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The range-Doppler algorithm and the chirp-scaling algorithm (CSA) process synthetic aperture radar (SAR) data with approximations to ideal SAR processing. These approximations are invalid for data from systems with wide beamwidths, large bandwidths, and/or low center frequencies. While simple and efficient, these frequency-domain methods are thus limited by the SAR parameters. This paper explores these limits and proposes a generalized chirp-scaling approach for extending the utility of frequency-domain processing. We demonstrate how different order approximations of the SAR signal in the 2-D frequency domain affect image focusing for varying SAR parameters. From these results, a guideline is set forth, which suggests the required order of approximation terms for proper focusing. A proposed generalized frequency-domain processing approach is derived. This method is an efficient arbitrary-order CSA that processes the data using the appropriate number of approximation terms. The new method is demonstrated using simulated data.