A method for detecting equidistant frequencies in the spectrum of a wideband signal

Examples are presented of using a signal processing technique that allows equidistant frequencies to be detected in broad-band oscillation spectra. This technique is based on analyzing the amplitude and phase correlation functions (APCF) of the oscillations. Equidistant frequencies can be detected in any broad-band spectrum based on the presence of periodic peaks related to such frequencies in APCF functions. An example of processing 1D resonator oscillations serves to show that the relationship between the eigenfrequencies in the spectrum and the APCF function peaks is similar to that between the optical grating slits and the interference line image on the screen. The proposed signal processing technique allows the difference between two adjacent frequencies of such a "grating" to be measured. The same analogy is true for a 2D resonator. In the latter case, two equidistant eigenfrequency gratings are shown to be present in the spectrum. Each grating corresponds to the eigenfrequencies of a 1D standing wave along each of the coordinates of a 2D resonator. The effect of small non-equidistance of the eigenfrequencies on the distortion and the location of the correlation function peaks is examined. The examples of processing two 1-h intervals of geomagnetic pulsation records are used to demonstrate the applicability of the APCF technique for real recorded magnetospheric oscillations.