Multidimensional Signal and Color Image Processing Using Lattices

2Continuous‐Domain Signals and Systems

2.1 Introduction

This chapter presents the relevant theory of continuous‐domain signals and systems, mainly as it applies to still and time‐varying images. This is a classical topic, well covered in many texts such as Papoulis's treatise on Systems and Transforms with Applications in Optics [Papoulis (1968)] and the encyclopedic Foundations of Image Science [Barrett and Myers (2004)]. The goal of this chapter is to present the necessary material to understand image acquisition and reconstruction systems, and the relation to discrete‐domain signals and systems. Fine points of the theory and vastly more material can be found in the cited references.

A continuous‐domain planar time‐varying image is a function of two spatial dimensions and , and time , usually observed in a rectangular spatial window over some time interval . In the case of a still image, ...