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Synthetic aperture radar (SAR) allows the observation of the sea surface over large areas regardless of weather conditions. In what follows we discuss a digital signal processing (DSP) formalism that makes use of polynomial filters such as Volterra models to extract the geophysical information from SAR images and to model several nonlinear transfer functions. Polynomial filters allow the extension of algorithms derived for the linear case to the nonlinear case. First, we will briefly discuss the types and sources of nonlinearities in SAR mapping of the ocean surface. Next, we will summarize the main characteristics of the Volterra filters and apply them to the understanding of hydrodynamic nonlinearities and instrumental nonlinearities. Then, we will combine their Volterra models to model the complete mapping process. Although we have only focused on the particular example of Volterra filters here, nonlinear autoregressive moving average (NARMA) models can also been applied to extract geophysical information from a nonlinear marine feature signature.