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Signal Representation and Quantization Jelena Kova ˇcevi ´c Bell Laboratories, Lucent Technologies Christine Podilchuk Bell Laboratories, Lucent Technologies 4 On Multidimensional Sampli

Signal

Representation

and Quantization

Jelena Kova ˇcevi ´c

Bell Laboratories, Lucent Technologies

Christine Podilchuk

Bell Laboratories, Lucent Technologies

4 On Multidimensional Sampling Ton Kalker

Introduction •Lattices•Sampling of Continuous Functions•From Infinite Sequences to Finite

Sequences •Lattice Chains•Change of Variables•An Extended Example: HDTV-to-SDTV

Con-version •Conclusions

5 Analog-to-Digital Conversion Architectures Stephen Kosonocky and Peter Xiao

Introduction •Fundamentals of A/D and D/A Conversion•Digital-to-Analog Converter

Archi-tecture •Analog-to-Digital Converter Architectures•Delta-Sigma Oversampling Converter

6 Quantization of Discrete Time Signals Ravi P Ramachandran

Introduction •Basic Definitions and Concepts•Design Algorithms•Practical Issues•Specific

Manifestations •Applications•Summary

SAMPLING THEOREMS CAN BE TRACED to the original paper by Whittaker in 1915 on

interpolation He proved the exactness of a method for interpolating between the samples from a function Nyquist then presented the sampling theory for sampled telephone signals

in 1928 establishing for the first time the term Nyquist frequency Shannon in 1948 and Kotel’nikov

in 1933 wrote additional treatises on this topic [1]-[4]

Extensions from one-dimensional to multidimensional sampling can be traced to papers by Bracewell in 1956, and to Miyakawa in 1959 Multidimensional Fourier analysis, however, can

be traced back to papers by Germain and Navier in the early 18th and 19th centuries [5]-[7]

c 1999 by CRC Press LLC

In this section, the first chapter, “On Multidimensional Sampling” by Kalker presents a thorough discussion of the techniques that are currently used and their underlying theory

Of related interest is structure of the conversion process from the analog domain to the digital do-main, and the chapter by Kosonocky and Xiao presents a thorough survey of the various architectures for analog-to-digital conversion

Finally, the process of quantization of discrete samples is discussed in the chapter by Ramachandran This discussion considers the accuracy issues arising due to quantization, in addition to other related topics

References

[1] Whittaker, E T.,Proc R Soc Edinburgh 35: 181-194, 1915.

[2] Nyquist, H., Certain topics in telegraph transmission theory,Trans AIEE 47: 617-644, 1928.

[3] Shannon, C E., A mathematical theory of communication,Bell System Technical Journal

27:379-423, 1948

[4] Sullivan, W et al.,The Early Years of Radio Astronomy, Cambridge University Press, Cambridge,

England, 1984

[5] Bracewell, R N., Two-dimensional aerial smoothing in radio astronomy,Aust J Phys 9:197-314,

1956

[6] Miyakawa, K., Sampling theory of stationary stochastic variables in multidimensional space,J Inst Elec Commun (Japan), 421-427, 1959.

[7] Bracewell, R N.,Two-Dimensional Imaging, Prentice-Hall, Englewood Cliffs, NJ, 1995.

c 1999 by CRC Press LLC