Two-dimensional spectral factorization with applications in recursive digital filtering

The concept of spectral factorization is extended to two dimensions in such a way as to preserve the analytic characteristics of the factors. The factorization makes use of a homomorphic transform procedure due to Wiener. The resulting factors are shown to be recursively computable and stable in agreement with one-dimensional (1-D) spectral factorization. The factors are not generally two-dimensional (2-D) polynomials, but can be approximated as such. These results are applied to 2-D recursive filtering, filter design, and a computationally attractive stability test for recursive filters.