This thesis proposes a new analysis/synthesis procedure for speech and image compression. The algorithm applies the discrete wavelet transform to subject data in order to obtain a set of multiresolution wavelet coefficients. The wavelet coefficients are then encoded by using the generalized Lloyd algorithm. The statistical properties of the wavelet coefficients are utilized to determine the number of resolution levels as well as the codebook size at each resolution level. Coding results show that the new procedure provides a significant improvement in the quality of the reproduced data. The tested data includes speech, image, and transient signals. Wavelet transforms, Vector quantization, Speech coding, Image coding.