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From: Rune Allnor on 12 Jan 2010 22:14
On 13 Jan, 04:06, Jerry Avins <j...(a)ieee.org> 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.

"Spatial frequency" seems to be universally useful - if not always
easily understandable - for data where at least one dimension of the
data is spatial...

> "Wave number" seems too abstruse to me.

....whereas "wavenumber" seems to be used more or less exclusively
in the context of PDEs where at least one dimension is spatial.

Rune
From: dbd on 12 Jan 2010 23:14
On Jan 12, 7:14 pm, Rune Allnor <all...(a)tele.ntnu.no> wrote:

> ...
> ...whereas "wavenumber" seems to be used more or less exclusively
> in the context of PDEs where at least one dimension is spatial.
>
> Rune

A wavenumber spectrum is the result of the fft of a set of uniformly
linearly spaced spatial samples. For some choices of sample interval,
array size and transform size the 'wavenumber' spectrum may be
equivalent to 'beam' spectrum for narrow frequency bands. 'wavenumber'
finds common usage in beamforming. Consider the two examples I gave
back in October when Chris had a related question:
http://groups.google.com/group/comp.dsp/browse_thread/thread/73cd21612e98ce1b/cce2c5d85c9014f2?hl=en&lnk=gst&q=frequency+beamforming#cce2c5d85c9014f2

A wavenumber-frequency spectrum is often interpolated to a beam-
frequency spectrum.

WSRL-0162-TR
at:
http://hdl.handle.net/1947/8750

ADA394281.pdf
at:
http://handle.dtic.mil/100.2/ADA394281

Title:
Derivation of Beam Interpolation Coefficients with
Application to the K-omega Beamformer

Dale B. Dalymple
From: glen herrmannsfeldt on 13 Jan 2010 00:12
Jerry Avins <jya(a)ieee.org> wrote:
(snip, someone wrote)

>> 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.

Wave vector in more than one dimension. It also has the 2pi
that frequency doesn't normally have. (Angular frequency does.)

The Wave number is 2 pi/wavelength. In a dispersive
medium, but not too dispersive, w/k is the phase velocity,
dw/dk the group velocity. (w is omega, angular frequency, I don't
have an actual omega on this news reader.)

As I understand it, part of the reason was that in the early
days of spectroscopy c wasn't so accurately known, so reciprocal
wavelength was used instead. (Proportional to energy, but avoids
c before c was defined.)

-- glen
From: Rune Allnor on 13 Jan 2010 00:18
On 13 Jan, 05:14, dbd <d...(a)ieee.org> wrote:
> On Jan 12, 7:14 pm, Rune Allnor <all...(a)tele.ntnu.no> wrote:
>
> > ...
> > ...whereas "wavenumber" seems to be used more or less exclusively
> > in the context of PDEs where at least one dimension is spatial.
>
> > Rune
>
> 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?

> spaced spatial samples.

Do you agree that CCDs produce 'spatial samples' of intensity?
If so, can you demonstrate that the term 'wavenumber' is used
in the context of image processing?

Rune
From: dbd on 13 Jan 2010 01:54
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.

>
> > 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?

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

>
> Rune

Dale B. Dalrymple
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