# Laplace Transform vs Fourier transform

Started by 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&#4294967295;am, Jerry Avins <j...@ieee.org> wrote:
>>>> robert bristow-johnson wrote:
>>>>
>>>> &#4294967295; &#4294967295;...
>>>>
>>>>> there's a part of that angular frequency that is mathematical, but not
>>>>> physical. &#4294967295;how do you physically measure negative frequency? &#4294967295;and
>>>>> negative frequency is in the F.T.
>>>>
>>>> Who said? You can just as well apply the negative sign in exp(-jwt) to
>>>> time. :-)
>>>>
>>>> &#4294967295; &#4294967295;...
>>>>
>>>
>>> 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&#4294967295;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&#4294967295;am, Jerry Avins <j...@ieee.org> wrote:
>>>> robert bristow-johnson wrote:
>>
>>>> &#4294967295; &#4294967295;...
>>
>>>>> there's a part of that angular frequency that is mathematical, but no
> t
>>>>> physical. &#4294967295;how do you physically measure negative frequency? &#4294967295;and
>>>>> negative frequency is in the F.T.
>>
>>>> Who said? You can just as well apply the negative sign in exp(-jwt) to
>>>> time. :-)
>>
>>>> &#4294967295; &#4294967295;...
>>
>>> we've been here before. &#4294967295;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&#4294967295;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&#4294967295;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&#4294967295;am, Jerry Avins <j...@ieee.org> wrote:
> >>>> robert bristow-johnson wrote:
>
> >>>> &#4294967295; &#4294967295;...
>
> >>>>> there's a part of that angular frequency that is mathematical, but no
> > t
> >>>>> physical. &#4294967295;how do you physically measure negative frequency? &#4294967295;and
> >>>>> negative frequency is in the F.T.
>
> >>>> Who said? You can just as well apply the negative sign in exp(-jwt) to
> >>>> time. :-)
>
> >>>> &#4294967295; &#4294967295;...
>
> >>> we've been here before. &#4294967295;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&#4294967295;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. &#4294967295;how do you physically measure negative frequency? &#4294967295;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.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```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.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```