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II
Signal
Representation
andQuantization
JelenaKova
ˇ
cevi
´
c
BellLaboratories,LucentTechnologies
ChristinePodilchuk
BellLaboratories,LucentTechnologies
4OnMultidimensionalSampling TonKalker
Introduction
•
Lattices
•
SamplingofContinuousFunctions
•
FromInfiniteSequencestoFinite
Sequences
•
LatticeChains
•
ChangeofVariables
•
AnExtendedExample:HDTV-to-SDTVCon-
version
•
Conclusions
5Analog-to-DigitalConversionArchitectures StephenKosonockyandPeterXiao
Introduction
•
FundamentalsofA/DandD/AConversion
•
Digital-to-AnalogConverterArchi-
tecture
•
Analog-to-DigitalConverterArchitectures
•
Delta-SigmaOversamplingConverter
6QuantizationofDiscreteTimeSignals RaviP.Ramachandran
Introduction
•
BasicDefinitionsandConcepts
•
DesignAlgorithms
•
PracticalIssues
•
Specific
Manifestations
•
Applications
•
Summary
S
AMPLINGTHEOREMSCANBETRACEDtotheoriginalpaperbyWhittakerin1915on
interpolation.Heprovedtheexactnessofamethodforinterpolatingbetweenthesamples
fromafunction.Nyquistthenpresentedthesamplingtheoryforsampledtelephonesignals
in1928establishingforthefirsttimethetermNyquistfrequency.Shannonin1948andKotel’nikov
in1933wroteadditionaltreatisesonthistopic[1]-[4].
Extensionsfromone-dimensionaltomultidimensionalsamplingcanbetracedtopapersby
Bracewellin1956,andtoMiyakawain1959.MultidimensionalFourieranalysis,however,can
betracedbacktopapersbyGermainandNavierintheearly18thand19thcenturies[5]-[7].
c
1999byCRCPressLLC
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, theprocessofquantizationofdiscretesamplesisdiscussedinthechapterbyRamachandran.
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
