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We propose a two-stage adaptive filtering process for canceling narrowband interference from a wideband signal process, based on a reference signal consisting of a Doppler shifted version of the interference. The first stage uses the time-varying behavior of NLMS with large step-size to produce an estimate of the interference signal, in which the Doppler shift is mitigated. The second stage uses NLMS with small step-size, as an approximation to the Wiener filter, in order to modify amplitude and phase of the Doppler-mitigated reference signal so that an estimate of the interference signal is produced suitable for interference cancellation. Simulations with a wideband QPSK signal corrupted by strong sinusoidal interference, for which a Doppler shifted reference is available, show the performance of the proposed approach in terms of signal-to-interference ratio and bit-error rate improvement.