A new model of white noise on the basis of the wavelet transform has been put forward. This model is more adequate for solving some radiophysical tasks such as the problem of electromagnetic waves reflection from the ionosphere. Moreover, it was shown that in terms of probabilistic description of the random-process trajectories, the wavelet implementation of this random process is more likely (using the probability density functional offered by I.N. Amiantov). The wavelet properties and the famous theorems of mathematical analysis and theory of chances were used to develop our model: the mean value theorem and Lyapunov’s central limit theorem. Our study resulted in a theorem on random-process expansion in terms of wavelet basis. It was also shown that the obtained results were in agreement with those of V.A. Kotelnikov.