Unique optimal solution o There is no such thing as a unique optimal solution to the adaptive filtering problem. have to do without a priori statistical information ● have to draw all their information from only one given realization of the process,i.e.one sequence of time samples. o Options based on what information is extracted how it is gathered how it is used in the algorithm 2020-01-18 11
2020-01-18 11 Unique optimal solution ? There is no such thing as a unique optimal solution to the adaptive filtering problem. have to do without a priori statistical information have to draw all their information from only one given realization of the process, i.e. one sequence of time samples. Options based on what information is extracted how it is gathered how it is used in the algorithm
A kit of tools o Time averaging estimates of the signal statistics In the stationary case,ergodicity Is no longer a useful tool in a nonstationary case o Instantaneous estimates of the signal statistics Given only one realization of the process Such estimates may be obtained in various ways o Therefore,we have a kit of tools'rather than a unique solution. This results in a variety of algorithms. Each alternative algorithm offers desirable features of its own. 2020-01-18 12
2020-01-18 12 A kit of tools Time averaging estimates of the signal statistics In the stationary case, ergodicity Is no longer a useful tool in a nonstationary case Instantaneous estimates of the signal statistics Given only one realization of the process Such estimates may be obtained in various ways Therefore, we have a ‘kit of tools’ rather than a unique solution. This results in a variety of algorithms. Each alternative algorithm offers desirable features of its own
Choice of one solution over another o Determined by ● convergence and tracking properties 。numerical stability ●robustness ●accuracy computational complexity ● amenability to hardware implementation (structure of the algorithm,for example, modularity and inherent parallelism are desirable in view of VLSI implementation) 2020-01-18 13
2020-01-18 13 Choice of one solution over another Determined by convergence and tracking properties numerical stability robustness accuracy computational complexity amenability to hardware implementation (structure of the algorithm, for example, modularity and inherent parallelism are desirable in view of VLSI implementation)
四位数的数值黑洞：6174 选择一个四位数，四个数不完全相同（如 7777) o将四个数按大到小排列成一个四位数ABCD, 然后从小到大也排列成一个四位数DCBA: o用ABCD-DCBA,其结果如果也是四位数，则 继续这个过程；如果结果是三位数、二位数、 一位数，则在前面补齐0凑成四位数，同样继 续以上的过程 0如此重复计算最多7次，一定会得出一个数值 2020-01-18 卡普雷卡尔常数 14
四位数的数值黑洞：6174 选择一个四位数，四个数不完全相同（如 7777）； 将四个数按大到小排列成一个四位数ABCD， 然后从小到大也排列成一个四位数DCBA； 用ABCD-DCBA，其结果如果也是四位数，则 继续这个过程；如果结果是三位数、二位数、 一位数，则在前面补齐0凑成四位数，同样继 续以上的过程。 如此重复计算最多7次，一定会得出一个数值 2020-01-18 卡普雷卡尔常数 14
S2.Adaptive filtering applications o (1)Identification applications o(2)Echo cancellation o (3)Interference/noise cancellation o (4)Inverse modeling o(5)Linear prediction o The essential difference arises in the manner in which the desired response is obtained 2020-01-18 15
2020-01-18 15 S2. Adaptive filtering applications (1) Identification applications (2) Echo cancellation (3) Interference/noise cancellation (4) Inverse modeling (5) Linear prediction The essential difference arises in the manner in which the desired response is obtained