In a first example, we applied the method to deconvolution on the helix Claerbout (1997) 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 3. 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.

Figure 3

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,

(14) |

iter | A | B |

1 | 0.0364715122 | 0.0442032255 |

2 | 0.0029259326 | 0.0002011458 |

3 | 0.0000014305 | 0.0000000199 |

4 | 0.0000000894 | 0.0000000199 |

5 | 0.0000000596 | 0.0000000000 |

6 | 0.0000000000 | 0.0000000000 |

7/5/1998