For linear-period-modulated (LPM) signals, the phase of the echo from a moving-point target contains information about range rate. When an LPM signal is transmitted, a Doppler-insensitive sonar processor is obtained by following a matched filter with an envelope detector. Velocity information can be extracted from the same echo, however, if the receiver is sensitive to phase. A receiver that envelope detects matched-filter responses and also estimates the phase of an echo can therefore be both Doppler tolerant and Doppler resolvent. If LPM is used, only two matched filters are needed to implement a sequence of M velocity hypotheses, rather than a bank of M different filters. LPM is thus an excellent signal format not only for Doppler-invariant range estimation and initial detection, but also for fine velocity resolution with minimum receiver complexity. The existence of velocity-induced phase transformations in LPM signals also leads to a new synthetic aperture sonar technique.