Abstarct: Due to some considerations such as daily increasing amount of audio data, bandwidth limitation, consumed memory, need to have acceptable audio quality, and better using of available resources, our need for audio coding methods is inevitable. Wedgelets is one of the successful tools for coding and noise reduction of images. The wedgelet decomposition consists of basis functions at multiple scales in the same way as the wavelets. Here, we employ and investigate the coding performance of extended wedgelets on audio data. In this thesis, first, we have a review of image coding baxsed on wedgelets and extended wedgelets. Then, we have discussed the problems of applying this method on audio signals and presented solutions for them. We used polynomial functions as the basis functions of the wedgelets. Since the coefficients we obtained are from the temporal space, and due to the correlation between these coefficients, three different methods of quantization are examined. In conjunction with our method, a Region of Interest (ROI) coding is presented to differentiate between voice and silence segments in speech signals. Performance of the proposed system is also evaluated in noisy environments. One of the advantages of the proposed method is that the compression ratio and the quality of the decompressed signal can be controlled. For evaluating, the proposed method is compared with two transform-baxsed methods including DWT and DCT. The results are compared using both objective and subjective measures, SNR and MOS. The results show that in terms of SNR, proposed method for speech signals, in average, has better result than DWT and DCT by 19.40% and 11.90% respectively. Also for audio signals, wedgelet baxsed audio coding have better results over DWT by 19.97%. The study leads us to conclude that wedgelet baxsed coding can be an efficient model for coding of different types of audio and speech signals.