Sampling theory for not necessarily band-limited functions: a historical overview

The historical development of sampling theory began with Charles-Jean Baron de la Vallee Poussin. His studies involved duration-limited functions which cannot be band-limited. Maria Theis was the first to establish convergence for continuous functions by replacing the kernel function sin x/x in de la Vallee Poussin's formula with (sin x/x) squared from Fejer's summation method for the Fourier series. K. Ogura, however, was the first mathematician to state and present a proof for de la Vallee Poussin's interpolation formula.