Fourier Analysis and Holographic Representations of 1D and 2D Signals

In this paper, we focus on Fourier analysis and holographic transforms for signal representation. For instance, in the case of image processing, the holographic representation has the property that an arbitrary portion of the transformed image enables reconstruction of the whole image with details missing. We focus on holographic representation defined through the Fourier Transforms. Thus, We firstly review some results in Fourier transform and Fourier series. Next, we review the Discrete Holographic Fourier Transform (DHFT) for image representation. Then, we describe the contributions of our work. We show a simple scheme for progressive transmission based on the DHFT. Next, we propose the Continuous Holographic Fourier Transform (CHFT) and discuss some theoretical aspects of it for 1D signals. Finally, some testes are presented in the experimental resultsComment: 13 page

Abstract 1 Holographic Images in Multimedia Information Systems

Multimedia information systems are based on the evolving capability of computers to handle diverse types of information. Their most important characteristic is the integration of all such information types. Due to the improvements in computer architectures, computational methods, and electro-optical technology in recent years, a new type of information will soon be available, also outside research laboratories: electro-holography, that is the computerbased generation of diffraction fringes from 3D input data and the display of the reconstructed object in real-time. This paper analyses which issues have to be solved in order to support the physical and logical coexistence and interactive use of holographic data in a multimedia information system. In particular the characteristics of holographic data and the current research results in the area of real-time holographic display systems are described. Besides, the requirements for integration of electro-holography into a multimedia system are analysed and the way this affects the functionalities of the system is described. The requirements on compression methods for holographic data are also discussed