Fractional Fourier Series Analysis of Gaussian Pulse Chirp Signal

As an extension of conventional Fourier transform and a kind of time-frequency signal analysis tool, Fractional Fourier Transform (FrFT) and Fractional Fourier Series (FrFS) are suitable for dealing with types of non-stationary signals. Taking advantage of their properties and non-stationary features of linear Chirp signal in the Fourier transform domain, several methods of extraction and parameter estimation for Chirp signal and Gauss pulse Chirp signal are proposed and a comparative study has been done in the case of FS estimation. Analysis and simulation results show that the meaning of this method is clear, the computation is simple, and it has no interference while fully retaining the advantages of FS. It also has excellent noise-reducing performance comparing with those in time domain, frequency domain or joint-frequency domain. Fractional Fourier series expansion of chirp signal and Gauss pulse chirp signal are analyzed and a comparative study has been taken. With necessary discussions of expansion coefficients and the computer simulations, the convergence performance, attenuation and oscillation has been studied.