Pio2001
Senior Member
I verified this in the last few hours.
Thank you Amir !
To understand all this, reading this presentation is very useful : https://www.klippel.de/fileadmin/us..._3D_Sound_Field_using_Near_Field_Scanning.pdf
As I understand it, sound field separation and sound field expansion are two different things.
Looking at pages 33, 37 and 39 in the above document, it seems to me that sound field separation is used at low frequencies (page 37), but that sound field expansion is used at all frequencies (page 33, the order of expansion has a strong effect at 10 kHz, and page 39, it says "wave expansion interpolates..." about data at 2.5, 5, 8 and 10 kHz ).
It makes sense: the scan is made at very short distances (30 cm from the speaker). Sound field expansion is useful to predict the response far from the speaker, even at high frequencies, especially off axis.
Thus, if I understand correctly, the system does, at low frequences:
Measurements -> sound field separation -> sound field expansion
And at high frequencies:
Measurements -> gating -> sound field expansion
In order to understand the fitting error graphs, we must look at page 32 and 41 (funny : they too measured a Neumann KH-80 for their presentation
The fitting error graphs are generated after each measurement using redundant data. They show how large is the variation coming from redundant data taken during the measurement.
In order to know the effet on the resulting frequency response, we must convert the error level in dB (from the fitting error graph) into an absolute number (10^(x/20)), then add 1 and divide by 1 in order to get the error ratio instead of error level, then convert back into dB:
Error on the FR graph (dB) = 20 log (1+10^(x/20)) where x is the error level on the fitting error graph.
It gives
Fitting error -20 dB -> FR curve accuracy 0.8 dB
Fitting error -10 dB -> FR curve accuracy 2.4 dB
Fitting error -5 dB -> FR curve accuracy 3.9 dB
Fitting error -4 dB -> FR curve accuracy 4.2 dB
Fitting error -2.5 dB -> FR curve accuracy 4.9 dB
Now, we can have a look at the measurements:
The default 500+ point and order 10 gets accuracy to about 6 kHz. Above that error climbs rapidly due to complexity of the soundfield:
View attachment 49245
Given the same number of points, the highest order I can increase in software is 14 and this is the results:
View attachment 49246
The error is pushed down in higher frequencies. Results are still not very good above 9 kHz.
Converting error level into accuracy of the frequency response, We can see that with order 10, the accuracy of the FR is
0.9 dB at 6000 Hz
1.6 dB at 7000 Hz
3.2 dB at 8000 Hz
3.9 dB at 9000 Hz
4.2 dB at 10 000 Hz
4.9 dB at 14 000 Hz
With order 14 the accuracy becomes
0.3 dB at 6000 Hz
0.4 dB at 7000 Hz
0.7 dB at 8000 Hz
1.4 dB at 9000 Hz
2.4 dB at 10 000 Hz
3.9 dB at 14 000 Hz
Comparing your two frequency response graphs, at orders 10 and 14, we can see that they are identical within 1 dB below 8000 Hz, they differ of 1 dB at 10 Khz, and there is a 2 dB difference at 14 kHz.
The consistency is much better than what is predicted by the fitting error. Are the fitting error graphs taken from the tweeter's measurement or from the center point measurement ? The second case would make more sense, but maybe the fitting error is a conservative number, and the averarge value is still accurate in spite of possible fitting errors.
Don't panic!The data I show you is independent of this:
View attachment 49247
Gating is used above 2 kHz where we have plenty of error margin in the previous graph.
I don't think so. As seen above, the absence of sound field separation (gating) doesn't mean the absence of sound field expansion (with fitting error).
Indeed, I compared the generated frequency response graphs and they are essentially identical regardless of expansion order (these are for the on-tweeter-axis):
View attachment 49248
View attachment 49249
That's right. But according to what you posted previously, high order expansion becomes critical when the tweeter point is not properly defined. Here, with the tweeter point properly set, high order expansion is not necessary.
The other graphs, with the wrong tweeter point, however, might look very different at order 10 and order 14.
I will resort to that if fitting error drops too low in the ungated area on complex speakers but for now, I think we are good with the number of measurement points.
In spite of the large fitting error (if it is indeed the fitting error from the measurements taken with the proper tweeter point) it seems that the curves are quite stable indeed.
Especially if we keep in mind that the green dashed curve (listening window) is probably more important than the black solid one (on-axis). That one (listening window, green) is identical up to 14 kHz, and it varies 1 dB at 20 kHz between order 10 and order 14.