14.5 INPUT DATA MANIPULATIONS [3, 4, 13, 19, 22]

In (14.13), the R matrix is obtained from the autocorrelations with different lags. However, this is not the only way to form the R matrix. The data can be manipulated differently to obtain different results. In other words, the autocorrelation matrix is not the only approach to obtain the a _i constants in (14.18). Some of the approaches can improve the quality of the spectrum estimation. In order to use other ways to adopt the input data, (14.19) is rewritten as

(14.29)

This equation is identical to (14.19), except that the matrix T is used to replace R.

Different ways of generating the T matrix from the same input data can produce quite different results. Two different ways to obtain T will be discussed. Assume there are N input data points from x(0) to x( N - 1).

14.5.1 Covariance Method

In this method the input data are related to matrix T as

(14.30)

This matrix is not Toeplitz. Although a special recursive method can be developed for this approach, the Levinson-Durbin method does not apply directly. In this approach, all the elements in the T matrix contain the same number of terms from the data points.

If p = 1 and N = 3, the data are x(0), x(1), and x(2), and the T matrix is

(14.31)

If p =...