Multi-Slit Spectrometry*

Golay, M.

doi:10.1364/josa.39.000437

Cited by 291 publications

(120 citation statements)

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“…Such a pair of sequences is called a Golay complementary sequence pair (often abbreviated to Golay sequence pair) of length s, after Golay [14], [15]; Shapiro [24] independently studied the same object. The initial investigation of Golay sequence pairs was restricted to the binary case.…”

Section: Introductionmentioning

confidence: 99%

Golay complementary array pairs

Jedwab

Parker

2007

Des. Codes Cryptogr.

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Section: Introductionmentioning

confidence: 99%

Golay complementary array pairs

Jedwab

Parker

2007

Des. Codes Cryptogr.

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“…However closely related (and most important) work had already been done, independently by Golay [13,14] in 1949-1951 and by H. S. Shapiro [25] in 1951.…”

Section: Historical Appendix On Ponsmentioning

confidence: 94%

“…In his 1949-1951 papers [13] and [14], M. J. E. Golay introduced the general concept of "complementary pairs" of finite sequences all of whose entries are ±1. This was motivated by a highly non-trivial application to infra-red spectrometry.…”

Section: Historical Appendix On Ponsmentioning

confidence: 99%

Pons, Reed-Muller Codes, and Group Algebras

Byrnes

Moran

et al.

NATO Science Series II: Mathematics, Physics and Chemistry

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In this work we develop the family of Prometheus orthonormal sets (PONS) in the framework of certain abelian group algebras. Classical PONS, considered in 1991 by J. S. Byrnes, turned out to be a rediscovery of the 1960 construction by G. R. Welti [28], and of subsequent rediscoveries by other authors as well. This construction highlights the fundamental role played by group characters in the theory of PONS. In particular, we will relate classical PONS to idempotent systems in group algebras and show that signal expansions over classical PONS correspond to multiplications in the group algebra.The concept of a splitting sequence is critical to the construction of general PONS. We will characterize and derive closed form expressions for the collection of splitting sequences in terms of group algebra operations and group characters.The group algebras in this work are taken over direct products of the cyclic group of order 2. PONS leads to idempotent systems and ideal decompositions of these group algebras. The relationship between these special systems and ideal decompositions, and the analytic properties of PONS, is an open research topic. A second open research topic is the extension of this theory to group algebras over cyclic groups of order greater than 2.

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“…In this case t 2 ) (0, 0)} and Π 9 is a special permutation matrix. From this expression we see that Prometheus functions up to constant factor are modulated Chrestenson-Clifford sequences (i.e., Clifford-valued characters of the group Z 2 3 ):…”

Section: Radix-n Fourier-prometheus Transformsmentioning

confidence: 99%

“…in 1949-1951 [2]- [7]. In 1961, Golay [3] gave an explicit construction for binary Golay complementary pairs of length 2 m and later noted [4] that the construction implies the existence of at least 2 m m!/2 binary Golay sequences of this length.…”

Section: Introductionmentioning

confidence: 99%