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As digitization of data becomes more prevalent, the demands on existing communications networks and computer systems to cope with this increase in data become overwhelming. Currently, the speech compression problem is handled using the CELP( Code Excited Linear Prediction) scheme and its derivatives. Such techniques are the most frequently used for speech compression at medium-to-low rate ranges. Recent research conducted into the area of cosine packets has proven this field to be readily adaptable to speech compression and coding. In this thesis, speech compression schemes are developed using cosine- packet decomposition, minimum entropy basis selection, and an adaptive thresholding scheme for selecting coefficients. In addition, voiced-unvoiced segmentation and a denoising scheme were implemented. Test results showed high compression ratios (1:50) with a good quality of reconstructed speech.