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The applicability of two relatively new linear FM matched filtering algorithms to the processing of synthetic-aperture radar (SAR) data is examined and compared to the fast-convolution algorithm. The algorithms, called basic spectral analysis and the step transform, use the properties of the linear FM signal to achieve some significant performance improvements. The algorithms are evaluated on the basis of their ability to deal with problems peculiar to the SAR application, such as multilooking, range-cell migration, and variations in the FM rate of the input signal. Computation rates are also derived as a function of resolution and target return signal aperture. It is shown that no one algorithm is optimal for all cases. The basic-spectral-analysis algorithm has the lowest computation rate at low resolutions, but has an output data rate which varies with the FM rate and cannot correct for nonlinear data shifts called range curvature. The step transform has the most efficient computation rate at high resolutions. It also has a constant output data rate and can correct for range curvature. The fast-convolution algorithm has a lower computation rate than the step transform at low resolutions and can meet all of the SAR requirements mentioned. All of the algorithms are able to perform multilook processing.