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Acoustic noise with energy greater or equal to the speech can be suppressed by adaptively filtering a separately recorded correlated version of the noise signal and subtracting it from the speech waveform. It is shown that for this application of adaptive noise cancellation, large filter lengths are required to account for a highly reverberant recording environment and that there is a direct relation between filter misadjustment and induced echo in the output speech. The second reference noise signal is adaptively filtered using the least mean squares, LMS, and the lattice gradient algorithms. These two approaches are compared in terms of degree of noise power reduction, algorithm convergence time, and degree of speech enhancement. Both methods were shown to reduce ambient noise power by at least 20 dB with minimal speech distortion and thus to be potentially powerful as noise suppression preprocessors for voice communication in severe noise environments.