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E.C. Real et al. have presented an algorithm for fast tracking of a signal subspace or interference subspace for application in adaptive detection or estimation (see ICASSP '97; IEEE Trans. Sig. Processing, vol.47, p.1036-45, 1999). For cases in which the signal matrix is formed from a single-channel discrete-time signal, we show how one can further reduce computation in the fast approximate subspace tracking (FAST) algorithm by using the fast Fourier transform.