Radix-2 DIF fast algorithms for polynomial time-frequency transforms

The polynomial time-frequency transform (PTFT) converts a one-dimensional polynomial-phase signal (PPS) into a multi-dimensional (MD) output array in the frequency domain from which the phase coefficients are estimated. To significantly reduce the prohibitive computational complexity to deal with high order PPSs, effective decomposition of the overall computational task is important for any practical applications. This paper derives a radix-2 decimation-in-frequency (DIF) fast algorithms for any order of the PPSs by using the periodic and symmetric properties of the PTFT. Compared with other reported fast algorithms, the proposed one is simple in concept and achieves a significant reduction of the required computational complexity.