TABLE OF CONTENTS The linear prediction defined in (14.6) and (14.7) can be considered as a filter with noise u( n) as input and x( n) as output. This filter is shown in Figure 14.1. Figure 14.1(a) shows the overall function of the filter and Figure 14.1(b) shows the feedback circuit. The first step is to find the coefficients of the filter. If the input u( n) is assumed to be an unknown response, the signal x( n) can be predicted only approximately from a linearly weighted summation of the past terms. As a result, the linear prediction expression can be written as
| (14.8) |  |
where 
represents the estimate of x( n). For simplicity, x( n) is used for 
in later discussion. Replacing x( n) by x( n - 1), x( n - 2), , x( n - p + 1), one can obtain a set of p linear equations. For example, if there are four data points x(1), x(2), x(3) and x(4), and p = 2, there will be two equations with constants a 1 and a 2. These equations can be written as
| (14.9) |  |
Since all the x( n) are known, theoretically, it is possible to determine the a values. This result will be equivalent to the Prony's method, which originates from a...
