Wiener filtering theory was put forward by mathematician n wiener (1894~ 1964) during the second world war. This scientific research achievement is one of the important scientific discoveries in this period. He put forward linear filtering and linear prediction theory, which played an important role in the development of communication engineering theory and application. Wiener filter is named to commemorate his important contribution.

The basic principle of Wiener filtering is that if the observed signal y(t) contains the desired signal x(t) and white noise ω(t) which are statistically independent from each other, the desired signal x(t) can be recovered from the observed signal y(t) through Wiener filtering. Let the impulse response of the linear filter be h(t), its input y(t) be y(t)=x(t)+w(t), and its output is graph 1.

Therefore, it can be concluded that the error of the expected signal of x(t) is as shown in Figure 2.

The mean square error is shown in Figure 3:

E[] stands for mathematical expectation. The impulse response hopt(t) of the linear filter with the minimum mean square error can be obtained mathematically, as shown in Figure 4.

Where Ryx(t) is the cross-correlation function of y(t) and x(t), and Ryy(τ-σ) is the autocorrelation function of y(t). The above equation is called Wiener-hopf equation. The impulse response hopt(t) of the optimal filter can be obtained by solving the Wiener-Hough equation. In general, the above equation is difficult to solve, which limits the application of this filtering theory to some extent. However, Wiener filtering develops the theory of filtering and prediction, which affects the future development of this field.