Fractional autocorrelation and its application to detection and estimation of linear FM signals

Abstract

We present an alternative, efficient implementation of fractional autocorrelation. The algorithm utilizes the fast discrete approximation of the fractional Fourier transform (FRFT) along with the FFT algorithm. We relate fractional autocorrelation with radial slices of the narrowband ambiguity function (AF) and demonstrate that relationship with simulation examples. We also show that fractional autocorrelation is related to a detection statistic previously proposed for detection of multicomponent linear FM signals. Since our fractional autocorrelation based detection algorithm does not require the calculation of either the AF or the Radon transform, we propose its use as a computationally fast alternative for detecting linear FM signals and estimating their chirp rates.