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David Slepian
David S. Slepian (June 30, 1923 – November 29, 2007) was an American mathematician. He is best known for his work with algebraic coding theory, probability theory, and distributed source coding. He was colleagues with Claude Shannon and Richard Hamming at Bell Labs.
==Life and work==
Born in Pittsburgh, Pennsylvania, he gained a B.Sc. at University of Michigan before joining the US Army in World War II,
as a Sonic deception officer in the Ghost army.
He received his Ph.D. from Harvard University in 1949, writing his dissertation in physics. After post-doctoral work at the
University of Cambridge and University of Sorbonne, he worked at the Mathematics Research Center at Bell Telephone Laboratories, where he pioneered work in algebraic coding theory on group codes, first published in the paper ''A Class of Binary Signaling Alphabets''. Here, he also worked along with other information theory giants such as Claude Shannon and Richard Hamming. He also proved the possibility of singular detection, a perhaps unintuitive result. He is also known for
Slepian's lemma in probability theory (1962), and for discovering a fundamental result in
distributed source coding called Slepian–Wolf coding with Jack Keil Wolf (1973).
He later joined the University of Hawaii. His father was Joseph Slepian, also a scientist.〔(【引用サイトリンク】title=IEEE Global History Network - David Slepian )〕 His wife is the noted children's author Jan Slepian.
==Slepians==
Slepian's joint work with H.J. Landau and H.O. Pollak on discrete prolate spheroidal wave functions and sequences (DPSWF, DPSS) eventually led to the naming of the sequences as `Slepians'
〔(【引用サイトリンク】 title=Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty -- I )〕
〔(【引用サイトリンク】 title=Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty -- II )〕
〔(【引用サイトリンク】 title=Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty -- III: The Dimension of the Space of Essentially Time- and Band-Limited Signals )〕
〔(【引用サイトリンク】 title=Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty -- IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions )〕
.〔(【引用サイトリンク】 title=Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty -- V: The Discrete Case )〕 The naming suggestion was provided by Bob Parker of Scripp's Institute of Oceanography, who suggested that `discrete prolate spheroidal sequences' was a `mouthful'.
This work was fundamental to the development of the multitaper, where the discrete form are used as an integral component.
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