In this thesis two methods of frequency-weighted linear predictive coding are studied. In the first method, input speech is first frequency-weighted, and then analyzed by the linear prediction method. In the second method linear prediction of speech has been done by the frequency-weighted block least-mean-square adaptive digital filtering (LMS ADF) method. In both methods, if the input speech is noisy, we use the spectral subtraction method to enhance it. For frequency weighting we use three weighting curves, C-message, Flanagan weighting, and modified articulation index weighting curves. Their common characteristic is that the second formant frequency region is more weighted than other region. According to the computer simulation result, with the method the second formant region can be represented more closely than other region. When we use an ADF for linear prediction, the residual signal is not white in the frequency domain. Consequently, the use of pulses or random noise to excite the synthesis filter formed by the ADF coefficients does not result good quality of synthetic speech. In order to improve the synthetic speech quality we use the RELP coding approach in which we transmit residual signal as the excitation signal. For residual coding we use a 2-bit APCM. The effectiveness of noisy speech enhancement has been measured by the LPC spectral distance measure. According to the results, when the SNR of the input speech ranges from 0 to 10 dB, a performance improvement of about 5 dB can be gained.