Minimum phase factors

The Wilson-Burg method of spectral factorization generates minimum phase factors. Wilson presents a rigorous proof. Here is an intuitive explanation: Both sides of () 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 () 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 () 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.