DocumentCode
934660
Title
The hexagon theorem
Author
Newman, Donald J.
Volume
28
Issue
2
fYear
1982
fDate
3/1/1982 12:00:00 AM
Firstpage
137
Lastpage
139
Abstract
We wish to 
the unit square, over all choices of 
which take just n values. For large n it is shown that approaches that function which on each face of a "hexagonal mesh" has the value of the centroid of that face. This problem in the design of quantizers for a pulse-code modulation (PCM) system arose in which pairs of adjacent samples are quantized in an effort to capitalize on the correlation between samples and on the geometry of the plane.
the unit square, over all choices of which take just n values. For large n it is shown that approaches that function which on each face of a "hexagonal mesh" has the value of the centroid of that face. This problem in the design of quantizers for a pulse-code modulation (PCM) system arose in which pairs of adjacent samples are quantized in an effort to capitalize on the correlation between samples and on the geometry of the plane.Keywords
Optimization methods; PCM communication; Quantization (signal); Signal quantization; Filtering; Geometry; Least squares methods; Mathematics; Phase change materials; Pulse modulation; Random variables; Sampling methods; Signal processing; Statistics;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.1982.1056492
Filename
1056492
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