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We obtain conditions for a trigonometric polynomial t of one variable toequal or be approximated by |p|^2 where p has frequencies in a Bohr set ofintegers obtained by projecting lattice points in the open planar regionbounded by the lines y = alpha*x +- beta where |beta| leq 1/4 and alpha iseither rational or irrational with Liouville-Roth constant larger than 2. Wederive and use a generalization of the Fejer-Riesz spectral factorization lemmain one dimension, an approximate spectral factorization in two dimensions, themodular group action on the integer lattice, and Diophantine approximation.

Spectral Factorization and Lattice Geometry