Comparison of Centered Discrete Fractional Fourier Transforms for chirp parameter estimation

The Discrete Fractional Fourier Transform (DFRFT) is a promising tool for multicomponent chirp parameter estimation. Computation of this transform and its chirp concentration properties are dependent on the basis of DFT eigenvectors used in the computation. Several DFT-eigenvector basis have been proposed for the transform and there is no common framework for comparing them. Furthermore, the analysis done in all prior work completely ignore the presence of noise. In this paper, we compare different versions of the transform using statistical consistency of the chirp parameter estimators as the criteria. Their impact on estimation errors, is evaluated by comparing them to the Cramer-Rao lower bound, with both conventional and recent super-resolution subspace extensions of the technique.