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.
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