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28th March 2018, 01:31 PM  #81  
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Join Date: Nov 2010

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The core idea for the scanner is that the sound field can be separated into components. First we separate out the time variability with phasor notation. Then we are left with a radial component and a directivity component. The idea is manifested in the maths as "separation of variable" in the differential equations. Separation of Variables also came up in your discussion with Putland about Oblate Spheriodal coordinates. You initially claimed that S. of V. meant that a 1 parameter solution of the wave equation was possible in OS coords. (for convenience I will use r, theta, phi for the coordinates in OS despite the fact they are not the same r, theta, phi we use in cylindrical coords) The idea was a solution of form F(r)G(theta)H(phi) could be equal to a solution of the form F(r)*constant with appropriate series expansion in the theta and phi functions. You later revisited the subject and dropped that claim. I remember when I first read the claim that it was not clear to me but it seemed plausible. Do you have a physical or intuitive explanation why it doesn't work? This may help me clarify S. of V. as we use it in this context. Best wishes David 

28th March 2018, 04:00 PM  #82  
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Join Date: Dec 2004
Location: Novi, Michigan

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So I never changed my claim, I only added a further restriction to it that applies in some (most) cases.
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Earl Geddes Gedlee Website Last edited by gedlee; 28th March 2018 at 04:05 PM. 

30th March 2018, 04:08 AM  #83  
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Join Date: Sep 2011

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How big of an effect the secondary reflections are likely depends on the size of the speaker being measured, with a small satellite probably not providing much in the way of a reflective surface until above 1kHz or so. 

30th March 2018, 12:53 PM  #84  
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Join Date: Nov 2010

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Can you explain how you have done it? I understand you take closer samples near the axis, I haven't yet worked out how to calculate the polars from this. If the number of samples can be reduced sufficiently then it is more realistic to avoid a complicated CNC scanner. Best wishes David Last edited by Dave Zan; 30th March 2018 at 01:11 PM. 

30th March 2018, 02:27 PM  #85 
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Join Date: Dec 2004
Location: Novi, Michigan

If you want to understand the details then you need to dig into the detailed math. It is not feasible to show that here, so you will have to take my word for it, but here is the gist of the thing.
In the radiation mode domain we have a sound field that is a sum of radiation modes. Each mode has a cutin frequency below which it does not contribute. In essence we thus have a problem of N samples to fit M modes. At the lowest frequencies I only need 1 point to fit the monopole mode, a little higher I need two for the dipole mode coming into play. Klippel shows this well in his slides. It takes about 13 modes to get good resolution up to 10 kHz from a normal sized speaker (size isn't critical though as doubling it only adds the need for one more mode) so I need 13 data points to fit these 13 modes. The nonuniform Fourier transform plays no role in any of this. It is more closely associated with the Hankel transform, but that is still not the way its done. The paper linked earlier shows this linear algebra approach very well.
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30th March 2018, 11:09 PM  #86  
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Join Date: Nov 2010

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Spherical Harmonics in this case. Best wishes David Last edited by Dave Zan; 30th March 2018 at 11:12 PM. 

31st March 2018, 07:38 PM  #87 
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Join Date: Feb 2003
Location: ..

probably not 'shoestring' Microphone Arrays  acousticcamera.com

31st March 2018, 07:50 PM  #88  
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Join Date: Jan 2004
Location: dorchester ma

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1st April 2018, 12:08 AM  #89  
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Join Date: Nov 2010

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It's kind of the flip side of the Klippel, it shows a 'picture' of the source whereas Klippel is optimized for the far field behaviour, polars and the like. Closely related maths but a different application. It would be fun to actually 'see' the source intensity, cabinet panel resonances, port turbulence noise and all. Maybe a separate project, I haven't even fully worked out the maths for this one yet. Best wishes David 

4th April 2018, 12:36 AM  #90  
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Join Date: Sep 2011

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I ran across those early in my investigations into the NFS, I think something like that would have some interesting applications for enthusiasts like ourselves. I'd like to read more about that, do you have any links? 

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