Families of atomic functions ch a, n (x) and fup n (x) in digital signal processing

Abstract

A new class of weight functions constructed on the basis of family of atomic functions and cha,n(x) and fupn(x) is proposed and substantiated. The study consists of three parts. In the first part, the definition of atomic functions and their convolutions are presented. In the second part, a definition of a new family of atomic functions cha,n(x) as convolutions of ha(x) is given. In the third part, a family of weight functions is constructed by truncation of cha,n(x) to the effective support. If smoothening with classical windows is applied after the truncation combined weight functions will be received. The physical characteristics of the weight functions constructed by the direct truncation and in combination with the Hamming and Riesz windows are presented. The found functions can find wide application in problems of digital signal processing, restoration of images, radar, radiometry, radio astronomy, remote probing, and other physical domains.