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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

These reflections happen every time we place a measurement microphone on a mic stand. The microphone picks up the direct sound from our system, but also the sound that bounces off the floor, as seen in Fig 7.

Other times that reflection can be produced by some element in the room or some obstacle that could be found in open air events. We need to learn to identify these reflections so as not to “fix” them with EQ.

It is important to note that the cancellation shown by the measurement software in these situations only happens at the specific position where the microphone is located. At other positions, where the difference in distance between direct and reflected sound is not the same, the same cancellation will not be seen, and another one or more will appear at different frequencies.

Hence, when applying EQ to “fix” the magnitude response at that specific position, we would be coloring it at the rest of positions (where the microphone is not located), unnecessarily forcing the transducer, with the consequent risk of damaging it, as well as degrading sound quality by introducing equalization that impairs the original signal.

Figure 7: Reflected (red) and direct sound (blue) when a measurement microphone is used on a mic stand.

If you’ve ever done this, now you’ll be wondering: Why is it that, whenever there is a reflection and we apply EQ, the measurement software responds to that EQ and we achieve the same magnitude response that we would get without the reflection? To understand it, the following argument must be carefully followed. We’ll make a distinction between the frequency at which total cancellation occurs and the nearby frequencies.

When two acoustical waves reach the same point with a time difference, there will be a total cancellation at the frequency or frequencies for which that time difference equals half a period or odd multiples of a half period, i.e., a difference of 180º or odd multiples of 180º in phase. At these frequencies, when the difference in phase is 180º or odd multiples of 180º, the resulting level is zero (i.e., no sound at all).

For frequencies above and below the first cancellation the phase difference will be lower than 180º, and hence we’ll say that the cancellation (or the sum) is partial or, more correctly, that the sum between them will take place with a phase difference that is progressively lower as we move away from the cancellation frequency, going progressively from a total cancellation to a +6dB sum at the more distant frequencies. The same will happen for the next cancellation frequencies.

The following table shows the resulting sum of two waves with the same level but different phase relationships. We can see that, naturally, the more the phase difference, the lower the result of the sum.

The sum being partial due to phase differences lower than 180º, when raising the level 10 or 15dB using EQ in the cancellation band, the measurement will show the magnitude response recovering. The fact that we see that level recovery for the frequencies with partial cancellation makes sense, specially with low frequency resolution and significant equalization, such as the 10 or 15dB mentioned earlier.

When summing two waves with an effective phase difference lower than 180º, a loss of level is produced which can be recovered by applying equalization, but at the expense of forcing the transducers.

But why does the measured response seem to show that the level at the frequency of total cancellation is also recovered? The answer is simple: due to the environmental noise in the rooms where we are measuring. When there is a total cancellation the resulting pressure level is zero at the microphone position (i.e., no sound at all).

However, the sound emitted by our loudspeaker at that frequency and reflected in the walls that comes back as background noise, results in the software showing that there is some level, which is what gets amplified when applying EQ. There is also the environmental noise in the room, that of the measurement and/or playback devices as well as the smoothing used in the measurement.

In other words, the result of the sum, at the microphone position, of the direct sound and the first reflection is a cancellation. However, the noise level at that same frequency is high due to the fact that equalization has increased the level of the secondary late reflections, of lower level than the first reflection and which phase depends on the distance difference.

Under normal circumstances it is mainly that background noise or reverberation that the measurement software is showing at the cancellation, and the reason for the low coherence level being shown is the low signal-to-noise ratio.

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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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