Who Invented the Z Transform

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The reviewer of Fred Astaire's Hollywood screen test opined that Astaire would be passable and added, "and he can dance a bit, too."
Jerry
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I just watched him with Judy Garland in "Easter Parade" yesterday. I never really knew what "dancing like Fred Astaire" meant until I saw that movie. (And the costumes!!! ...)
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Wasn't there this Russian ... ?
:-)
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There was a Russian who also discovered the sampling theorem.
Sanctus
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Nyquist -- Swedish -- 1927
Kotelnikov -- Russian
Zhukovskii (Joukowski) -- Russian In mathematics today the conformal mapping of the complex plane z z + 1/z is called the Joukowski transformation. This gave Zhukovskii [2]:- ... a means of designing aerofoils using conformal mappings and the techniques of complex variables. Those Joukowski aerofoils were actually used on some aircraft, and today these techniques provide a mathematically rigorous reference solution to which modern approaches to aerofoil design can be compared for validation.
begin 666 rarrow.gif M1TE&.#EA# `2`( ``/___P```"P`````# `2```"%(2/J<OM#Z.<] 08+LB\ (<Y8U6M44`#L` ` end
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So what did Shannon do?
Sanctus
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He formalized the already known results (due to Whitaker, Kotelnikov, Hartley, and Nyquist) and mentions at the front of one of his papers on sampling that these ideas are known to anyone skilled in the art. But he is the one that connects them together in a formal sense. Also he goes on to define entropy (as applied to information and not thermodynamics) and then provides both the noiseless and noisy coding theorems, both of which are completely new.
Clay
"A Mathematical Theory of Communication" A must read for DSPers http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf
His complete bibliography: http://www.research.att.com/~njas/doc/shannonbib.html
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wrote:>i just ran into Lotfi Zadeh in the EE main office today. in honoring

Neat! Thanks Jul.
[-Rick-]
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Andor wrote:

Hurewicz was Polish, but born under the Czar's rule.
From http://www-history.mcs.st-and.ac.uk/Mathematicians/Hurewicz.html :
"Witold Hurewicz's father was an industrialist. Witold attended school in a Russian controlled Poland but with World War I beginning before he had begun secondary school, ..."
From http://www.ling.upenn.edu/courses/ling525/z.html :
"A method for solving linear, constant-coefficient difference equations by Laplace transforms was introduced to graduate engineering students by Gardner and Barnes in the early 1940s. They applied their procedure, which was based on jump functions, to ladder networks, transmission lines, and applications involving Bessel functions. This approach is quite complicated and in a separate attempt to simplify matters, a transform of a sampled signal or sequence was defined in 1947 by W. Hurewicz as
[not reproduced here]
which was later denoted in 1952 as a "z transform" by a sampled-data control group at Columbia University led by professor John R. Raggazini and including L.A. Zadeh, E.I. Jury, R.E. Kalman, J.E. Bertram, B. Friedland, and G.F. Franklin.
"The Hurewicz equation is not expressed in the same way as the z transform we have introduced -- it is one-sided, and it is expressed as a function of the sampled data sequence f rather than the complex number z -- but the relationship is clear, and the applications were similar from the beginning. So perhaps the z transform should really be called the "Hurewicz transform".
"In any case, it is presumably not an accident that the z transform was invented at about the same time as digital computers."
Make of this what you will. I first heard if Hurewicz in 1953 or so, from an instructor who joked that symbolic logic is just "Booleshit". Don't confuse him with Hurwitz.
Jerry
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Engineering is the art of making what you want from things you can get.

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What about Tustin in England, didn't he do a lot of work in this area?
fred.
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Fred Stevens wrote:

Wasn't he the bilinear guy?
Jerry
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Engineering is the art of making what you want from things you can get.

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I think the Z transform was discovered by Zefram Cochran; the guy who will invent the warp drive.
--
Al Clark
Danville Signal Processing, Inc.
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