A method is given for nonstationary signal filtering in wavelet-mapping domain for information-measurement systems. The method is based on the statistical wavelet coefficients (WC) distribution for signals and noise of different types and dynamic adaptation to their nonstationary properties. We obtained the WC probability distribution in the form of exponential law and determined its parameters. We also expressed analytically the dependence of the WC discrimination threshold on WC distribution parameters and on the noise type and power. This makes more precise Donoho and Johnstone's results. At the same time the expression for the WC discrimination threshold is a generalization of Cramer's formula which assumed a Gauss distribution. A speech signal and four types of noise were used as a general form of nonstationary signal.