Prev: Affine Projection Algorithm
Next: Map controller output to PWM duty-cycle
From: Jerry Avins on 13 Jan 2010 10:16
dbd 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 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

I understand "wave number". To emphasize that it's a spatial frequency,
I would have called it "wave count". As usual, I wasn't there in time to
proffer my advice. :-)

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
From: Jerry Avins on 13 Jan 2010 10:20
Rune Allnor wrote:
> 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?

Not just any spatial measure, but the count of waves in a given
distance. http://en.wikipedia.org/wiki/Wave_number Interferometers are
discussed this way.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
From: glen herrmannsfeldt on 13 Jan 2010 10:24
Jerry Avins <jya(a)ieee.org> wrote:
(snip regarding wave number)

> I understand "wave number". To emphasize that it's a spatial frequency,
> I would have called it "wave count". As usual, I wasn't there in time to
> proffer my advice. :-)

I suppose 1/wavelength could be a count of waves per unit distance,
though it doesn't have to be integer. (Counts usually are.)

The usual wavenumber that I know is 2pi/wavelength, so unlikely
to be integer.

I have seen k-bar, that is, k/2pi.

-- glen
From: Jerry Avins on 13 Jan 2010 10:25
glen herrmannsfeldt wrote:
> 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.)

Not exclusively. According to Wikipedia,
"Wavenumber in Physics is a property of a wave defined as either

the number of wavelengths per unit distance, that is, 1/λ where
λ=wavelength,
or alternatively as 2π/λ, sometimes termed the angular wavenumber or
circular wavenumber or, simply wavenumber."

So without the "circular" designation, it can include 2π or not.

> 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.)

Right or not, that's rational, :-)

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
From: Jerry Avins on 13 Jan 2010 10:29
glen herrmannsfeldt wrote:
> 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!
Words fail me! That bears deeper thought than I can do right now.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
First  |  Prev  |  Next  |  Last
Pages: 1 2 3 4 5
Prev: Affine Projection Algorithm
Next: Map controller output to PWM duty-cycle