On Interpolation and Resampling of Discrete Data

This letter introduces a new representation of discrete signals based on the mathematical notions of functionals and continuous dual spaces. A new and more general sampling theorem is also suggested. Next, the problems of interpolating and resampling discrete signals are addressed; and a general solution using functional interpolation—which is applicable to many different settings—is proposed. Families of resampling filters dubbed de Boor–Ron filters that use de Boor–Ron interpolation are introduced, and their numerical realization is discussed. Some applications of this research are suggested.