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From: Rune Allnor on 13 Jan 2010 02:04
On 13 Jan, 07:54, dbd <d...(a)ieee.org> wrote:
> On Jan 12, 9:18 pm, Rune Allnor <all...(a)tele.ntnu.no> wrote:
>
> > On 13 Jan, 05:14, dbd <d...(a)ieee.org> wrote:
> > ...
> > > A wavenumber spectrum is the result of the fft of a set of uniformly
> > > linearly
>
> > Are you excluding non-uniform and / or non-linear spatial
> > samples from the definition?
>
> I've only said that usual definition of the fft produces a wavenumber
> spectrum from uniform samples, other calculations can transform
> nonuniform samples to a wavenumber spectrum. I've given an example of
> a common practice in the sonar community with examples from the navies
> of two nations.

Can't see such examples in any prost in this thread?

Apart from that, most navies I have had insight into, got that
wrong. Just about everyone have tried to get beamformers to work
in shallow waters, with little luck. I got my prototype processor
working in a couple of afternoons, merely by paying attention to
semantic detail.

> > > spaced spatial samples.
>
> > Do you agree that CCDs produce 'spatial samples' of intensity?
>
> Agree with whom about what? Are you claiming that CCDs produce the
> coherent samples that would be required to be appropriate to the
> coherent processes discussed in this thread?

Again, you seem to refer to stuff I can't find. No one have
made any references or restrictions to particular applications.
Quite the contrary.

As I am sure you are aware, a CCD samples an intensity field in
two spatial dimenstions. Those data can be processed by FFTs or
other routines to produce spectra.

Again: Do you consider spectra produce from such data as
'wavenumber spectra'?

> > If so, can you demonstrate that the term 'wavenumber' is used
> > in the context of image processing?
>
> What would that have to do with the content of this thread?

It cust straight to the core about whether a general terminology
exists.

> What would
> that have to do with whether 'wavenumber' is commonly used in coherent
> sonar processing as well as in PDEs?

There is no 'as well'. Beamformers in sonar processing are
hands-on applications of PDEs. The fact that you are not
aware of this trivial fact goes a long way to explain why
no one in the sonar community were able to come up with a
half-decent functional shallow-water beamformer.

Rune
From: Fred Marshall on 13 Jan 2010 02:14
Jerry Avins wrote:
> robert bristow-johnson wrote:
>> On Jan 12, 8:52 am, Chris Bore <chris.b...(a)gmail.com> wrote:
>>> Is there a generic way to name what are usually the 'time' and
>>> 'frequency' domains for digital filtering?
>>>
>>> I seek a single term that can be applied for instance when the data to
>>> be filtered may be a (frequency) spectrum, or spatial positions, or
>>> angles.
>>
>> this isn't really the answer to your question but instead of
>> "frequency domain", i sometimes say "reciprocal-<unit> domain".
>>
>> but, i remember once having trouble explaining what little i knew
>> about image processing. can't remember what i called the x and y axis
>> of the pic. "length domain" or more likely "position domain", i
>> dunno. but i called the other one the "frequency domain" and that
>> didn't make sense (if we got careless with units) so i called it
>> "reciprocal-position" or something like that.
>
> "Spatial frequency" is widely used. "Wave number" seems too abstruse to me.
>
> Jerry

"Spatial frequency" is generally applied to those situations where one
is measuring things that vary in spatial dimensions - like an image of a
picket fence has a "strong fundamental" in spatial frequency.

Then, the transform of such yields a measure of the amplitude of those
frequencies.
If the original indices are X, then the new indices are in 1/X and are
referred to as Wave Number.

It gets really interesting when doing line array beamforming using
"frequency domain beamforming" and getting out spectra as a function of
frequency and pointing angle. The first transform taken from the
sensors is a spatial transform yielding wave number sequences as I
recall. Multiples of those create temporal records for each wave number
which are then transformed into spectra. The wave number is equivalent
to the look angle or the sin of the look angle.....

Fred
From: Rune Allnor on 13 Jan 2010 04:53
On 13 Jan, 08:14, Fred Marshall <fmarshallx(a)remove_the_xacm.org>
wrote:
>  The wave number is equivalent
> to the look angle or the sin of the look angle.....

Not necessarily.

We agree to the point where the spatial dimension of the 2D FT of
a (t,x) signal is termed 'wavenumber spectrum', but from there on
you need to specify exactly what you are up to.

You are right in that *one* way to proceed is to specify some
wave speed c and some reference direction phi, and then *interpret*
the wavenumber in terms of some factor sin(phi) that one artificially
introduce in the dispersion equation for the wave field.

However, it is also possible to specify the direction phi up front,
and then use the wavenumber spectrum to estimate the wave speed c.
It works quite well - I used that very trick in my PhD thesis.

Rune
From: glen herrmannsfeldt on 13 Jan 2010 06:25
Rune Allnor <allnor(a)tele.ntnu.no> wrote:
> On 13 Jan, 08:14, Fred Marshall <fmarshallx(a)remove_the_xacm.org>
> wrote:
>> ?The wave number is equivalent
>> to the look angle or the sin of the look angle.....

> Not necessarily.

> We agree to the point where the spatial dimension of the 2D FT of
> a (t,x) signal is termed 'wavenumber spectrum', but from there on
> you need to specify exactly what you are up to.

(snip)

This reminds me that I was recently reading about ocean (water
surface) waves and wave interaction. The claim is that surface
waves can interact (I think this would be scatter in physics
terminology) when the sum of the frequencies and vector sum
of the wave vectors is zero. That is obvioulsy true only if
some of the frequencies are negative. Ocean (deep water surface)
waves have the dispersion relation w**2=g k where k is the
magnitude of the wave vector, which allows for either positive
or negative w.

This reminded me of the discussion here on the meaning of
negative frequency. Here is an equation that only works if
you allow for negative frequencies!

-- glen
From: Rune Allnor on 13 Jan 2010 06:39
On 13 Jan, 12:25, glen herrmannsfeldt <g...(a)ugcs.caltech.edu> wrote:
> Rune Allnor <all...(a)tele.ntnu.no> wrote:
> > On 13 Jan, 08:14, Fred Marshall <fmarshallx(a)remove_the_xacm.org>
> > wrote:
> >> ?The wave number is equivalent
> >> to the look angle or the sin of the look angle.....
> > Not necessarily.
> > We agree to the point where the spatial dimension of the 2D FT of
> > a (t,x) signal is termed 'wavenumber spectrum', but from there on
> > you need to specify exactly what you are up to.
>
> (snip)
>
> This reminds me that I was recently reading about ocean (water
> surface) waves and wave interaction.  The claim is that surface
> waves can interact (I think this would be scatter in physics
> terminology) when the sum of the frequencies and vector sum
> of the wave vectors is zero.

Sounds like interference to me? One trivial case is waves
travelling at the same speed in opposite directions. Not
awfully easy to obtain at sea in real life, but still...?

> That is obvioulsy true only if
> some of the frequencies are negative. Ocean (deep water surface)
> waves have the dispersion relation w**2=g k where k is the
> magnitude of the wave vector, which allows for either positive
> or negative w.  

The usual derivations of the separable wave equation reach
some point where the dispersion equation goes something like

w^2 = c^2 k^2

where w is angular frequency, c is a function of the wave
speed(s) in the (possibly inhomogeneous) medium, and k is
the wavenumber vector.

One separates this by allowing only positive values for c
(the wave speed of the medium must be positive), allowing
the vector components of k to be either positive or negative
(indicating the wave's direction of propagation through the
medium) and allowing w to be conjugate symmetric to constrain
the wave field to be strictly real-valued.

Rune
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