Insight into the Fourier Transform Band Pass Filtering Technique

In this work theoretical foundations of the Fourier Transform Band Pass Filter (FTBPF) technique are developed which show that such procedure is applicable to extraction of irregular monochromatic oscillations with time-varying amplitudes and phases from the analyzed signal data. Considerations concerning the statistical error of the FTBPF coherence between two filtered oscillations are included. Further certain method of the filter pass-band width parameter determination is proposed and relation between applying the FTBPF to realvalued signals and forming the so called complex-valued analytic oscillations based on the Hilbert transform is indicated.