Fractional Fourier Transform, Wigner Distribution, and Filter Design for Stationary and Nonstationary Random Processes

@article{Pei2010FractionalFT,
  title={Fractional Fourier Transform, Wigner Distribution, and Filter Design for Stationary and Nonstationary Random Processes},
  author={Soo-Chang Pei and Jian-Jiun Ding},
  journal={IEEE Transactions on Signal Processing},
  year={2010},
  volume={58},
  pages={4079-4092}
}
In this paper, we derive the relationship among the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the stationary and nonstationary random processes. We find many interesting properties. For example, if we perform the FRFT for a stationary process, although the result is no longer stationary, the amplitude of the autocorrelation function is still independent of time. We also find that the LCT of a white noise is still a white one. For the FRFT of a stationary… CONTINUE READING
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