The Kolmogoroff algorithm Claerbout (1976); Kolmogoroff (1939) is widely used by the geophysical community since it is the most computationally efficient. However, it is not without its problems: as with all frequency domain methods, it assumes circular boundary conditions. Time-domain functions, especially those with zeros close to the unit circle, often require extreme amounts of zero-padding before they can be safely factored.
The Wilson-Burg method, introduced below, provides an algorithm for spectral factorization that is based on Newton's iteration for square-roots. Despite its iterative nature, we show that convergence is quadratic, providing a time-domain algorithm that is potentially cheaper than Kolmogoroff. In addition we describe how the algorithm can be extended to factor cross-spectra.