Based on building up a model of echo canceller, the convergence of gradient-type stochastic adjustment algorithm of an adaptive filter under the mean-squared error criterion is discussed.

Using white noise to drive shaping filter, the interference model of wave is acquired on the basis of stable stochastic process theory, and the simulation results are satisfactory.

Using the methods of time series spectral analysis and Kalman filter, this article discussed the additive problems of two stochastic processes, mainly Auto Regression Moving Average (ARMA) processes.