signal. At the second stage the residual data series were passed through an ideal filter tuned to the frequency band of the wave process.

                        After appropriate adaptation the developed data processing method could be applied to the analysis of remote observations of the ionosphere and in other data mining areas.