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A new two-step algorithm for removing impulse noise from speech data is outlined. In the first step, a threshold detection scheme is used to determine whether or not the speech sample in question is corrupted by an impulse. The threshold is derived using a statistical theory. In the second step, when the sample has been determined to be noise corrupted, the noisy sample is replaced by a sample generated using a simple least square interpolation scheme. Otherwise, no filtering is done if the sample is determined to be noise free. The performance of the proposed algorithm is shown to be comparable to the more well-known DDC scheme in reducing the noise.