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This paper presents a new method for compression of audio and speech signals based on sinusoidal modeling with added wavelet based coding of the residual signal. Wavelets are introduced as effective tool for representation and compression of atonal and transient signals. The method is proposed for usage in speech databases. The presented method is evaluated by the means of PSNR and PESQ/ODG. The results are compared with performance of common methods. The results show that the presented method provides a promising tool for speech compression and speech databases.