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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 audio and speech databases. There are compared two variants of presented method, one using 1D wavelet transform with 1D SPIHT codec, the other using 2D wavelet transform with 2D SPIHT codec and beat detection. The results are compared with performance of common methods. The results show that the presented method provides a promising tool for audio and speech databases.