Discrete chirp-Fourier transform

摘要

In this paper, we study discrete chirp-Fourier transform (DCFT), which is analogous to the Discrete Fourier transform (DFT). Besides the multiple frequency matching similar to the DFT, the DCFT can be used to match the multiple chirp rates in a chirp-type signal with multiple chirp components. We show that the magnitudes of all the sidelobes of the DCFT of a quadratic chirp signal are 1 while the magnitude of the mainlobe of the DCFT is $YLD@N, where N is a prime and is the length of the signal. With this result, an upper bound for the number of the detectable chirp components using the DCFT is provided in terms of signal length, signal and noise powers. We also show that the N-point DCFT performance optimally when N is a prime.