Fractional power spectrum

Abstract—In this paper, by investigating the definitions of the fractional power spectrum and the fractional correlation for the deterministic process, we consider the case associated with the random process in an explicit manner. The fractional power spectral relations for the fractional Fourier domain filter are derived, and the expression for the fractional power spectrum in terms of the fractional correlation is obtained. In addition, the definitions and the properties of the fractional white noise and the chirp-stationary process are presented. Simulation results verify the theoretical derivations and demonstrate the potential applica-tions, such as detection and parameter estimation of chirp signals, fractional power spectral estimation and system identification in the fractional Fourier domain. Index Terms—Fractional correlation function, fractional Fourier transform, fractional power spectrum, fractional white noise. I