A new representation of power spectral density and correlation function by means of fractional spectral moments

In this paper, a new perspective for the representation of both the power spectral density and the correlation function by a unique class of function is introduced. We define the moments of order γ ( γ ∈ C ) of the one sided power spectral density and we call them Fractional Spectral Moments (FSM). These complex quantities remain finite also in the case in which the ordinary spectral moments diverge, and are able to represent the whole Power Spectral Density and the corresponding correlation function.