Dunno. The two meanings of the word "pole" in English are "stake, tall
skinny tree, post" (think "flag pole"), and "pivot, center" (think
"north pole").
Either one would be a likely candidate, but I suspect the "pivot"
meaning, because one's analysis has to rotate around the pole when one
is trying to do math in it's vicinity.
--
Tim Wescott
Control system and signal processing consulting
Maybe because modulus looks like steep hill.
Matlab 'please forgive me' code:
%L=(0.3*(1.2-s)/(s^2+s+1)); used during my maximum modulus theorem fun,
one zero, two poles
h=inline( '20*log10(abs(0.3* (1.2-Re+j*Im)/ ( (Re+j*Im)^2+(Re+j*Im) +1) ))
','Re','Im');
ezmesh(h)
The term was in wide use in theoretical mathematics well before DSP (or
indeed any signal processing) was practiced. See
http://mathworld.wolfram.com/Pole.html
Jerry
--
Discovery consists of seeing what everybody has seen, and thinking what
nobody has thought. .. Albert Szent-Gyorgi
It's because EEs are lazy (*), and say "there's a pole at 1 kHz" rather
than -1j kHz. A pole is an infinite singularity in the complex plane,
and if you look at a 3-d plot of its magnitude vs x+jy, you'll rapidly
see why it's called that.
Cheers
Phil Hobbs
(*) I hasten to add that we physicists are lazy too, but in different
ways, e.g. our tendency to put gigaohm resistors on cables.
The question was *why* an infinite singularity is called a pole. It's a
language question. There is a horticultural technique known as
"layering". Someone who doesn't know the term is unlikely to guess what
the technique is. I know the technique, but I don't how it got its name.
Jerry
--
Discovery consists of seeing what everybody has seen, and thinking what
nobody has thought. .. Albert Szent-Gyorgi
I answered that. If you look at a 3-d plot, you'll see this big tall
spike going off to infinity from a flat background. Looks just like,
um, a pole.
Cheers
Phil Hobbs
That may be why you were told that a pole is called a pole -- it's what
I was told, too.
But that may not _be_ why the word "pole" was chosen, and in fact that
may not be the "pole" that was chosen at all. In the year 1000, budding
astronomers were told that the planets were affixed to great crystalline
spheres, but just because they were told that didn't make it so. Just
because you and I were told -- by mathematicians and engineers, not
etymologists, that this is so, doesn't make it so, any more than
Copernicus being told that the planets were mounted on crystalline
spheres made _that_ so.
--
Tim Wescott
Control system and signal processing consulting
Well, it seems to have been introduced by Weierstrass,
http://preview.tinyurl.com/ybu4sgd
and the idea of a pole as a centre of rotation was probably in there
too. It's quite an evocative word now that I think of it.
Cheers
Phil Hobbs
The original term was "ausserwesentliche singulaer Stelle", literally
"not-essential singular place", although "ausserwesentlich" translates
literally to "outside of essential".
The French translation uses 'pole', which more or less means 'place',
and comes close to "pole" as in "north pole" or "pole of attraction".
It does not mean "perche", "long skinny thing that holds stuff up".
We are victims of the 19th century predilection of English speakers to
think that anything French makes one insufferably cool, and to just
adopt French words into English as if we were all still being ruled by
Normans. Never mind that the four letters p-o-l-e already mean
something in English -- we'll just adopt them, and expect folks to
remember that we mean the French "pole ay".
Well, enough of this. I'm off to the new French restaurant in town:
their chef is from France and can be exceedingly rude to Americans he
thinks are pretentious. They've got a new dish on special today. It's
called Frites de Merde du Chien. I have no idea what it is, but it's a
French dish, so it has to be tasty!
--
Tim Wescott
Control system and signal processing consulting
Does he collect the morsels Fr: morceau) in the park? If I lived closer,
I could add Mooch's contribution, but I doubt they would allow it
through the mail.
Jerry
P.S. Is it served on a shingle?
--
Discovery consists of seeing what everybody has seen, and thinking what
nobody has thought. .. Albert Szent-Gyorgi
The Middle Ages were actually pretty civilized and intellectually
astute--within certain limitations, which were basically due to an
exaggerated and uncritical respect for ancient authors of all
sorts--pagan, Christian, and even Muslim.
The crystalline spheres were invented by Eudoxus, a follower of Plato,
around 400 BC. And Copernicus didn't get rid of spheres and epicycles
and so on, he just moved the centre of the Ptolemaic system to the Sun
instead of the Earth.
Cheers
Phil Hobbs
I have read an article (or book -- dang my memory!) that made the point
that the transition from the Middle Ages to the Renaissance happened
because, in trying to revive the ancient knowledge, western culture
managed to exceed it. The author's opinion was that at first, folks
didn't realize they had done so -- and when they had, that's what
_really_ spurred the Renaissance on.
--
Tim Wescott
Control system and signal processing consulting
The 'Renaissance' is really a creation of the 18th Century
neoclassicists, who were one of those groups who think that They Know
Best. They decided that Latin should be written and spoken as Cicero
did, and as a result killed off what was then still a living language.
(We suffer from similar busybodies today, but having by now completed
the destruction of the humanities, they've moved on to science and
politics.) Those folks lumped everything they happened to like under
the term 'Renaissance', even though that allegedly coherent historical
period was in the 14th Century in Italy and the 16th and 17th Centuries
in England--a time span longer than the High Middle Ages.
They also tried to take credit for the 'revival of learning' which was
actually due to the Turks having overrun the Byzantine Empire, burned
the libraries, and pushed whatever was left of the learning of the
ancient world westward into Europe.
Early modern times were just another unsettled period, albeit one in
which both modern science and the modern 'occult' (magic and many other
kinds of superstition) were born. Frequently it wasn't altogether clear
which was which--Kepler cast horoscopes for part of his living, for
instance--but it was very largely the real upswing in witchcraft, which
was widely believed in at the time that was responsible for the early
modern ('Renaissance') witch-burnings.
But don't get me started, or I might go off-topic. ;)
Cheers
Phil Hobbs
Thanks for the replies everyone. I think Jerry and Phil are basically
saying the same thing anyway. If you check the link Jerry provides
( http://mathworld.wolfram.com/Pole.html ), a pole is described as a
singularity... that is, a tall skinny spike going to infinity. Looks
like a ``pole'' to me.
Comment: I was being rather lazy when I posted my original question,
and didn't look at my undergrad text, Feedback Control of Dynamic
Systems by Franklin-Powell-Emami. In Ch. 3, Sec. 1.8 (pg 116 in the
fourth ed.) there is a footnote that reads
`` The meaning of the pole can also be appreciated by visualized a
three-dimensional plot of the transfer function, where the real and
imaginary parts of s are plotted on the x and y axes, and the
magnitude of the transfer function is plotted on the vertical z axis.
For a single pole, the resulting three-dimensional plot will look like
a tent with the ``tent-pole'' being located at the pole of the
transfer function! '' (exclamation mark included in actual quote).
On one hand I should apologize for bothering everyone. On the other,
now we all know!
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