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ADPCM, Adaptive Differential Pulse Code Modulation, is a way an analog signal can be converted to a digital signal. In the 1980s that was first standardized by the CCITT in G.721 for 32 kbps. Later came the standards G.726 and G.727 for 40, 32, 24 and 16 kbps.
G.726 specifies how a 64 kbps A-law or µ-law PCM signal can be converted to 40, 32, 24 or 16 kbps ADPCM channels where the 24 and 16 kbps channels are used for voice in Digital Circuit Multiplication Equiment (DCME) and the 40 kbps is for data modem signals (especially modems doing 4800 kbps or higher) in DCME.
The PCM signal is a quantitized version of the actual analog signal. ADPCM only records the difference between the two measurements and therefor uses less bandwidth.