Some important maps in interval digital signal processing

Abstract

In recent years there has been an increasing attention to intervals since an interval supplies necessary constraints on the uncertainties that arise from real world problems. Especially, in signal processing, when a signal value in a time $t$ is completely unknown, intervals are used to process such signals, Mathematically, a signal is defined as a function from a subset of $\mathbb{R}$ into $\mathbb{C}$. The notion of interval signal is a function from a subset of $\mathbb{R}$ into $\mathbb{I}_{\mathbb{R}}$ which is the set of all intervals. This paper presents some elemental maps for the mathematical functions of interval digital signal processing. Finally, the interval circular convolution map is introduced to provide a suitable way for processing of interval signals.