Spectral property of prolate spheroidal wave functions signals after operation

Prolate spheroidal wave function(PSWF) with the best energy concentration in time and frequency domain have natural advantages in improving spectral efficiency and reducing interference of inter-frequency. Since the spectral of PSWF varies during engineering practice such as signal detection, signal amplification and filtering, the spectral property of PSWF signal after addition, multiplication and convolution is analyzed. Moreover, some change rules of PSWF after operation are summarized, as well as the influence from operation between PSWFs to the using of PSWFs in engineering practice are analyzed, which provides the theoretical foundation for the research of PSWF signals.