Chapter

Informatics in Control, Automation and Robotics

Volume 174 of the series Lecture Notes in Electrical Engineering pp 117-128

Analysis of a Class of Infinite Dimensional Frames

  • Cishen ZhangAffiliated withFaculty of Engineering and Industrial Sciences, Swinburne University of Technology
  • , Jingxin ZhangAffiliated withDepartment of Electrical and Computer Systems Engineering, Monash University
  • , Xiaofang ChenAffiliated withSchool of Electrical Electronic Engineering, Nanyang Technological University

Abstract

Frames are a mathematical tool which can represent redundancies in many application problems. In this article, a class of infinite dimensional and bi-directional frames are studied. It is shown that the infinite dimensional and bi-directional frames can be represented by milti-input, multi-output state space equations. Such a state space representation can enable the application of powerful linear system methods and numerical tools to the performance analysis and evaluation of frames.

Keywords

Frames Linear systems Mixed causal-anticausal realizations State space equations