While working on voice support for OsmocomBB I had to look in detail at how the audio path in the TI Calypso chipset works. Basically it is not very complicated:
The Uplink path consists of an amplifier for the microphone and an ADC, the digital samples are transferred to the DSP which takes care about the encoding according to the selected GSM voice codec.
In the Downlink path the decoded samples from the DSP are sent to a DAC which is followed by an amplifier and the loudspeaker.
Some additional details are that you can select the analog input/output (e.g. if the headset connector is used). Parameters which can be adjusted are the gain of the amplifiers and the sidetone level (a feedback between the uplink and the downlink audio path).
The digital samples for the DSP use a sample rate of 8 kHz. A not so obvious feature is that there are two FIR (Finite Impulse Response) digital filters with 31 taps in the DSP, one for the uplink, the other for the downlink. Those filters can be used to improve the voice quality or reduce ambient noise. So far those filters are set to not modify the signal (the filter coefficient of the first tap is 1, all others are 0). The format of the filter coefficients is signed fixed-point Q2.14, so for example 0x4000 means 1.