This paper describes a system that can enhance the quality of speech signals that are severely band limited during regular telephone speech transmission. We have already proposed a spectrum widening method that utilizes aliasing in sampling rate conversion and digital filtering for spectrum shaping. This paper proposes a new method using linear prediction (LP) residual error processing and parameter (coefficients) mapping using linear extrapolation that offers improved performance in terms of the spectrum distortion characteristics. Real time hardware implementation procedures are discussed. The proposed method can effectively enhance speech quality.