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Understanding How the Klippel NFS Works

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NTK

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I'll discuss in this post the sources of errors of the NFS measurements. Please be reminded that these are my personal opinions based on my (limited) understanding of the theory and Klippel's implementation. I can be wrong and probably have left out others too.

Fitting and approximation errors
The mathematical model of the speaker is based on spherical wave expansion functions. When the sound sources are compact, the spherical wave functions are capable of approximating them efficiently (i.e. requiring only the lower order functions). However, when the sound sources are of high aspect ratio (i.e. either long and thin and/or flat and thin), the spherical wave functions are less efficient and the approximation errors will be higher.

So when do we have high aspect ratio sound sources? Remember if we measure in a reflective room, the reflections are also sound sources the spherical wave functions need to account for, and these reflections extend the size and alter the shape of the total/combined sound source. Thus, having a large amount of reflections will have a negative effect.

On 'fitting' errors, I don't know exactly how Klippel estimates them. From what I've read, it seems to me those are residuals from the least squares fit. Residuals are usually not considered a very good estimate of the generalization errors due to the possibility of over-fitting. Klippel didn't mention using any kind of regularization in their least squares fits. Without regularization, the computed fitting coefficients are not constrained, and can be susceptible to measurement errors which can cause over-fitting.

Reference on regularization:
A very math heavy paper by Earl Williams on the use of regularization in nearfield acoustical holography.
https://www.researchgate.net/public..._Journal_of_the_Acoustical_Society_of_America

Systematic errors
Setup error of the speaker is one source of systematic error. It is easy to mis-aim the reference axis by a few degrees, especially for a small, non-rectangular-box-shaped, speaker.

A second source of systematic error is positioning error of the microphone. The Klippel robot is a very simple 3-axis robot with precision linear and rotary actuators. Positioning error should therefore be very well controlled. The largest sources of the robot positioning error, in my estimation, are in the alignment/parallelism of the axis of the vertical linear actuator to the rotational axis, and the perpendicularity of the horizontal linear actuator to the vertical linear actuator and how well it intersects the rotational axis.

Other systematic errors may include microphone calibration errors, non-uniform directional response of the microphone, etc.

Noise and environmental conditions
The mathematics of the NFS is entirely in the frequency domain. It basically assumes/requires that all measurements be made in the exact same conditions (time invariant). That means if we have varying environmental noise, errors will be introduced into the model. The NFS mitigates this issue by measuring at nearfield to maximize signal-to-noise ratio, and to use double layer measurements to estimate the actual signal-to-noise ratio. Movements of the NFS robot during the test also cause some changes to the sound diffractions/reflections, and violate the time invariant requirement.

Environmental temperature can also affect the results as the speed of sound is proportional to the square root of the absolute air temperature. Changes in the speed of sound alter the ratio between wavelength to physical dimension, and can change the behavior of diffractions and acoustical interference.

Characterization of the system
Please do not consider these as my recommendations to Amir. I am expressing my opinions only.
If I have an NFS (or if I were to build one), here are the steps I will take to characterize the effects of these sources of errors.

Sound field separation
Erect some large plywood boards to act as reflectors around the NFS setup. Compare test results with a few, with many, and without these reflectors.

Positioning effects (system repeatability)
Test the speaker upright, sideways, and upside down. Compare results.

Environmental conditions
Compare the test results of the same speaker tested at different room temperatures.
Play a constant noise in the room and run the test. Repeat with a varying noise. Compare results to no added noise.
 
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Noise and environmental conditions
The mathematics of the NFS is entirely in the frequency domain. It basically assumes/requires that all measurements be made in the exact same conditions (time invariant). That means if we have varying environmental noise, errors will be introduced into the model. The NFS mitigates this issue by measuring at nearfield to maximize signal-to-noise ratio, and to use double layer measurements to estimate the actual signal-to-noise ratio. Movements of the NFS robot during the test also cause some changes to the sound diffractions/reflections, and violate the time invariant requirement.
Your write-ups are much appreciated and excellent as always.

On this point, the Klippel NFS software runs on the underlying measurement system in Klippel where normal tests are run. There, one sets the resolution, frequency range and importantly in this case, whether you want multiple measurements that are averaged. By default no averaging was there for NFS use and that is how I ran the early measurements.

Since then I have added averaging of 3 times. This improved signal to noise ratio in low frequencies where the response of many speakers drops off. You can use very high averaging but that linearity increases the measurement time. So I experimented and found that 3-scans gave almost all the benefits but without a ton of time added to the measurement cycle.

High frequency signal to noise ratio was excellent as the room is pretty quiet (we live in the middle of nowhere) and it is only low frequencies that penetrate.
 

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Systematic errors
Setup error of the speaker is one source of systematic error. It is easy to mis-aim the reference axis by a few degrees, especially for a small, non-rectangular-box-shaped, speaker.
This is the case. I do a lot since early days to align the speaker but at the limit, it is an impossible task for some speakers with curved surfaces and such as you mention. The error though, nicely shows up in the directivity plot where the image is not fully symmetrical.

Since we never listen at a fixed angle to the speaker anyway, I don't consider this an issue in practice. I supposed if I were designing speakers, I would build a fixture to ensure 100% alignment since speaker would not change. But that is not practical for what I do.
 

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On 'fitting' errors, I don't know exactly how Klippel estimates them. From what I've read, it seems to me those are residuals from the least squares fit. Residuals are usually not considered a very good estimate of the generalization errors due to the possibility of over-fitting. Klippel didn't mention using any kind of regularization in their least squares fits. Without regularization, the computed fitting coefficients are not constrained, and can be susceptible to measurement errors which can cause over-fitting.
I don't know how they do it either. Fortunately there is high transparency in the system in the way it shows what it is projecting, and what the actual measurements are at redundant points in space. I provided one such example in the last review I did:

index.php


Here, fitting error became large above 10 kHz and we see that in the difference between red (actual, in-room measurement) and blue (computed soundfield). When the fitting errors are small, the graphs always land right on top of each other so whatever failings are in the algorithm, they seem to not impact the results. You can see this in the range above "Reflection Free Frequency" where gating is used so in-room measurements are reflection-free. We see that the two graphs match each other well. And what difference there is, is not material.

When I am able to get the error below -20 dB (1%), the graphs are right on top of each other.
 
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amirm

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Sound field separation
Erect some large plywood boards to act as reflectors around the NFS setup. Compare test results with a few, with many, and without these reflectors.
Nice suggestion. Can't do that reasonably with heavy plywood but maybe I use some 1/4 inch panels that don't weigh as much. And if they fall, they don't delimb me. :D
 

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Sound field separation
Erect some large plywood boards to act as reflectors around the NFS setup. Compare test results with a few, with many, and without these reflectors.

Positioning effects (system repeatability)
Test the speaker upright, sideways, and upside down. Compare results.

Environmental conditions
Compare the test results of the same speaker tested at different room temperatures.
Play a constant noise in the room and run the test. Repeat with a varying noise. Compare results to no added noise.
These are interesting and very practical tests given the problems you discussed.

I wonder how the absorptive properties of plywood would affect the results for the midrange and below.
 
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These are interesting and very practical tests given the problems you discussed.

I wonder how the absorptive properties of plywood would affect the results for the midrange and below.
Don't know. I am just throwing out plywood as something easy to get and to handle. Wonder if plexiglas is more sound reflective.
 

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I forgot to mention, in terms of agreement between measurements, per CTA-2034A, ±1.5 dB is considered to be good. So let's not sweat over anything less than that.
View attachment 68207
I need to frame this and stick it on my forehead. :)
 

amirm

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I wonder how the absorptive properties of plywood would affect the results for the midrange and below.
I think the fact that it flexes will cause more of an issue for lows than anything else (it acts like an absorber). The wavelengths are too large there to matter with respect to texture of the plywood.
 

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I'll discuss in this post the sources of errors of the NFS measurements. Please be reminded that these are my personal opinions based on my (limited) understanding of the theory and Klippel's implementation. I can be wrong and probably have left out others too.

Fitting and approximation errors
The mathematical model of the speaker is based on spherical wave expansion functions. When the sound sources are compact, the spherical wave functions are capable of approximating them efficiently (i.e. requiring only the lower order functions). However, when the sound sources are of high aspect ratio (i.e. either long and thin and/or flat and thin), the spherical wave functions are less efficient and the approximation errors will be higher.

So when do we have high aspect ratio sound sources? Remember if we measure in a reflective room, the reflections are also sound sources the spherical wave functions need to account for, and these reflections extend the size and alter the shape of the total/combined sound source. Thus, having a large amount of reflections will have a negative effect.

...
How to use the Klippel near-field to measure a speaker that, being quasi-line-source, will have a response that varies greatly with listening distance?

AFAICT measuring a quasi-line up-close can give a very wrong impression.

I'm very interested in how this is handled.

P.S. I asked this question in the Magnepan LRS thread, where Amir has just mentioned that the LRS has arrived for testing. But this might be an even better place to discuss how to use the system with line-source speakers (most of which are quasi-lines like the LRS).
 

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How to use the Klippel near-field to measure a speaker that, being quasi-line-source, will have a response that varies greatly with listening distance?

AFAICT measuring a quasi-line up-close can give a very wrong impression.
The whole point of NFS is to solve your last sentence. It measures in near-field, but then computes the far field.

As to line source, it all depends on complexity of its soundfield in near field. If it is very complex then you may need a lot of measurement points, and lots of computation time.

If the line source is made out of individual drivers, then each one can be measured independently and them summed together. That is an extra cost option which I did not purchase.
 

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The whole point of NFS is to solve your last sentence. It measures in near-field, but then computes the far field.

As to line source, it all depends on complexity of its soundfield in near field. If it is very complex then you may need a lot of measurement points, and lots of computation time.

If the line source is made out of individual drivers, then each one can be measured independently and them summed together. That is an extra cost option which I did not purchase.

I don't think it will solve the unique line-source open baffle behaviour, as per the following diagram (from Martin Colloms, "High Performance Loudspeakers"), unless there is a control that allows the user to specify that speaker type.
Line Source Open Baffle -- Colloms.png


(Note: 'r' is mislabeled 't' on the diagram)

1597257899607.png


Of particular relevance is the difference between the frequency responses at 0.316m (suggestive of measurement distance) and 3.16m (suggestive of listener distance).

I am interested in how you are going to correct for the above difference in your upcoming test of the Magnepan LRS, and any similar speaker types that you may measure in the future.

cheers
 
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I don't think it will solve the unique line-source open baffle behaviour, as per the following diagram (from Martin Colloms, "High Performance Loudspeakers"), unless there is a control that allows the user to specify that speaker type.
View attachment 77796

(Note: 'r' is mislabeled 't' on the diagram)

View attachment 77794

Of particular relevance is the difference between the frequency responses at 0.316m (suggestive of measurement distance) and 3.16m (suggestive of listener distance).

I am interested in how you are going to correct for the above difference in your upcoming test of the Magnepan LRS, and any similar speaker types that you may measure in the future.

cheers
When I started this thread, I rushed and jumped into the mathematical theory right away. I should have backed-up a little bit and explained the fundamental differences between how the Klippel NFS works versus the traditional loudspeaker measurement methods.

When measurements are taken the traditional way, such as in an anechoic chamber with a mic or a set of mics, the measurements are the reported results. That means, if I measured a certain dB SPL at a certain azimuthal angle and elevation angle at a certain distance, that is what goes in the report. These type of measurements needs to be taken in the far field, where the inverse distance (1/R) law for sound pressure applies, so that we can perform distance scaling. ANSI/CTA-2034A specifies a measurement distance of 2 m and report the results that are scaled to 1 m.

The NFS process works differently. All of the nearfield measurements are further processed to create a mathematical model of the sound pressure field in 3D (using spherical wave expansion functions). That's why the technique is called nearfield acoustical "holography" (NAH) -- recreation the 3D field from 2D measurements. If you need to report the SPL at a certain location given by its azimuthal angle, elevation angle, and distance, these coordinates are fed into the model and the SPL at that location is calculated and reported. The NAH technique is fundamentally different from the traditional methods, and works for both nearfield and far field.

Here is a link to one of the original papers on the discovery/development of NAH by Dr. Earl Williams and colleagues.
https://www.researchgate.net/public...ralized_holography_and_the_development_of_NAH

The method is further developed by Professor Sean Wu who came up with the "Helmholtz equation least squares method" which is what the Klippel NFS uses. Here is a link to an overview of the various implementations of NAH by Dr Wu (the second article under the Features heading).
http://www.sandv.com/feb10.shtml
 

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In that case, I will be interested to see Amir's NFS measurement of the Magnepan LRS (quasi-line, open-baffle, dipole) shown as Spinorama and beamwidth plots modelled at 2m and at 6m distances, which are realistic ranges for home listening, and which the graph I shared above predicts will differ in more than just SPL.
 
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In that case, I will be interested to see Amir's NFS measurement of the Magnepan LRS (quasi-line, open-baffle, dipole) shown as Spinorama and beamwidth plots modelled at 2m and at 6m distances, which are realistic ranges for home listening, and which the graph I shared above predicts will differ in more than just SPL.
Me too, and I am sure the same for many others here. I am also very interested to find out how many measurement points the NFS needs to measure this speaker.
 

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I don't think it will solve the unique line-source open baffle behaviour, as per the following diagram (from Martin Colloms, "High Performance Loudspeakers"), unless there is a control that allows the user to specify that speaker type.
I have read the paper and I don't think it invalidates what I said and what NFS does. Yes, the response will be distance dependent and NFS allows one to input that. Ultimately the field equation must work for a line source as well as any other source.

But yes, to the extent the line source is made out of an array of drivers, then there is that optional module that sums the response of each. And you do tell the system how many drivers there are, etc.

Without that, it may require such high order expansion, longer measurement distance, or too many measurement points to be practical. We will find out but first I have to build a platform to put the speaker on.
 

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Thanks Amir.
 

RichB

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Crutchfield has announced that they have "the most comprehensive and accurate product info available... We even measure to 1/16'th of an inch." Take that ASR :p

CrutchfieldMeasurements.jpg


- Rich
 
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pozz

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Crutchfield has announced that they have "the most comprehensive and accurate product info available... We even measure to 1/16'th of an inch. Take that ASR :p

View attachment 78546

- Rich
There is so much superfluous information packed into the page of each product.

Actual measured dimensions are pretty useful, all said and done.
 
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