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Recently, we observed zero phase and undershoot patterns in data processed by a minimum-variance deconvolution (MVD) filter. These observations motivated a careful analys is of the MVD filter, which, as we demonstrate in this paper, explains both the zero phase and undershoot patterns. This analysis also connects the MVD filter with the well-known prediction-error filter , and Berkhout's two-sided least-squares inverse filter . We show that the performance of the MVD filter depends heavily on the bandwidth of the source wavelet, and signal-to-noise ratio, and only slightly on data length.