Forums

Laplace Transform vs Fourier transform

Started by fisico32 October 27, 2009
On 2009-10-29 15:00:06 -0300, Rich Webb <bbew.ar@mapson.nozirev.ten> said:

> On Thu, 29 Oct 2009 17:38:31 GMT, Gordon Sande > <g.sande@worldnet.att.net> wrote: > >> On 2009-10-29 14:20:36 -0300, robert bristow-johnson >> <rbj@audioimagination.com> said: >> >>> On Oct 29, 10:52&#2013266080;am, Jerry Avins <j...@ieee.org> wrote: >>>> robert bristow-johnson wrote: >>>> >>>> &#2013266080; &#2013266080;... >>>> >>>>> there's a part of that angular frequency that is mathematical, but not >>>>> physical. &#2013266080;how do you physically measure negative frequency? &#2013266080;and >>>>> negative frequency is in the F.T. >>>> >>>> Who said? You can just as well apply the negative sign in exp(-jwt) to >>>> time. :-) >>>> >>>> &#2013266080; &#2013266080;... >>>> >>> >>> we've been here before. for the record, i actually think that the >>> term "imaginary" for imaginary numbers is apt, appropriate, and >>> descriptive. >> >> Like surds, irrational, etc. Mathematical terminology from the middle ages >> tended to be very unkind to all sorts of new fangled things as told by >> any history of mathematics book. That was back when solving a quadratic >> equation was a big deal and solution to quartics was a closely guarded >> trade secret. It is too bad that 500 year old attitudes are taken seriously >> by some current folks. > > Middle Ages? It wasn't that long ago that simple negative numbers were > not universally accepted by mathematicians. A brief discussion at: > http://nrich.maths.org/5961
There are always a few who have trouble staying current. ;-)
On 2009-10-29 14:51:17 -0300, robert bristow-johnson 
<rbj@audioimagination.com> said:

> On Oct 29, 1:38&#2013266080;pm, Gordon Sande <g.sa...@worldnet.att.net> wrote: >> On 2009-10-29 14:20:36 -0300, robert bristow-johnson >> <r...@audioimagination.com> said: >> >> >> >>> On Oct 29, 10:52&#2013266080;am, Jerry Avins <j...@ieee.org> wrote: >>>> robert bristow-johnson wrote: >> >>>> &#2013266080; &#2013266080;... >> >>>>> there's a part of that angular frequency that is mathematical, but no > t >>>>> physical. &#2013266080;how do you physically measure negative frequency? &#2013266080;and >>>>> negative frequency is in the F.T. >> >>>> Who said? You can just as well apply the negative sign in exp(-jwt) to >>>> time. :-) >> >>>> &#2013266080; &#2013266080;... >> >>> we've been here before. &#2013266080;for the record, i actually think that the >>> term "imaginary" for imaginary numbers is apt, appropriate, and >>> descriptive. >> >> Like surds, irrational, etc. Mathematical terminology from the middle age > s >> tended to be very unkind to all sorts of new fangled things as told by >> any history of mathematics book. That was back when solving a quadratic >> equation was a big deal and solution to quartics was a closely guarded >> trade secret. It is too bad that 500 year old attitudes are taken serious > ly >> by some current folks. > > am i one of them current folk, Gordon? > > r b-j
If you act like an imaginary number is a invention of the devil then all one can say is "If the shoe fits ..."
robert bristow-johnson wrote:
> just to add to what brent and Jerry and Hardy said... > > On Oct 27, 9:39 pm, "fisico32" <marcoscipio...@gmail.com> wrote: >> everyone is familiar with the Fourier transform and its importance. >> Its independent variable, the angular frequency w, is a measurable >> physical quantity. > > there's a part of that angular frequency that is mathematical, but not > physical. how do you physically measure negative frequency? and > negative frequency is in the F.T.
(snip)
> r b-j
Configure a CRO for XY mode. Connect the I signal to the X channel and the Q signal to the Y channel. The spot traces an anti-clockwise circular path for positive frequency signals; clockwise for negative frequency. Count the number of circles per second and attach the appropriate sign. Regards, John
On Oct 29, 2:41&#2013266080;pm, Gordon Sande <g.sa...@worldnet.att.net> wrote:
> On 2009-10-29 14:51:17 -0300, robert bristow-johnson > <r...@audioimagination.com> said: > > > > > On Oct 29, 1:38&#2013266080;pm, Gordon Sande <g.sa...@worldnet.att.net> wrote: > >> On 2009-10-29 14:20:36 -0300, robert bristow-johnson > >> <r...@audioimagination.com> said: > > >>> On Oct 29, 10:52&#2013266080;am, Jerry Avins <j...@ieee.org> wrote: > >>>> robert bristow-johnson wrote: > > >>>> &#2013266080; &#2013266080;... > > >>>>> there's a part of that angular frequency that is mathematical, but no > > t > >>>>> physical. &#2013266080;how do you physically measure negative frequency? &#2013266080;and > >>>>> negative frequency is in the F.T. > > >>>> Who said? You can just as well apply the negative sign in exp(-jwt) to > >>>> time. :-) > > >>>> &#2013266080; &#2013266080;... > > >>> we've been here before. &#2013266080;for the record, i actually think that the > >>> term "imaginary" for imaginary numbers is apt, appropriate, and > >>> descriptive. > > >> Like surds, irrational, etc. Mathematical terminology from the middle age > > s > >> tended to be very unkind to all sorts of new fangled things as told by > >> any history of mathematics book. That was back when solving a quadratic > >> equation was a big deal and solution to quartics was a closely guarded > >> trade secret. It is too bad that 500 year old attitudes are taken serious > > ly > >> by some current folks. > > > am i one of them current folk, Gordon? > > > If you act like an imaginary number is a invention of the devil then > all one can say is "If the shoe fits ..."
well, you'll have to judge if i act like that. from where i stand, all's i'm saying is that real (meaning that they really exist) physical quantities are measured as real numbers. r b-j
On Oct 29, 7:21&#2013266080;pm, John Monro <johnmo...@optusnet.com.au> wrote:
> robert bristow-johnson wrote: > > just to add to what brent and Jerry and Hardy said... > > > On Oct 27, 9:39 pm, "fisico32" <marcoscipio...@gmail.com> wrote: > >> everyone is familiar with the Fourier transform and its importance. > >> Its independent variable, the angular frequency w, is a measurable > >> physical quantity. > > > there's a part of that angular frequency that is mathematical, but not > > physical. &#2013266080;how do you physically measure negative frequency? &#2013266080;and > > negative frequency is in the F.T. > > (snip) > > > r b-j > > Configure a CRO for XY mode. > Connect the I signal to the X channel and the Q signal to > the Y channel. > The spot traces an anti-clockwise circular path for positive > frequency signals; clockwise for negative frequency. > Count the number of circles per second and attach the > appropriate sign. >
that's fine and a legit human interpretation or abstraction of what is happening with two real and physically related signals are observed on an oscilloscope in XY mode. you still measure the Y signal at any instance in time as a real value. r b-j
robert bristow-johnson <rbj@audioimagination.com> wrote:
 
> well, you'll have to judge if i act like that. from where i stand, > all's i'm saying is that real (meaning that they really exist) > physical quantities are measured as real numbers.
Many physical quantities aren't necessarily real. Index of refraction is usually complex. Closer to DSP, impedance is often complex. -- glen
John Monro wrote:
> robert bristow-johnson wrote: >> just to add to what brent and Jerry and Hardy said... >> >> On Oct 27, 9:39 pm, "fisico32" <marcoscipio...@gmail.com> wrote: >>> everyone is familiar with the Fourier transform and its importance. >>> Its independent variable, the angular frequency w, is a measurable >>> physical quantity. >> >> there's a part of that angular frequency that is mathematical, but not >> physical. how do you physically measure negative frequency? and >> negative frequency is in the F.T. > > (snip) > >> r b-j > > > Configure a CRO for XY mode. > Connect the I signal to the X channel and the Q signal to the Y channel. > The spot traces an anti-clockwise circular path for positive frequency > signals; clockwise for negative frequency. > Count the number of circles per second and attach the appropriate sign.
Activate the INVERT switch on the vertical channel and watch time run backwards. 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;
robert bristow-johnson wrote:
> On Oct 29, 7:21 pm, John Monro <johnmo...@optusnet.com.au> wrote: >> robert bristow-johnson wrote: >>> just to add to what brent and Jerry and Hardy said... >>> On Oct 27, 9:39 pm, "fisico32" <marcoscipio...@gmail.com> wrote: >>>> everyone is familiar with the Fourier transform and its importance. >>>> Its independent variable, the angular frequency w, is a measurable >>>> physical quantity. >>> there's a part of that angular frequency that is mathematical, but not >>> physical. how do you physically measure negative frequency? and >>> negative frequency is in the F.T. >> (snip) >> >>> r b-j >> Configure a CRO for XY mode. >> Connect the I signal to the X channel and the Q signal to >> the Y channel. >> The spot traces an anti-clockwise circular path for positive >> frequency signals; clockwise for negative frequency. >> Count the number of circles per second and attach the >> appropriate sign. >> > > that's fine and a legit human interpretation or abstraction of what is > happening with two real and physically related signals are observed on > an oscilloscope in XY mode. > > you still measure the Y signal at any instance in time as a real > value. > > r b-j
This is because the magnitude of the imaginary component of a complex signal is a real signal. Regards, John
Jerry Avins wrote:
> John Monro wrote: >> robert bristow-johnson wrote: >>> just to add to what brent and Jerry and Hardy said... >>> >>> On Oct 27, 9:39 pm, "fisico32" <marcoscipio...@gmail.com> wrote: >>>> everyone is familiar with the Fourier transform and its importance. >>>> Its independent variable, the angular frequency w, is a measurable >>>> physical quantity. >>> >>> there's a part of that angular frequency that is mathematical, but not >>> physical. how do you physically measure negative frequency? and >>> negative frequency is in the F.T. >> >> (snip) >> >>> r b-j >> >> >> Configure a CRO for XY mode. >> Connect the I signal to the X channel and the Q signal to the Y channel. >> The spot traces an anti-clockwise circular path for positive frequency >> signals; clockwise for negative frequency. >> Count the number of circles per second and attach the appropriate sign. > > Activate the INVERT switch on the vertical channel and watch time run > backwards. > > Jerry
I tried that experiment, but noticed that I had finished AFTER I started rather than before. I therefore concluded that the observed change in the motion of the dot on the CRO screen was probably not due to a change in the direction of time. Regards, John
John Monro wrote:
> robert bristow-johnson wrote: >> On Oct 29, 7:21 pm, John Monro <johnmo...@optusnet.com.au> wrote: >>> robert bristow-johnson wrote: >>>> just to add to what brent and Jerry and Hardy said... >>>> On Oct 27, 9:39 pm, "fisico32" <marcoscipio...@gmail.com> wrote: >>>>> everyone is familiar with the Fourier transform and its importance. >>>>> Its independent variable, the angular frequency w, is a measurable >>>>> physical quantity. >>>> there's a part of that angular frequency that is mathematical, but not >>>> physical. how do you physically measure negative frequency? and >>>> negative frequency is in the F.T. >>> (snip) >>> >>>> r b-j >>> Configure a CRO for XY mode. >>> Connect the I signal to the X channel and the Q signal to >>> the Y channel. >>> The spot traces an anti-clockwise circular path for positive >>> frequency signals; clockwise for negative frequency. >>> Count the number of circles per second and attach the >>> appropriate sign. >>> >> >> that's fine and a legit human interpretation or abstraction of what is >> happening with two real and physically related signals are observed on >> an oscilloscope in XY mode. >> >> you still measure the Y signal at any instance in time as a real >> value. >> >> r b-j > > This is because the magnitude of the imaginary component of a complex > signal is a real signal.
Of course. All things measurable are real. "Complex" numbers are merely a clever and useful bookkeeping scheme for manipulating related pairs of real quantities. 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;