Split-Radix Algorithms for Arbitrary Order of Polynomial Time Frequency Transforms

The polynomial time frequency transform is one of important tools for estimating the coefficients of the polynomial-phase signals (PPSs) with the maximum likelihood method. The transform converts a one-dimensional (1-D) data sequence into a multidimensional output array from which the phase coefficients of the data sequence are estimated. A prohibitive computational load is generally needed for high-order polynomial-phase signals although the 1-D fast Fourier transform (FFT) algorithm can be used. Based on the split-radix concept, this paper derives a fast algorithm for arbitrary order of polynomial time frequency transforms to significantly reduce the computational complexity. Comparisons on the computational complexity needed by various algorithms are also made to show the merits of the proposed algorithm