Who Invented the Z Transform

It's pretty easy to figure out who was responsible for the Fourier transform, ditto for the Laplace.
Does anybody out there know who dreamed up the z transform (Please tell
me it wasn't someone named 'Z')?
------------------------------------------- Tim Wescott Wescott Design Services http://www.wescottdesign.com
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"The techniques of the z-transform method are not new, for they can be actually traced back as early as 1730 when DeMoivre introduced the concept of the 'generating function' (which is actually identical to the z-transform) to probability theory."
Jury, E. I., Theory and Application of the z-Transform Method, (c) 1964, John Wiley & Sons, New York, Page 1.
References at the end of Chapter 1 show:
[5] Helm, H. A., "The z-Transformation," B.S.T. Journal, Vo 38, No. 1, 1956, pp 177-196
[32] Lago, G. V., "Additions to z-Transformation Theory for Sampled-Data Systems," Trans. AIEE Vol. 74, Part II, 1955, pp. 403-408
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Tim Wescott wrote:

His name actually _ends_ with z: Witold Hurewicz, in 1947. It was named in 1952 by a sampled-data control group at Columbia University, one of who's grad student members taught a course at CCNY a year or two later that I audited and promptly forgot. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hurewicz.html
Jerry
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Complex variables have been known since the time of Cauchy in the 18th century - remember all those contour integrals? You mean for engineering applications I presume? Also sampled systems were known in stats by Whittaker in the 1920s I think in Edinburgh who also discovered the sampling theorem.I also heard (in this newsgroup) that it was Prof Zadeh who coined the term z-transform though he did not name it Z after his own name.
Sanctus
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Sanctus wrote:

Complex variables are a bit removed from difference equations. The analysis of sampled data was cumbersome until Hurewitz simplified it. Like many other simple ways to look at something, you can find lots of antecedents once it is isolated. (Special relativity is implicit in Maxwell's Treatise. Maxwell masked it with "aether".)
Jerry
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wrote:

Hi,
It was I who asked Julius Kasuma (by the way, what's happened to Julius?) to ask Prof. Zadeh if the z-transform (created by Zadeh and his colleagues at Columbia University years ago) was named after Zadeh himself.
Julius was a grad student at Berkeley at the time of my question and Prof. Zadeh was also at Berkeley.
Julius approached the professor & according to Julius, Prof. Zadeh said they used the letter "z" because that letter wasn't typically used for anything else (like "e" for voltage, "i" for current, "R" for resistance, etc.) in electral engineering.
Interesting huh?
See Ya', [-Rick-]

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Rick Lyons wrote:
...

Impedance? OK, that's capitalized.
Jerry
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I got into this thread late: but it wasn't Laplace that invented the S-transform: it was Olover Heavaside. It's sometimes called the Heaviside Transform.
Pure mathematicians rejected his work because of a lack of proof to their expected standards but engineers used it becuase it worked. Engineers still use Heaviside Functions albeit modified to conform more to the pure mathematicians Laplace transform.
Hilbert Transforms were ofcourse developed by Hilbert and the Dirac delta by Dirac. Hilbert incidently had developed relativity before Einstein: Einstein who had read Hilberts papers simply 'gazzumped' him to publication and has been reaping the publicity since.
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The "delta function" came before Dirac, but it was little known. He popularized the concept and showed how useful it can be to applications in quantum mechanics.

Really? Which aspects of relativity theory did David Hilbert invent?
Clay
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Clay S. Turner wrote:

Most detailed histories of almost any scientific activity show that there was someone who did some piece of work and another who later realized that it had a much broader scope. The recognition tends to go to the worker who realizes the importance.
All of the Maxwell equations were know before Maxwell but they had not been collected into a system to provide a common example of this.
Einstein's special relativity used the known Lorentz transformation.

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Actually Maxwell introduced the concept of displacement current. And with this modification the system became complete. He certainly based his work on Gauss, Faraday, and Ampere. But before he did his modification to Ampere's law, the only theoretical way to produce a magnetic field was to have a current (charges in motion). He added the notion that a time varing electric field also produced a magnetic field. He set up an experiement where a constant current was charging a capacitor and noted that a magnetic field existed in between the plates of the cap where there was clearly no current flowing. He also noted that this magnetic field had the same total flux as the field surounding the conductors leading to and from the capacitor.
While Einstein used the Lorentz transform, he changed the reasoning behind its usage and its actual interpretation. However people still call the Lorentz transform a "Lorentz" transform. Einstein's greatest work was in GR. SR is pretty easy to follow, but Einstein had the forthought to choose the proper two axioms (velocity of light is constant in vacuo and physics is the same everywhere) and show that Maxwell's wave equation is invariant under Lorentz transformation. GR took a lot more vision and the use of tensors. The biggest contributor would be Poincare'.
His work on GR cost him 11 years of work after SR and his marriage. Other scientists warned him to not work on gravity since it is too hard. Not to take away from Hilbert's mathematical ability, I never seen his work mentioned in relativity books saying that he predated Einstein.
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Clay wrote:

And his Nobel Prize in 1921 was not for relativity, but for explaining the photoelectric effect, essentially laying the foundation for quantum mechanics.
Jerry
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Clay wrote:

I suppose the OP was referring to Hilbert's action principle (for gravitation as a consequence of space-time curvature). According to Misner, Thorne, and Wheeler (see section 21.2 of their book _Gravitation_) Hilbert published this all of 5 days before Einstein published his field equation, but in their words "animated by Einstein's earlier work". The Einstein field equation (for empty space-time at least) follows from Hilbert's principle, which is basically the principle of least action applied to a Lagrangian proportional to the Ricci curvature scalar. I don't think there's any doubt that credit for the field equation (and so for general relativity) belongs solely to Einstein, but Hilbert's work also seems to me to be worth noting.
Hope that clears things up.
Robert E. Beaudoin
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Robert E. Beaudoin wrote:
(snip)

I haven't seen a copy for many years. The story I used to hear was that only three people really understood the book.
-- glen
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Hello Robert,
Thanks for the response. My interpretation of the OP's statement was Hilbert beat Einstein to the result and then Einstein stole all of the glory. Hilbert's approach is certainly notewothy since least action principles abound in physics and alternative mathematical methods often prove to be illuminating on their own[1]. However I suspect Hilbert was familiar with Einstein's result and therefore not only had the problem but also had the solution. This is quite different than working out a solution where the destination is unknown. But even if Hilbert found this solution without knowing the field equation (a great feat the principle of equivalence is bypassed yielding a theory without an obvious physical basis (The few references I've found so far give little to no detail). I don't have Wheeler handy. Einstein's approach is rooted in a physical basis. And today most who study his work celebrate his acheivements.
Clay
[1] Hamilton's modification to the LaGrangian method of classical mechanics turns out to be the usual approach in quantum mechanics.
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Clay wrote:

Hi Clay,
Just in case it wasn't clear: I agree with you on all of this.
Bob Beaudoin
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in
It was Heviside who wrote the vector form of Maxwells equations - the ones we recognise - not Maxwell.
Shytot
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On Mon, 01 Aug 2005 13:19:42 GMT, Gordon Sande

Hi,
I read somewhere that when Maxwell died, there were twenty "Maxwell's equations", and that it was Oliver Heaviside who reduced those down to the current-day four equations.
See Ya', [-Rick-]
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Rick Lyons wrote:

Maxwell's equations were originally four _sets_ of integral equations, one in each set for one axis in space, for a total of 12. He also expresses the relations in quaternions and vector analysis (curl and all that). Dover has an unabridged two-volume set of "A Treatise on Electricity and Magnetism". I bought mine long ago. The set was $4. Reading it gives one much respect for the ancients.
Jerry
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Jerry Avins wrote:

>>

There are also Maxwell's relations which are fundamental in thermodynamics. The story has it that an eminent physicist, active in thermodynamics, once did a review of Maxwell's work which included a line that "Maxwell also did some work in electromagnetism".

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