Adaptive Filtering

6	Eigenvalues of Rx Properties of the Error Surface

6.1    THE EIGENVALUES OF THE CORRELATION MATRIX

Let R_x be an M × M correlation matrix of a wide-sense (or weakly) stationary (WSS) discrete-time process computed from a data vector x(n). This symmetric and nonnegative matrix (see Problem 6.1.1) can be found as follows: We find the data vector x(n) using the MATLAB command: x=randn(1,64). From this data vector, we first find its autocorrelation function r_xx (m) = [1.0414 0.0136 0.0823] using the Book m-function: rx=lms_sample_biased_autoc(x,3). We can also use the Book m-function: rx=lms _ sample _ biased _ cross _ cor(x,x,3). Next, we obtain the correlation matrix R_x:

$R_x=\left[\begin{array}{ccc}1.0414& 0.0136& 0.0823\\ 0.0136& 1.0414& 0.0136\\ 0.0823& 0.0136& 1.0414\end{array}\right]$

The above ...