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In this paper, we present a frequency-modulated continuous-wave radar interrogation concept, based on direct digital synthesis (DDS), that operates without the commonly necessary high-frequency DDS reference oscillator. As the generated frequency sweeps are nonlinear, standard Fourier transform methods for baseband signal evaluation cannot be applied directly. We show the corresponding signal model, derive a linearization concept on the basis of resampling, and demonstrate the linearization algorithm on simulated data, as well as on real wireless interrogations of surface acoustic-wave sensors.