Forums

Who Invented the Z Transform

Started by Tim Wescott June 30, 2005
What about Tustin in England, didn't he do a lot of work in this area?

fred.

Fred Stevens wrote:
> What about Tustin in England, didn't he do a lot of work in this area? > > fred.
Wasn't he the bilinear guy? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Jerry Avins <jya@ieee.org> wrote in news:1qednboPe9cB_ljfRVn-qQ@rcn.net:

> Fred Stevens wrote: >> What about Tustin in England, didn't he do a lot of work in this area? >> >> fred. > > Wasn't he the bilinear guy? > > Jerry
I think the Z transform was discovered by Zefram Cochran; the guy who will invent the warp drive. -- Al Clark Danville Signal Processing, Inc. -------------------------------------------------------------------- Purveyors of Fine DSP Hardware and other Cool Stuff Available at http://www.danvillesignal.com
"John E. Hadstate" <jh113355@hotmail.com> wrote in message
news:J89xe.13711$Tt.10257@bignews3.bellsouth.net...
> > "Sanctus" <sanctus@upthere.com> wrote in message > news:8e7xe.11826$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 > >
So what did Shannon do? Sanctus
On Fri, 1 Jul 2005 17:03:45 +1200, "Sanctus" <sanctus@upthere.com>
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. >> &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095; > >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
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-]
> >
Rick Lyons 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?
Impedance? OK, that's capitalized. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
"Sanctus" <sanctus@upthere.com> wrote in message 
news:FyWxe.12312$U4.1524914@news.xtra.co.nz...
> > "John E. Hadstate" <jh113355@hotmail.com> wrote in message > news:J89xe.13711$Tt.10257@bignews3.bellsouth.net... >> >> "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 >> >> > So what did Shannon do? > > Sanctus > >
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
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.

Gee, is it me or did we a thread  on the same lines like a couple of months
back? I clicked on the links Jerry provided to read about Witold Hurewicz
and it felt like a second coming. Or did I belong in my previous birth?

--Bhooshan


		
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<eunometic@yahoo.com.au> wrote in message 
news:1122873344.917693.210890@g14g2000cwa.googlegroups.com...
> > Hilbert Transforms were ofcourse developed by Hilbert and the Dirac > delta by Dirac.
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.
> 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.
Really? Which aspects of relativity theory did David Hilbert invent? Clay