Infinite Line Source: analysis
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gedlee
diyAudio Member

Join Date: Dec 2004
Location: Novi, Michigan
Quote:
 Originally Posted by jlo I don't use any Green function. The simulated acoustic radiation is a brute force approach based on Huygens-Fresnel decomposition of sources and real-time superposition of all radiations at listener place.
I looked up Huygens-Fresnel in Wiki and it appears that these are based on a Greens function. That's what the propagation function is.

Quote:
 Why not do it here ?
Personally, I'd like the OP to confirm that. It's his tread and I liked what he was doing.
__________________
Earl Geddes Gedlee Website

 4th December 2017, 03:25 AM #102 werewolf   diyAudio Member   Join Date: Feb 2004 Location: Austin, TX POST #7 C. Infinite Line Source: frequency-domain pressure response Coordinates : Imagine, if you will, a rather standard 3-D (rectangular) coordinate system, comprised of the 3 classic, orthogonal axes : x, y and z We'll consider the x-y plane being the "horizontal" plane, with the z-axis extending "vertically". We're going to build our Infinite Line Source along (coincident with) the vertical z-axis The Infinite Line Source will have a constant volume acceleration per-unit-length of "Al". But we start with baby steps Here's how we proceed : First, let's consider a little (VERY little) "piece" of the Infinite Line Source, at some point "z" along the z-axis (meaning, our little "piece" will be at a distance "z" from the origin). Our little "piece" of the Infinite Line Source has a small (VERY small) length of "dz". Now the clever bit : our little (VERY little) piece behaves just like an elemental monopole point-source ... which we just analyzed ... radiating with constant volume acceleration of (Al*dz) What we need, to complete our fist step, is to identify the pressure measured at some random point in space, resulting from our little piece/elemental monopole. Let's start by placing our measuring point on the specific x-y plane of z=0, at a radial distance of "r" from the z-axis. The symmetry of our arrangement dictates that all measuring points at a distance of "r" from the z-axis will receive the same pressure from our little piece, no matter where in the x-y plane those measuring points reside. We also know that our little piece of the line is acting like an elemental monopole at some vertical height of "z". What's the distance from the little piece to our measuring point? Let's call it "R" ... Pythagoras reveals the result for us : R^2 = r^2 + z^2 R = sqrt[r^2 + z^2] Now we have what we need, to write the pressure from our little piece (VERY little) ... where the little piece is at some point "z" along the line, and we are measuring at some radial distance "r" from the line, in the x-y plane of z=0 We'll simply recall the pressure we discussed from a point-source, to identify : pressure at "r" from little piece of line = {Al*dz} * {exp[jwt]} * {[rho/(4pi*R)] * exp[-jkR]} where k = wavenumber = w/c w= frequency c = speed of sound (we'll soon be ignoring that exp[jwt] term, because it's the time-dependent excitation ... which i like to separate from my "transfer function" analysis) next up : we'll add-up all of our little pieces, to form the infinitely long line
werewolf
diyAudio Member

Join Date: Feb 2004
Location: Austin, TX
Quote:
 Originally Posted by gedlee I looked up Huygens-Fresnel in Wiki and it appears that these are based on a Greens function. That's what the propagation function is. Personally, I'd like the OP to confirm that. It's his tread and I liked what he was doing.
Gentlemen, thank you for the respect please feel free to take this thread in any direction at all, i rather like the engagement ... including detours

I'm labeling the main direction with "post numbers", so that readers can stay on the main street easily, if they so choose

jlo
diyAudio Member

Join Date: Nov 2004
Location: france
Quote:
 Originally Posted by gedlee I looked up Huygens-Fresnel in Wiki and it appears that these are based on a Greens function. That's what the propagation function is.
Green's functions are solutions to wav equation in case of Huygens-Fresnel sources, but I don't need to use Green's functions.

I will try to explain the bases : look at post #7 just above and consider just one tiny point source. Signal at listener place is same as source signal but delayed and attenuated depending on this source to listener distance.
Consider another tiny point source : signal at listener is same as this source signal but delayed and attenuated depending on this distance.
Now total signal at listener due to those two sources is simply the real time addition of both signals.
For many sources, just add all signals : divide each loudspeaker in many tiny point sources. And a line array is just many loudspeakers.
Now computers are fast enough to process thousands of signals in real time.
With this brute force approach, you don't need to solve any equation.
It's quite simple but I have not seen this method used before.
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jl ohl

Last edited by jlo; 4th December 2017 at 08:32 PM.

 4th December 2017, 08:35 PM #105 gedlee   diyAudio Member     Join Date: Dec 2004 Location: Novi, Michigan Whether or not you realize it you are using exactly the Green's Function approach to find the attenuation and the delay of each element, and the functions that you are using are the free field ones, hence you are not accounting for many aspects of the problem like diffraction of the enclosure, etc. Its an interesting approach to "real time" analysis, but people have been doing this off-line for more than a century. I am not sure that the limit on accuracy required to do real-time is a major advantage to a more accurate model that just takes a few more minutes. BEM and FEA, for example, can do this problem to an extremely high accuracy, just not in real time. __________________ Earl Geddes Gedlee Website
jlo
diyAudio Member

Join Date: Nov 2004
Location: france
Quote:
 Originally Posted by gedlee Whether or not you realize it you are using exactly the Green's Function approach to find the attenuation and the delay of each element, and the functions that you are using are the free field ones, hence you are not accounting for many aspects of the problem like diffraction of the enclosure, etc. Its an interesting approach to "real time" analysis, but people have been doing this off-line for more than a century. I am not sure that the limit on accuracy required to do real-time is a major advantage to a more accurate model that just takes a few more minutes. BEM and FEA, for example, can do this problem to an extremely high accuracy, just not in real time.
For attenuation and delay, I just have to calculate the distance. Diffraction of the enclosure is simulated by many secondary sources. Reflections (walls, floor,...) are simulated by image sources. It is just a question of accuracy vs computing power.
Also, for accuracy of primary sources and diffraction sources, you may not allways use point sources : an obliquity factor (see Kirchhof's diffraction) should sometimes be used.

One advantage is a true real time auralization (not a convolution) : you can change a parameter or a position while listening to the result.
__________________
jl ohl

Last edited by jlo; 4th December 2017 at 08:54 PM.

 7th December 2017, 07:36 PM #107 jlo   diyAudio Member   Join Date: Nov 2004 Location: france To explain the method, I just published a (basic) video here : lapa - YouTube __________________ jl ohl ohl about audio Last edited by jlo; 7th December 2017 at 07:42 PM.
 7th December 2017, 08:08 PM #108 gedlee   diyAudio Member     Join Date: Dec 2004 Location: Novi, Michigan Looks like a nice piece of software. Why does the screen change for every type of analysis? Does each analysis have to be compiled or do the variables automatically show up as sliders? I have never been much in favor of auralization except in the case of research, because in valid tests of "sound quality" they must be done blind. However a researcher could setup very nice tests with your software, which I would love to do. The only thing is that we have no money at all for this kind of testing - I typically do all the simulations myself and Lidia just uses her lab. Funding is never available. How would you like to donate this software for studies of diffraction, etc? __________________ Earl Geddes Gedlee Website
 7th December 2017, 08:28 PM #109 jlo   diyAudio Member   Join Date: Nov 2004 Location: france My basic question was : what phenomenas (distortions) are audible and to which level ? And to understand, you need to separate variables. So I did one software to listen to diffraction, one for crossover auralization, one for reflexions and room modes, one for arrays, one for cardioid loudspeakers in a room, etc.... At the end, I could mix everything into one software only. The main problem would be too many parameters to set. One tricky simulation is the waveguide (Earl knows it well), I tried to simulate it with image sources but it quickly gets very complicated. To Earl : for research purposes, I would be glad to give you any software (for free of course). __________________ jl ohl ohl about audio Last edited by jlo; 7th December 2017 at 08:37 PM.
 7th December 2017, 08:36 PM #110 gedlee   diyAudio Member     Join Date: Dec 2004 Location: Novi, Michigan And what about the head diffraction? Do you have any, a generic model or does it allow for specific HRTFs to be used? The reason that I ask is that Lidia and I are currently doing some research on very early wall reflections. We could certainly use software like that to generate our test signals. You could generate them and we would credit the software in our paper. That could be a big boost to your marketing. E-mail me directly at egeddes@gedlee.com if this interests you. __________________ Earl Geddes Gedlee Website Last edited by gedlee; 7th December 2017 at 08:39 PM.

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