  A canonical system is a kind of first-order system of ordinary differential
equations on an interval of the real line parametrized by complex numbers. It
is known that any solution of a canonical system generates an entire function
of the Hermite-Biehler class. In this paper, we deal with the inverse problem
to recover a canonical system from a given entire function of the
Hermite-Biehler class satisfying appropriate conditions. This type inverse
problem was solved by de Branges in 1960s. However his results are often not
enough to investigate a Hamiltonian of recovered canonical system. In this
paper, we present an explicit way to recover a Hamiltonian from a given
exponential polynomial belonging to the Hermite-Biehler class. After that, we
apply it to study distributions of roots of self-reciprocal polynomials.
