In this paper a new algorithm to compute an additive synthesis model of a signal is presented. An analysis based on the Continuous Wavelet Transform (CWT) has been used to extract the time-varying amplitudes and phases of the model. A coarse to fine analysis increases the algorithm efficiency. The computation of the transient analysis is performed using the same algorithm developed for the sinusoidal analysis, setting the proper parameters. A sinusoidal plus transient schema is obtained. Typical sound transformations have been implemented to validate the obtained results.