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We can now extend the equations derived for real numbers to
polynomials of Z, with , and obtain spectral
factorization algorithms similar to the WilsonBurg method
Sava et al. (1998), as follows:
 
(8) 
If L represents the limit of the series in (8),
and so
Therefore, L represents the causal or anticausal part of the given
spectrum .
Table 3 summarizes the spectral factorization
relationships equivalent to those established for real numbers in
Table 1.
Table 3:
Spectral factorization
General 

Muir 

Secant 

Newton 

Ideal 

The convergence properties are similar to those derived for
real numbers. As shown above, the NewtonRaphson method should have
the fastest convergence.
Next: A comparison with the
Up: Sava & Fomel: Spectral
Previous: The convergence rate
Stanford Exploration Project
4/20/1999