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AMR refers to Adaptive Multi-rate Compression, or AMR-NB for Adaptive Multi-rate Narrow Band. It is a codec that was adopted by 3GPP for use over mobile networks, carrying speech data. In use it uses one of 8 different bitrates based on link conditions to meet local channel and capacity requirements. AMR is also used by many mobile phones and some other portable gadgets to allow the user to record voice data.
The 8 different bit-rates supported by AMR from lowest to highest are 4.75, 5.15, 5.90, 6.70, 7.40, 7.95, 10.2 and 12.2kb/s. To reduce bandwidth usage, AMR adopts Voice Activity Detection and Comfort Noise Generation technology to detect when there is lower voice activity.
Since it is optimized for speech coding, AMR doesn't generally provide decent quality for audio recordings compared to low-bitrate MP3 and other forms of lossy compression that are commonly used with portable devices.
Software, both free and commercial, exists to convert AMR format recordings to MP3 or other common recording formats that enjoy a wider range of support by software and hardware alike. The commonly used file extension for an AMR recording is .amr.