The implementation of Speech Enhancement using Spectral Subtraction method and Kalman Filtering method are presented here. Spectral subtraction mainly removes the background noise from noisy speech spectrum. Original speech is obtained by subtracting noise spectrum from noisy speech spectrum. The main disadvantage of spectral subtraction is the presence of musical noise in enhanced speech signal. Secondly, to filter out the background noise from the desired speech signal several speech filtering algorithms has been introduced in last few years. In this paper Kalman Filter for speech enhancement has been proposed. It is observed that spectral subtraction method is very efficient for noise elimination in high SNR condition but performance degrades with reduction in SNR. It is observed that Kalman Filter is efficient in reduction of noise particularly at low SNR conditions. The two designs are modelled using MATLAB for seven different noise types and the SNR are compared.