The Wilson-Burg method of spectral factorization generates minimum phase
factors. Wilson 1969 presents a rigorous proof.
Here is an intuitive explanation: Both sides of
(5) are positive. Both terms on the
right are positive. Since the Newton iteration always overestimates,
the 1 dominates the rightmost term. After masking off the negative
powers of *Z* (and half the zero power), the right side of
(5) adds two wavelets. The 1/2 is wholly real, and
hence its real part always dominates the real part of the rightmost
term. Thus (after masking negative powers) the wavelet on the right
side of (5) has a positive real part, so the phase
cannot loop about the origin. This wavelet multiplies *A*_{t}(*Z*) to give
the final wavelet *A*_{t+1}(*Z*) and the product of two minimum-phase
wavelets is minimum phase.

7/5/1998