Example

In a first example, we applied the method to deconvolution on the helix () using the factors obtained with the Wilson-Burg spectral factorization. We take the auto-correlation to be the negative of the Laplacian operator, and convolve it with a spike placed in the middle of each panel in Figure . We use the Wilson-Burg method to find the wavelet with this auto-correlation and then deconvolve (do polynomial division) on the helix to find back the input spike.

 

autolapfac
Figure 3 Wilson factorization of the Laplacian. From left to right: the input filter; its auto-correlation; the factors obtained with the Wilson-Burg method; the result of the deconvolution using the Wilson-Burg factors.

In another example, we analyzed the rate of convergence of the Wilson-Burg method. We selected a simple polynomial which is the cross-correlation of two triangle functions,

(236)

Table  shows the quadratic rate of convergence, defined using a relation similar to equation () for the coefficients of the two factors, A and B.

 

iter A B 1