The new procedure of sequential noise suppression in transient signals has been developed. The additive, convolutional and multiplicative noises are reduced to the additive forms by appropriate homomorphic transformation. In the decomposition of the signal by wavelets, the additive noise component is identified with the detailizing parts of this expansion. It is found that the Daubechies wavelets would be used as the basis functions. The specific features of the thresholds choice for noise suppression are discussed. According to the results of numerical simulations, it is ascertained that in certain cases the main role in the forming of transients belongs to convolutional noise.