9.2.1 Features of Adaptive Filters -Adaptation algorithm. Q&A for understanding“Adaptive Algorithm” Q1:What does the adaptive algorithm do? The adaptive algorithm uses 1)the value of COP or its function, 2)the measurements of the input and desired response(if possible) to decide how to modify the parameters of the filter to improve its performance. Q2:How is the complexity of adaptive algorithm? The complexity and the characteristics of the adaptive algorithm are functions of the filtering structure and the COP
Q1: What does the adaptive algorithm do? The adaptive algorithm uses 1) the value of COP or its function, 2)the measurements of the input and desired response (if possible) to decide how to modify the parameters of the filter to improve its performance. Q2: How is the complexity of adaptive algorithm? The complexity and the characteristics of the adaptive algorithm are functions of the filtering structure and the COP. 9.2.1 Features of Adaptive Filters － Adaptation algorithm. Q&A for understanding “Adaptive Algorithm
9.2.1 Features of Adaptive Filters Supervised adaptation Desired Performance response evaluation y(n) x(n) Filtering (n) Input structure Output e(n) signal signal Filter coefficients Error Adaptation algorithm FIGURE 9.8 Basic elements of a supervised adaptive filter
FIGURE 9.8 Basic elements of a supervised adaptive filter y ˆ(n) Supervised adaptation. 9.2.1 Features of Adaptive Filters
9.2.1 Features of Adaptive Filters Unsupervised adaptation.When the desired response is unavailable In some applications,the input signal has some measurable property (i.e.,constant envelope)that is lost by the time it reaches the adaptive filter.The adaptive filter adjusts its parameters in such a way as to restore the lost property of the input signal. 例如：无线通信中接收机的AGC
Unsupervised adaptation. When the desired response is unavailable. In some applications, the input signal has some measurable property (i.e., constant envelope) that is lost by the time it reaches the adaptive filter. The adaptive filter adjusts its parameters in such a way as to restore the lost property of the input signal. 例如：无线通信中接收机的AGC 9.2.1 Features of Adaptive Filters
9.2.2 Optimum versus Adaptive Filters 回想：5代表什么？ y(n,) Desired response x(n,) m,) x(n,) c,(n) c(n-1,6) (n) Input Input eln,() signal signal Eror Solve R(n)c,(n)=d(n) Adaptive algorithm (a) () Optimal filter Adaptive filter
9.2.2 Optimum versus Adaptive Filters 回想： 代表什么？ Optimal filter Adaptive filter
9.2.2 Optimum versus Adaptive Filters Optimum filters.If we know the second-order moments of the SOE (Signal operating environment) R(n)c(n)=d(n) (9.2.6) R(n)-E{x(n,)xH(n, (9.2.7) d(n)-E{x(n,y*(n,s (9.2.8) Wiener-Hopf方程的FIR解
Optimum filters. If we know the second-order moments of the SOE （Signal operating environment） 9.2.2 Optimum versus Adaptive Filters Wiener-Hopf 方程的FIR解