This paper introduces the cross-terms in Wigner-Ville distribution to explore the time-frequency mechanism and regular of interaction between Prolate Spheroidal Wave Function (PSWF). By establishing the relationship between time-frequency characteristics of cross-terms and the excellent characteristics of PSWF and its Hilbert signal, the relationship between the cross-terms of PSWF signal and the characteristics of PSWF signal is mainly studied, such as parity feature and the best energy clustering, and the regular of the energy density of cross-terms in time domain, frequency domain, and time-frequency domain is studied. Both the mathematical deduction and simulation result show that the time-frequency characteristics of cross-terms have good symmetry and energy clustering. Meanwhile, the time-frequency localization characteristics of Wigner-Ville distribution have close relationship with the order and power spectrum density of PSWF signal, reflecting the degree of coherence between PSWF signals. Furthermore, those characteristics of cross-terms which are found can provide reference basis for the research on efficient time-frequency detection method for PSWF signal.
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