Wikipedia
Transcoder and Rate Adaptation Unit, or TRAU, performs transcoding function for speech channels and RA (Rate Adaptation) for data channels in the GSM network. The Transcoder/Rate Adaptation Unit (TRAU) is the data rate conversion unit. The PSTN/ISDN switch is a switch for 64 kbit/s voice. Current technology permits to decrease the bit-rate (in GSM radio interface it is 13 kbit/s for full rate and 6.5 kbit/s for half rate). Since MSC is basically a PSTN/ISDN switch its bit-rate is still 64 kbit/s. That is why a rate conversion is required in between the BSC and MSC...
Transcoding is the compression of speech data from 64 kbit/s to 13/12.2/6.5 kbit/s in case FR/EFR/HR (respectively) speech coding.
Rate adaptation without transcoding allows Tandem Free Operation (TFO), allowing the original encoded speech data to be carried in a 64 kbit/s channel. TFO offers benefits because transcoding can lead to a degradation of speech quality and requires computational resources.
Usage examples of "trau".
In the year 1104 Coloman reduced the maritine country as far as Trau and Saloma, (Katona, Hist. Crit.