Characterization of the Divisibility of DFT HTFs for C2

We expand on a prior result about the cardinalities of harmonic tight frames generated from the discrete Fourier transform. Harmonic finite unit-norm tight frames (FUNTFs) constructed from the first two rows of the M ×M discrete Fourier transform have previously been described and characterized as prime or divisible, where M ≥ 2 is an integer. We generalize the result to any choice of two rows b and c for which c− b has up to two distinct prime factors. These new results allow for much more flexibility in constructing harmonic FUNTFs from M -th roots of unity.