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In this paper, we study the noise-reduction problem in the Karhunen-Loeve expansion domain. We develop two classes of optimal filters. The first class estimates a frame of speech by filtering the corresponding frame of the noisy speech. We will show that several well-known existing methods belong or are closely related to this category. The second class, which has not been studied before, obtains noise reduction by filtering not only the current frame, but also a number of previous consecutive frames of the noisy speech. We will discuss how to design the optimal noise-reduction filters in each class and demonstrate the properties of the deduced optimal filters.