An extension to the sampling theorem for lowpass bandlimited periodic time functions using Nth-order sampling schemes

An extension to the sampling theorem is developed for the case of lowpass bandlimited periodic time functions based on a finite set of coordinate samples taken arbitrarily within the periodic time interval. An exact reconstruction formula is given, and is later utilized in the derivation of an explicit nonequispaced to equispaced sample transformation formula resulting in a discrete Fourier transform (DFT) for nonequispaced sampled data. For completeness the inverse cases are also given