Factoring trigonometric polynomials regarded as entire functions of exponential type

We investigate theoretical and computational aspects of factorizing two-dimensional trigonometric polynomials regarded as entire functions of exponential type. A complete description of the irreducible factors of a trigonometric polynomial is derived. The problem of estimating a band-limited function from its modulus, which is a special case of factorizing, is formulated as a problem of minimizing a function bearing a formal analogy to the energy function arising in certain statistical lattice physics models. The analogy suggests that phase retrieval for an object having a nearly symmetric energy distribution and a high frequency content may be computationally intractable.

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