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