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Present plans for a defense communications digital voice network require both 16 kbit/s delta modulation (DM) and 2.4 kbit/s linear predictive coding (LPC). Unfortunately, when the output of a delta modulator receiver is used as the input to an LPC system, the speech synthesized by the LPC receiver is noticeably degraded. This paper investigates the use of sequential estimation algorithms to reduce this degradation without changing the given DM and LPC system designs. It is found that a particular scalar sequential filtering structure reduces the Itakura spectral distance measure by 60 percent, provides a more accurate LPC output spectrum, and provides a definite perceptual improvement in output speech quality. Most of the improvement is at higher frequencies, however.