Complementary vector codes with applications to measuring and imaging problems

Pekka Hiismäki

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

A vector notation is developed for describing complementary codes defined at finite apertures of particular relevance to measuring and imaging problems. The original complementary series of Golay defined at one-dimensional linear apertures, are extended for more general apertures, notably in two dimensions. Two generating rules of the codes are formulated, namely the doubling rule familiar from the one-dimensional Golay series, and the point symmetry rule for adding just one vector element to a code of a strict rotational symmetry. Both on-off-type and polarity-type modulation are included and decoding algorithms are presented based on the ideal delta-function-type autocorrelation function of the codes without any side structure. Statistical analysis of the application of the complementary vector codes to a modulated Poisson process is given and implementation of the codes to ultrasonics, powder diffraction and X-ray astronomy discussed.

Original languageEnglish
Pages (from-to)709 - 716
Number of pages8
JournalMeasurement Science and Technology
Volume2
Issue number8
DOIs
Publication statusPublished - 1991
MoE publication typeA1 Journal article-refereed

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Imaging
Imaging techniques
Delta functions
Astronomy
apertures
Autocorrelation
Decoding
Statistical methods
Ultrasonics
X-ray Astronomy
Modulation
poisson process
X rays
Rotational symmetry
Series
Delta Function
delta function
symmetry
Polarity
decoding

Cite this

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title = "Complementary vector codes with applications to measuring and imaging problems",
abstract = "A vector notation is developed for describing complementary codes defined at finite apertures of particular relevance to measuring and imaging problems. The original complementary series of Golay defined at one-dimensional linear apertures, are extended for more general apertures, notably in two dimensions. Two generating rules of the codes are formulated, namely the doubling rule familiar from the one-dimensional Golay series, and the point symmetry rule for adding just one vector element to a code of a strict rotational symmetry. Both on-off-type and polarity-type modulation are included and decoding algorithms are presented based on the ideal delta-function-type autocorrelation function of the codes without any side structure. Statistical analysis of the application of the complementary vector codes to a modulated Poisson process is given and implementation of the codes to ultrasonics, powder diffraction and X-ray astronomy discussed.",
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Complementary vector codes with applications to measuring and imaging problems. / Hiismäki, Pekka.

In: Measurement Science and Technology, Vol. 2, No. 8, 1991, p. 709 - 716.

Research output: Contribution to journalArticleScientificpeer-review

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