>What is the physical significance of having an impulse response with
>complex coefficients ie
>
>{h0,h1,h2...hn}  where the h values are complex.
>
>
>Hardy
>
Regarding original question...
My perspective is the case you want to shape baseband signal asymmetrically
when upconverted to RF. A real filter cannot do that but a complex pair
can.

kadhiem

Mikolaj <sterowanie_komputerowe@poczta.onet.pl> writes:

> on 07-04-2010 o 13:53:36 glen herrmannsfeldt <gah@ugcs.caltech.edu> wrote:
>
> (...)
>> I believe that in some cases complex physical quantities
>> that are in exponents have a physical interpretation.
>> As examples, the dielectric constant and its square root,
>> the index of refraction.  Other than in exponents,
>> the use of complex numbers for physical quantities,
>> such as describing phase shifts, seems more of a
>> convenience, and not something with a physical
>> interpretation.
> (...)
>
> It seems that sometimes, luckily
> when you use complex (compressed, packed, combined, compact)
> way of describing few dependent physical things
> their imaginary part (additional dimension used for compression)
> can be human understandable
> and could have interpretation.
>
> But you can always decompress complex matrix
> to it's scalar version equations.

You can "decompress" modulo arithmetic as well; does that 
make it any less of a distinct arithmetic system? 
-- 
Randy Yates                      % "And all you had to say
Digital Signal Labs              %  was that you were 
mailto://yates@ieee.org          %  gonna stay."
http://www.digitalsignallabs.com % Getting To The Point', *Balance of Power*, ELO

On 10-04-2010 at 19:51:37 Randy Yates <yates@ieee.org> wrote:

(...)
> You can "decompress" modulo arithmetic as well; does that
> make it any less of a distinct arithmetic system?

Modulo arithmetic is of the same kind the imaginary number is.
It is a tool.
Describing physical world
is on a diffrent level of abstraction.
We use tools for description.
Sometimes our tools fit to some parts of physical laws.
We want them to fit.
But the nail doesn't fit and doesn't represent the whole house.
We could decomposite house
but if we decomposite nail
we will be talking on a different level of complexity.

It's a bit messy philosophy.
Let's stay close to the main subject.
Does imaginary FIR coefficients fit, in any way, to reality.
No.

-- 
Mikolaj

Michael Plante wrote:
>glen wrote:
>>Michael Plante <michael.plante@n_o_s_p_a_m.gmail.com> wrote:
>>(snip, I wrote)
>>
>>>>I believe that in some cases complex physical quantities
>>>>that are in exponents have a physical interpretation.
>>(snip)
>> 
>>> Complex eigenvalues often have physical interpretation.  A
>non-hermitian
>>> hamiltonian is sometimes used when particles leave the group of states
>>> being considered (for example, atoms that become ionized, and assume
>that
>>> you no longer care about those as part of your ensemble, so you don't
>>> consider those states).  It is a bit of a hack, but the point is that
>the
>>> complex eigenvalues in that case then have the interpretation of loss
>over
>>> time (where, for other situations, "loss" might be of either sign).
>>
>>Are these solutions of differential equations such that the
>>complex value is in an exp()?  If so, then the imaginary terms
>>(multiplied by i) are the decay (or absorption) term.
>
>It's similar to your example.  One could find a basis where the time
>evolution operator U=exp(-i.H.t/hb) is diagonal.  So it could be seen
that
>way.


While what I wrote was inspired by your post, my point was not so much
about the ability to reduce it to that form, which depends on being able to
find a clean solution, since this sort of perturbation is probably less
necessary in simple cases.  Rather, the value is in being able to directly
interpret perturbations to the Hamiltonian without trying to find a
solution.

An interesting application is when a suitable "gain" mechanism is present
(not explicitly included) to balance this loss, but the the gain introduces
unpolarized atoms, whereas the "loss" removes from consideration whatever's
available.  Then the interpretation of this perturbation is depolarization
of the ensemble over time.

Michael

>Michael Plante <michael.plante@n_o_s_p_a_m.gmail.com> wrote:
>(snip, I wrote)
>
>>>I believe that in some cases complex physical quantities
>>>that are in exponents have a physical interpretation.
>(snip)
> 
>> Complex eigenvalues often have physical interpretation.  A
non-hermitian
>> hamiltonian is sometimes used when particles leave the group of states
>> being considered (for example, atoms that become ionized, and assume
that
>> you no longer care about those as part of your ensemble, so you don't
>> consider those states).  It is a bit of a hack, but the point is that
the
>> complex eigenvalues in that case then have the interpretation of loss
over
>> time (where, for other situations, "loss" might be of either sign).
>
>Are these solutions of differential equations such that the
>complex value is in an exp()?  If so, then the imaginary terms
>(multiplied by i) are the decay (or absorption) term.

It's similar to your example.  One could find a basis where the time
evolution operator U=exp(-i.H.t/hb) is diagonal.  So it could be seen that
way.

Michael Plante <michael.plante@n_o_s_p_a_m.gmail.com> wrote:
(snip, I wrote)

>>I believe that in some cases complex physical quantities
>>that are in exponents have a physical interpretation.
(snip)
 
> Complex eigenvalues often have physical interpretation.  A non-hermitian
> hamiltonian is sometimes used when particles leave the group of states
> being considered (for example, atoms that become ionized, and assume that
> you no longer care about those as part of your ensemble, so you don't
> consider those states).  It is a bit of a hack, but the point is that the
> complex eigenvalues in that case then have the interpretation of loss over
> time (where, for other situations, "loss" might be of either sign).

Are these solutions of differential equations such that the
complex value is in an exp()?  If so, then the imaginary terms
(multiplied by i) are the decay (or absorption) term.

-- glen 

glen wrote:
>Mikolaj <sterowanie_komputerowe@poczta.onet.pl> wrote:
>(snip)
> 
>> I can just put 'j' or 'i' befor any physical value
>> and than interpret it at will.
>> I can fit j to anything I want.
> 
>> But when we have description of something
>> than partial imaginary result numbers
>> can have no physical interpretation.
>
>I believe that in some cases complex physical quantities
>that are in exponents have a physical interpretation.
>As examples, the dielectric constant and its square root,
>the index of refraction.  Other than in exponents,
>the use of complex numbers for physical quantities,
>such as describing phase shifts, seems more of a
>convenience, and not something with a physical
>interpretation.

Complex eigenvalues often have physical interpretation.  A non-hermitian
hamiltonian is sometimes used when particles leave the group of states
being considered (for example, atoms that become ionized, and assume that
you no longer care about those as part of your ensemble, so you don't
consider those states).  It is a bit of a hack, but the point is that the
complex eigenvalues in that case then have the interpretation of loss over
time (where, for other situations, "loss" might be of either sign).

on 07-04-2010 o 13:03:04 Mikolaj <sterowanie_komputerowe@poczta.onet.pl>  
wrote:


> It seems that sometimes, luckily
> when you use complex (compressed, packed, combined, compact)
> way of describing few dependent physical things

the imaginary part of that complex representation (additional dimension  
used for compression)

> can be human understandable
> and could have interpretation.
>
> But you can always decompress complex matrix
> to it's scalar version equations.


-- 
Mikolaj

Mikolaj <sterowanie_komputerowe@poczta.onet.pl> wrote:
(snip)
 
> I can just put 'j' or 'i' befor any physical value
> and than interpret it at will.
> I can fit j to anything I want.
 
> But when we have description of something
> than partial imaginary result numbers
> can have no physical interpretation.

I believe that in some cases complex physical quantities
that are in exponents have a physical interpretation.
As examples, the dielectric constant and its square root,
the index of refraction.  Other than in exponents,
the use of complex numbers for physical quantities,
such as describing phase shifts, seems more of a
convenience, and not something with a physical
interpretation.
 
> Can you interpret imaginary impulse response?
> I can travel back in time on a paper.

-- glen
 

on 07-04-2010 o 13:53:36 glen herrmannsfeldt <gah@ugcs.caltech.edu> wrote:

(...)
> I believe that in some cases complex physical quantities
> that are in exponents have a physical interpretation.
> As examples, the dielectric constant and its square root,
> the index of refraction.  Other than in exponents,
> the use of complex numbers for physical quantities,
> such as describing phase shifts, seems more of a
> convenience, and not something with a physical
> interpretation.
(...)

It seems that sometimes, luckily
when you use complex (compressed, packed, combined, compact)
way of describing few dependent physical things
their imaginary part (additional dimension used for compression)
can be human understandable
and could have interpretation.

But you can always decompress complex matrix
to it's scalar version equations.


-- 
Mikolaj