自适应滤波adaptivefilteringchapter.pptVIP

* * CHAPTER 3 Adaptive Tapped-delay-line Filters Using the Gradient Approach Adaptive Filtering In the case of known correlation expression the solution for the optimal coefficients of the tapped-delay-line filter was (1.25) Where R was the correlation matrix of the filter tap inputs and p was the cross-correlation between the input vector and a desired response. If the filter operates in an environment where R and p are unknown, we may use all the data collected up to and including time n to compute the estimates and in order to solve the normal equations. When, however the tapped-delay-line filter contains a large number of coefficients this procedure is highly inefficient. A more efficient approach is to use an adaptive filter. Adaptive Tapped-delay-line Filters Using the Gradient Approach Figure 3.1 Block diagram of adaptive filter Processes: 1) adaptive or training process 2) filtering or operating process. (d(n)= desired response must be provided) Adaptive Tapped-delay-line Filters Using the Gradient Approach Let y(n) denote the output of the tapped-delay-line filter at time n, as shown by the convolution sum (3.1) the error signal is The error signal e(n) is utilized by the adaptive process to generate corrections at each iteration to be applied to the tap coefficients in order to move closer to the optimum Wiener configuration. (3.2) Adaptive Tapped-delay-line Filters Using the Gradient Approach (3.3) where the quantities , and are results of ensemble averaging. Adaptive Tapped-delay-line Filters Using the Gradient Approach Assuming the values of h(1,n), h(2,n), . . . , h(M,n) are known, the value of the mean squared error is Adaptive Tapped-delay-line Filters Using the Gradient Approach The Method of Steepest Descent The dependence of ?(n) on the filter coefficient can be visualized as a bow