The properties of acoustic-gravity waves (AGWs) in the atmosphere can be determined to a greater extent by the features of the propagation medium than by the sources of these disturbances. In the presence of spatial inhomogeneities of atmospheric parameters, significant deviations of AGW characteristics from theory are observed. This complicates the experimental diagnosis of waves and the search for a connection with their potential sources. AGW observations from the Dynamics Explorer 2 satellite indicates the predominance of waves with certain spectral characteristics in the polar thermosphere. It has been found that AGWs with large amplitudes are spatially consistent with areas of strong winds, while AGWs move mainly toward the wind. In order to explain the observed AGW properties, we investigate the filtering of the spectrum of these waves in the presence of a spatially inhomogeneous wind. It is shown that the direction and magnitude of the wave vector change in a special way in the oncoming inhomogeneous wind. In this case, with an increase in the speed of the headwind, the wave vector gradually tilts toward the horizontal plane. The vertical component of the wave vector decreases rapidly, and its horizontal component tends to some threshold value, which is predominant in observations. In addition, in the oncoming inhomogeneous flow, the frequencies and amplitudes of the waves increase. As a result, high-frequency wave harmonics with a small angle of inclination of the wave vector to the horizontal plane and a characteristic horizontal wavelength will prevail in a strong headwind from the continuous spectrum of atmospheric AGWs that can be generated by a hypothetical source. Since the wave vector and the group velocity vector in AGWs are almost perpendicular to each other, such waves provide efficient energy transfer in the vertical direction. In this regard, AGWs play an important role in the energy balance of the polar atmosphere by redistributing the energy of horizontal wind currents in the vertical direction.