  Entanglement in finite and semi-infinite free Fermionic chains is studied. A
parallel is drawn with the analysis of time and band limiting in signal
processing. It is shown that a tridiagonal matrix commuting with the
entanglement Hamiltonian can be found using the algebraic Heun operator
construct in instances when there is an underlying bispectral problem. Cases
corresponding to the Lie algebras $\mathfrak{su}(2)$ and $\mathfrak{su}(1,1)$
as well as to the q-deformed algebra $\mathfrak{so}_q(3)$ at $q$ a root of
unity are presented.
