A partial digestion of the HRT counterexample

A function of one variable can be translated in space by a spatial shift to obtain a new function and also modulated in frequency by a frequency shift to obtain a new function One can compose these two operations to obtain a time-frequency shift: (This can be viewed of as a portion of the Weyl representation of the Heisenberg group, but we will not adopt a representation-theoretic perspective here.) Some functions obey finite linear relations between their time-frequency shifts. For instance, a ...