In this thesis work, we have studied an ADPCM coder with the transmission rate of 16 kbits/s and the enhancement of noisy speech. To improve the performance of the 16 kbits/s ADPCM coder and to make the system compatible with higher rates coders already in use or recommended by CCITT, we utilized the 32 kbits/s CCITT-recommended ADPCM coder and delayed decision algorithm. Also we have studied noise spectral shaping of the ADPCM coder to improve the subjective listening by using the pre-/post-filtering approach. The filters used are pre-/de-emphasis filters and pre-/post-filters based on C-message weighting. For the enhancement of noisy speech, we have studied new algorithms based on forward/backward adaptive digital filtering. The forward/backward adaptive digital filter (FBADF) method is effective for enhancement of wide-band noisy speech with low SNR. To improve the enhancing ability further, we introduce modified FBADF method. This method having a simple structure works for any kind of additive noise. The enhancing scheme we studied is applied to ADPCM coding system to reduce the speech independent noise (e.g., granular noise) introduced during the coding process.