In this paper we investigate the impact on the performance of Speaker Verification (SV) systems of the signal and channel coding in GSM cellular telephone networks. In this study only the effects of the codec are investigated. This is done by transcoding the signals in an existing speech corpus, recorded in the fixed network, to GSM. We compared text dependent SV performance of systems trained with A-law speech and tested with A-law and GSM speech, as well as systems trained with GSM speech and tested with GSM speech. All SV systems compared were based on continuous density Gaussian mixtures HMM models, differing in acoustic resolution. We have compared several parameter representations derived from FFT and LPC based spectral estimates. It is shown that (and why) LPC based estimates are to be preferred. It is also shown that it pays to extend the analysis bandwidth to the full 4 kHz offered by the digital telephone network. The major conclusion of our research is that the impact of GSM coding on the parameter representations is marginal and can effectively be ignored.