On the group of rational spectral units with finite order

The problem of phase retrieval is a difficult one which remains far from solved. Two homometric sets are always connected by way of a convolution product by some spectral unit, though not necessarily in a unique way. Here we elucidate one small aspect, the subgroup of spectral units with finite order. Its elements are completely characterized by relations between their eigenvalues. This sheds some light on the beltway problem.