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Transfer Function Measurements With Smaart v8

Why measurements are a quicker and safer way to optimize a sound system than doing it by ear...

By Joan La Roda January 30, 2019

Image courtesy of Rational Acoustics

Coherence Graph

Quoting the Smaart v8 manual, chapter 6, in the “Coherence” paragraph says: “Coherence is a statistical estimation of the causality or linearity between the reference and measurement signals in a transfer function measurement. Coherence does a good job of detecting contamination of the measurement signal by unrelated signals such as background noise and reverberation… The coherence calculation essentially asks the question, “How confident can we be that what we are seeing in the measurement signal at this frequency was caused by the reference signal?”

As per Smaart v8’s manual, coherence is mainly affected by these three factors:

a) “A problem with the measurement system.” For instance, we may not have synchronized the reference signal with the measurement signal by clicking on “Find.” It could also be the presence of electronic noise, distortion, compression, limiting or crosstalk, though none of those are common according to the Smaart v8 User Guide.

b) “Environmental noise causing measurement signal contamination.”

c) “Reverberation.”

As stated earlier, quoting Smaart v8’s manual, coherence detects if the measurement signal is contaminated by environmental noise or reverberation, i.e. it detects a low signal-to-noise ratio.

There is a case of low signal-to-noise ratio that is specially interesting, and that is when there are reflections or the signals from two systems arrive at different times. In those cases, since a cancellation is produced in one or more bands, the signal-to-noise ratio in those bands becomes very low, and, therefore, so does coherence. This is the case that we’ll encounter most often and the one we’ll discuss below.

Coherence is represented as a graph in the upper part of the magnitude response, and goes from 0% to 100%. There also exists the possibility of adjusting a coherence threshold such that the screen will not show those bands for which coherence is lower than the threshold we have set.

With electro-acoustic measurements it is very common that coherence is above 80% in the most part of the spectrum and that some bands appear for which coherence is low, which will typically indicate that there are two waves arriving at different times, normally due to the presence of a reflection.

A common error is to equalize a trough in the magnitude response for a band that has very low coherence. With all probability, that loss of level, combined with a low coherence level, is indicating that there is a reflection.

The next image shows the measurement of a system where a strong reflection can be appreciated in the impulse response, in the top window. Cancellations can be seen in the magnitude response around 400Hz, 1100Hz and 1700Hz, and low coherence at those frequencies as well as nearby ones. Also, at higher frequencies “rippling” can be observed which is due to cancellations that are very close to each other, and hence relatively low coherence can be appreciated at the frequencies at which those cancellations happen.

Figure 5: Effect of a reflection in an electro-acoustic measurement.

For comparison with the image above, for which we artificially produced a reflection for demonstration purposes, Fig 6 shows the same measurement without the reflection.

Figure 6: Same configuration as for Fig 5 but without the obstacle that caused the strongest reflections.

Fig 6 shows a single impulse response (though followed by other smaller ones further in time). The strong cancellations we saw before are no longer present, nor such low coherence can be observed, and no “rippling” appears at high frequencies. Furthermore, a more regular phase curve can be seen.

If we made the mistake of EQing the cancellation produced by a reflection we would see that the magnitude curve would get “fixed,” but if we looked at the coherence graph we would see that it would not change, it would continue being very low. And if we looked at the phase curve we would see a deformation, resulting from the different arrival times of the two signals as shown in figure 5.

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Fedele says

For now i have just read only introduction and... desagree.
Sofwares are just tools based on numbers! Calculations on numbers, made across many kayers of approximation and errors.
Reality, the Sound Phenomena, the Human way to ear, are more complex tan that.
In a concert, there are many forms of energies that analyzer don’ t measure ( remember...also just calculations on numbers and a 1/4 capsule here or there) but that caracterize our complex sensation.

Seth Morth says

Fedele is missing the point, and should have read the rest of the article before commenting.

This is a helpful guide in how to use Smaart8 to get the sound system to an (objectively) calibrated baseline. Occasionally this is referred to as "flat" but that is rather misleading; consider it "time aligned, checked for phase, and compensated for detrimental artifacts".

From this milestone you can then trust your ears to make (subjectively) changes as desired to have it sound the way you would like it to.

I would in fact like to hear more from Joan La Roda, as well as José Brusi, Xesc Canet, Pepe Ferrer, José Moldes, Germán Ramos, James Woods, and Jamie Anderson. They always have an open invitation to visit my workplace and command my attention when they publish an article.

Fedele says

And also.....
There are other conditions for cancellation!! It is not only problem of relative time As it is writed.

Fedele says

Good evening.
In addition to what I have already written, and which I will soon write,...
I also have to underline how, quoting this part of the text:
"When two acoustical waves reach the same point with a time difference, there will be a total cancellation ...etc"
There are other conditions for cancellation!! It is not only problem of relative time.
Fedele De Marco

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