ABSTRACT
This chapter develops a class of linear optimum discrete-time filters known as the Wiener filters. These filters are optimum in the sense of minimizing an appropriate function of the error, known as the cost function. The cost function that is commonly used in filter design optimization is the mean square error (MSE). Minimizing MSE involves only second-order statistics, and leads to a theory of linear filtering that is useful in many practical applications. This approach is common to all optimum filter designs. The superscript "o" indicates the optimum Wiener solution for the filter. Filtering of noisy signals is extremely important and the method has been used in many applications such as speech in noisy environment, reception of data across a noisy channel, enhancement of images. The filter coefficients do not change with time, the output of the filter is equal to the convolution of the input and the filter coefficients.
