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Employing Orthogonal Frequency Division Multiplexing (OFDM) signaling over time-varying channels results in inter-carrier interference (ICI) and degraded detection error probability due to the loss of orthogonality among the subcarriers. This problem is particularly exacerbated for systems operating in highly mobile scenarios such as underwater acoustic (UWA) communications, digital video broadcasting (DVB) for mobile devices and vehicle-to-vehicle (V2V) networks. To address the problem of data detection in such scenarios, we propose a novel demodulation strategy using several partial interval Fast Fourier Transforms (FFTs) instead of a conventional, single full interval FFT. Algorithms for computing the weights used to combine the outputs of the partial FFT are presented for three scenarios: full, partial and no knowledge of the time varying channel. Numerical simulations and an approximate theoretical analysis show that significant performance gains can be obtained over traditional equalizers at a very moderate complexity.