Range Resampling in the Polar Format Algorithm for Spotlight SAR Image Formation Using the Chirp $z$ -Transform

Besides an inverse two-dimensional (2-D) Fourier transform, the polar format algorithm (PFA) for the spotlight synthetic aperture radar (SAR) image formation can be normally divided into two cascaded processing stages, which are called the range and azimuth resampling, respectively. This paper focuses on a new implementation of the first stage, i.e., the range resampling, using the chirp z-transform (CZT). The presented algorithm requires no interpolation. It works for the SAR system directly digitizing the echo signal, as well as that employing the dechirp-on-receive approach. The parameters of the CZT, including the frequency spacing and the start frequency, are derived to accommodate the PFA in both cases. Related filtering and compensation procedures are developed for the chirp z-transformed range signal with and without dechirp, respectively, in order to achieve a signal format entirely suitable for the azimuth resampling. Furthermore, incorporating the new algorithm with the existing CZT-based azimuth resampling and focusing algorithm, we can achieve a PFA totally free of interpolation. The presented approach has been validated by point target simulation, and the test is carried out with a very critical relative bandwidth of 30%

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