Abstract
In this paper, we discuss the relations among the random process, the Wigner distribution function, the ambiguity function, and the fractional Fourier transform (FRFT). We find many interesting properties. For example, if we do the FRFT for a stationary process, although the result in no longer stationary, the amplitude of its covariance function is still independent of time. Moreover, for the FRFT of a stationary random process, the ambiguity function will be a radiant line passing through (0, 0) and the Wigner distribution function will be invariant along a certain direction. We also define the fractional stationary random process and find that a non-stationary random process can be expressed a summation of fractional stationary random processes. The proposed theorems will be useful for filter design, noise synthesis and analysis, system modeling, and communication.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
