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Backgrounds of adaptive Fourier transform and analytical wavelet transform have been briefly described in comparison with traditional Fourier transform using a time window. As an example, all three transforms are used to analyze quasiperiodic wave-like processes in the ionosphere, which accompanied the passage of the solar terminator and rocket launch from the Plesetsk site. The advantages of adaptive Fourier transform and analytical wavelet transform as compared to traditional Fourier transform, which make it possible to reliably detect wave-like disturbances against a background of noise at a signal-to-noise ratio not less than 0.1, have been demonstrated.
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Leonid F. Chernogor (2008) studied this question.
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