Comments on discrete chirp-Fourier transform and its application to chirp rate estimation [and reply]

This comment points out that the sample rate of the discrete chirp-Fourier transform (DCFT) proposed by Xia (see ibid., vol.48, p. 3122-33, 2000) is not sufficient to avoid severe "picket-fence" effect and causes some restrictions for its practical applications. By increasing the sample rate and modifying the DCFT definition, a new robust DCFT is proposed. Xia (see ibid., vol.50, no.12, p.3116, 2002) replies by first correcting an error on the analog-to-discrete parameter conversions of a chirp signal. Xia also add that when the chirp rate detection resolution is increased, it is more robust to the chirp rate error. On the other- hand, what is sacrificed by doing so is that the magnitudes of the sidelobes of the transform are increased, which may limit its capability of detecting chirps in a multicomponent or low SNR signal. Therefore, which DCFT needs to be used has to depend on the practical application.