Hello Forum,

everyone is familiar with the Fourier transform and its importance.
Its independent variable, the angular frequency w, is a measurable
physical quantity.

What about the Laplace transform? What is, conceptually, the advantage of
taking the Laplace transform of a signal instead of the Fourier transform?
I know that by looking at its zeros and poles we can assess the stability
of the system for example.... is that not possible with the FT alone?

Does the Laplace transform show information on the system that the FT does
not?

Hello Forum,

everyone is familiar with the Fourier transform and its importance.
Its independent variable, the angular frequency w, is a measurable
physical quantity.

What about the Laplace transform? What is, conceptually, the advantage of
taking the Laplace transform of a signal instead of the Fourier transform?
I know that by looking at its zeros and poles we can assess the stability
of the system for example.... is that not possible with the FT alone?

Does the Laplace transform show information on the system that the FT does
not?

thanks
fisico32

Hello Forum,

everyone is familiar with the Fourier transform and its importance.
Its independent variable, the angular frequency w, is a measurable
physical quantity.

What about the Laplace transform? What is, conceptually, the advantage of
taking the Laplace transform of a signal instead of the Fourier transform?
I know that by looking at its zeros and poles we can assess the stability
of the system for example.... is that not possible with the FT alone?

Does the Laplace transform show information on the system that the FT does
not?

thanks
fisico32

everyone is familiar with the Fourier transform and its importance.
Its independent variable, the angular frequency w, is a measurable
physical quantity.

What about the Laplace transform? What is, conceptually, the advantage of
taking the Laplace transform of a signal instead of the Fourier transform?

I know that by looking at its zeros and poles we can assess the stability
of the system for example.... is that not possible with the FT alone?

Does the Laplace transform show information on the system that the FT does
not?

On Thu, 29 Oct 2009 17:38:31 GMT, Gordon Sande
g.sande at (no spam) worldnet.att.net> wrote:

On 2009-10-29 14:20:36 -0300, robert bristow-johnson
rbj at (no spam) audioimagination.com> said:

On Oct 29, 10:52 am, Jerry Avins <j... at (no spam) ieee.org> wrote:
robert bristow-johnson wrote:

   ...

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.

Who said? You can just as well apply the negative sign in exp(-jwt) to
time. :-)

   ...


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

On Oct 29, 1:38 pm, Gordon Sande <g.sa... at (no spam) worldnet.att.net> wrote:
On 2009-10-29 14:20:36 -0300, robert bristow-johnson
r... at (no spam) audioimagination.com> said:



On Oct 29, 10:52 am, Jerry Avins <j... at (no spam) ieee.org> wrote:
robert bristow-johnson wrote:

   ...

there's a part of that angular frequency that is mathematical, but no
t
physical.  how do you physically measure negative frequency?  and
negative frequency is in the F.T.

Who said? You can just as well apply the negative sign in exp(-jwt) to
time. :-)

   ...

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 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

On 2009-10-29 14:51:17 -0300, robert bristow-johnson
r... at (no spam) audioimagination.com> said:



On Oct 29, 1:38 pm, Gordon Sande <g.sa... at (no spam) worldnet.att.net> wrote:
On 2009-10-29 14:20:36 -0300, robert bristow-johnson
r... at (no spam) audioimagination.com> said:

On Oct 29, 10:52 am, Jerry Avins <j... at (no spam) ieee.org> wrote:
robert bristow-johnson wrote:

   ...

there's a part of that angular frequency that is mathematical, but no
t
physical.  how do you physically measure negative frequency?  and
negative frequency is in the F.T.

Who said? You can just as well apply the negative sign in exp(-jwt) to
time. :-)

   ...

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 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 ..."

robert bristow-johnson wrote:
just to add to what brent and Jerry and Hardy said...

On Oct 27, 9:39 pm, "fisico32" <marcoscipio... at (no spam) 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.

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.

just to add to what brent and Jerry and Hardy said...

On Oct 27, 9:39 pm, "fisico32" <marcoscipio... at (no spam) 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.

r b-j

robert bristow-johnson wrote:
just to add to what brent and Jerry and Hardy said...

On Oct 27, 9:39 pm, "fisico32" <marcoscipio... at (no spam) 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.

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.

Complex numbers are a clever and useful way to represent those
quantities in cases where phase shift has meaning.

Compact notations expand out ability to comprehend (same root as in
prehensile) complicated things. Vector analysis, quaternions, complex
numbers, matrix algebra .. without them, we'd be hard pressed to
express, let alone understand, some phenomena as concepts. Nevertheless,
being built up from simpler stuff (Shall we go back to Peano's axioms?)
thay constitute the HLLs of math. Ultimately, all running code executes
assembly language.

Jerry Avins <jya at (no spam) ieee.org> wrote:
(snip, someone wrote)

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.

Or pairs of real numbers are a convenient way of measuring complex
quantities.

Impedance and index of refraction are both complex, and for similar
reasons. We can separately measure resistance and reactance, or
the real and imaginary parts of the index of refraction.
(The imaginary part comes from absorption.) Both are due to
the interaction of electrons with atoms, and with each other.

Often the available materials are fairly close to ideal, such
that we can separate the quantities. Resistors do have inductance,
inductors (except superconductors) do have resistance.