tailieunhanh - Digital Signal Processing Handbook P4

Sampling of Continuous Functions From Infinite Sequences to Finite Sequences Ton Kalker Philips Research Laboratories, Eindhoven Lattice Chains Change of Variables An Extended Example: HDTV-to-SDTV Conversion Conclusions References Appendix Proof of Theorem Proof of Theorem Proof of Theorem Proof of Theorem Proof of Theorem Glossary of Symbols and Expressions This chapter gives an overview of the most relevant | Kalker T. On Multidimensional Sampling Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC On Multidimensional Sampling Ton Kalker Philips Research Laboratories Eindhoven Introduction Lattices Definition Fundamental Domains and Cosets Reciprocal Lattices Sampling of Continuous Functions The Continuous Space-Time FourierTransform The Discrete Space-Time Fourier Transform Sampling and Periodizing From Infinite Sequences to Finite Sequences The Discrete Fourier Transform Combined Spatial and Frequency Sampling Lattice Chains Change of Variables An Extended Example HDTV-to-SDTV Conversion Conclusions References Appendix Proof of Theorem Proof of Theorem Proof of Theorem Proof of Theorem Proof of Theorem Glossary of Symbols and Expressions This chapter gives an overview of the most relevant facts of sampling theory paying particular attention to the multidimensional aspect of the problem. It is shown that sampling theory formulated in a multidimensional setting provides insight to the supposedly simpler situation of one-dimensional sampling. Introduction The signals we encounter in the physical reality around us almost invariably have a continuous domain of definition. We like to model a speech signal as continuous function of amplitudes where the domain of definition is a finite length interval of real numbers. A video signal is most naturally viewed as continuous function of luminance chrominance values where the domain of definition is some volume in space-time. In modern electronic systems we deal with many in essence continuous signals in a digital fashion. This means that we do not deal with these signals directly but only with sampled versions of it we only retain the values of these signals at a discrete set of points. Moreover due to the inherently finite 1999 by CRC Press LLC precision arithmetic .