  Spectrally constrained sequences (SCSs) play an important role in modern
communication and radar systems operating over non-contiguous spectrum. Despite
numerous research attempts over the past years, very few works are known on the
constructions of optimal SCSs with low cross-correlations. In this paper, we
address such a major problem by introducing a unifying framework to construct
unimodular SCS families using circular Florentine rectangles (CFRs) and
interleaving techniques. By leveraging the uniform power allocation in the
frequency domain for all the admissible carriers (a necessary condition for
beating the existing periodic correlation lower bound of SCSs), we present a
tighter correlation lower bound and show that it is achievable by our proposed
SCS families including multiple SCS sets with zero correlation zone properties.
