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A novel imaging algorithm to be used under the condition of having an image scene in the far field of a linear radar aperture is presented. This is an application scenario that is drastically different from those of spaceborne and airborne synthetic aperture radar (SAR) systems, which has not been properly addressed to date. The technique is particularly tailored for a stepped-frequency continuous wave (CW) or frequency-modulated CW radar. The radar aperture must be linear and can be formed either with a physical or synthetic array. With the suggested method, the radar reflectivity of the image scene is obtained through an interpolation-free series expansion, where only 2-D fast Fourier transforms of the frequency-domain backscatter data are required. The resulting image is sampled on a ldquopolarlikerdquo or pseudopolar grid, which is introduced to simplify the formulation. The main advantages of this method are its extremely low computational cost and the high accuracy of the resulting imagery. The technique is extensively validated both with numerical simulations and two ground-based SAR data sets. Last but not least, numerical simulations show that this technique can be used with an ultrawideband radar of 1 GHz of bandwidth.