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

# Who Invented the Z Transform

Started by ●June 30, 2005

Reply by ●June 30, 20052005-06-30

"Tim Wescott" <tim@seemywebsite.com> wrote in message news:11c93cfmsvmrjfb@corp.supernews.com...> 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')?"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

Reply by ●June 30, 20052005-06-30

Tim Wescott wrote:> 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')?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 -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●July 1, 20052005-07-01

"Jerry Avins" <jya@ieee.org> wrote in message news:nsidnQRcyaknA1nfRVn-vw@rcn.net...> Tim Wescott wrote: > > 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')? > > 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 > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������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

Reply by ●July 1, 20052005-07-01

Reply by ●July 1, 20052005-07-01

"Andor" <an2or@mailcircuit.com> wrote in message news:1120204205.455249.101130@f14g2000cwb.googlegroups.com...> Wasn't there this Russian ... ? > > :-) >There was a Russian who also discovered the sampling theorem. Sanctus

Reply by ●July 1, 20052005-07-01

"Andor" <an2or@mailcircuit.com> wrote in message news:1120204205.455249.101130@f14g2000cwb.googlegroups.com...> Wasn't there this Russian ... ? > > :-) >see.. <kus...@eecs.berkeley.edu> wrote:>i just ran into Lotfi Zadeh in the EE main office today. in honoring >Rick's request, i politely asked him about the Z-transform. Prof. Zadeh >was very nice and he said that he is credited with making it popular, from >a paper published in 1952 (almost 50 years now, hint hint!).>however, the choice of 'Z' was not to interject himself. it was chosen >because 'S' was used for the continuous-time version, so he picked 'Z' for >teh discrete-time work.>anyways, i thought this would be of interest to DSP-ers.>julius >back from exile for the next few daysNeat! Thanks Jul. [-Rick-]

Reply by ●July 1, 20052005-07-01

"Sanctus" <sanctus@upthere.com> wrote in message news:8e7xe.11826$U4.1484931@news.xtra.co.nz...> > "Andor" <an2or@mailcircuit.com> wrote in message > news:1120204205.455249.101130@f14g2000cwb.googlegroups.com... >> Wasn't there this Russian ... ? >> >> :-) >> > There was a Russian who also discovered the sampling > theorem. > > Sanctus > >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

Reply by ●July 1, 20052005-07-01

Sanctus wrote:> "Jerry Avins" <jya@ieee.org> wrote in message > news:nsidnQRcyaknA1nfRVn-vw@rcn.net... > >>Tim Wescott wrote: >> >>>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')? >> >>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 >>-- >>Engineering is the art of making what you want from things you can get. >>����������������������������������������������������������������������� > > > 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.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 -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●July 1, 20052005-07-01

Andor wrote:> Wasn't there this Russian ... ? > > :-)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 -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������