A Fractional Fourier Based Correlator for Detecting Joint Time and Frequency Offsets

In this paper a parametric correlation measure is introduced based on the fractional Fourier transform. Based on fundamental properties of this transform maximum correlation of two signals is identified with a line in the time-frequency plane. Performing the correlation for different values of the parameter yields intersecting lines whose intersection is identified as the joint time-frequency offset between the correlated signals. Both theoretical and practical aspects of the method are discussed, while an example illustrates both the performance of the method and the geometric concept behind. The approach is designed for analysing measured signals with different onset time (travel time) and frequency shift (Doppler) as compared to a given signal model.