TABLE OF CONTENTS In (14.19), all the diagonal elements including the off diagonal of the R matrix are equal. This kind of matrix is called Toeplitz. A Toeplitz matrix equation can be solved through the Levinson-Durbin algorithm, which is a recursive approach and more calculation-efficient than directly solving from the Yule-Walker equation. The results of the recursive equation can be written as
| (14.25) |  |
where ? j is called the prediction error power, which may be used to determine the order of the AR method. The first subscript in a j , i is the numerical order to the constants and the second subscript is the number of recursions. The value of ? j should decrease when j increases. When the correct order is reached theoretically, its value will stay constant.
The illustration of using (14.25) can be shown as follows. For a final order of p = j = 2, the first order is j = 1, there are R(0) and R(1), with ? 0 = R(0) and a 1,1 = -R(1)/ R(0). For the second order, there are R(0), R(1), and R(2) a 2,2 = - [ R(2) + a 1,1 R(1)]/ 
, where 
, and 
. The final results are a 1,2 = a 1 and a 2,2 = a 2 where a 1 and a 2 are the...
