Generalization of sampling theorem by blurring operation
Taizo Iijima · Electronics and Communications in Japan (Part I Communications) · 1983
Abstract The sampling theorem established by Someya and Shannon is presntly finding wide applications in various fields. However, it often happens in actual application that the assumption of band‐limitation which is a prerequisite of the theorem is difficult to verify. From such a viewpoint, this paper generalizes the sampling theorem to remedy the problem. the blurring operation originally has the function of positively suppressing the higher‐order harmonic components. It is a regular linear operation for which the inverse operation exists. Utilizing this property and combining the operation with the traditional sampling theorem, a new sampling theorem is derived, by which only those components of the object function in the limited band can be extracted. the generalized sampling function derived first in this paper is a natural extension of the traditional sampling function. With its analytical structure as well as the clearly stated method of computation, the generalized sampling theorem derived in this paper is applicable widely to actual problems.