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The problem of designing a digital low-pass filter is considered from different points of view, including two approaches which have not received sufficient attention. One approach is based on the prolate-spheroidal-function filters of Slepian, Pollak, and Landau. The other is the incompletely specified least mean-square error (LMSE) method which has been proposed by Rorabacher. We find that, compared with minimax and LSME designs, the prolate-spheroidal digital filters have very low sidelobes, at the expense of more deviation from a flat passband. If a transition band or "don't care" region of the frequency response is assumed, then the results of the minimax and LSME methods are nearly the same.