Spline function approach to digital signal processing

Abstract

Models of digital signal processing are built on the signal spaces composed of spline functions. It is revealed that the models include and generalize the ideal model on the band-limited signal space, and the conventional model used in practice, with a zero-order or a first-order hold circuit. The models can be implemented accurately using real circuits so far as they are not identical with the ideal model because a spline function can be generated as a piecewise polynomial. Thus the models make it possible to treat signal processing systems which exist between the conventional ideal model and the conventional model used in practice, in design through implementation.