After you take several measurements and average them together, what do you expect to see?

If these two measurements are averaged, what do you expect?

Is zero the average of -6dB and 6dB, or something else?

Here are four possible averages you may have guessed, depending on which audio analyzer you use.

Here are demos from a selection of audio analyzers in alphabetical order.

Crosslite+ v2.0.0 8

Along with options for pre and post processing, Crosslite+ offers four different options.

“Arithmetic Average Complex” : Arithmetic mean in complex values.

“Quadratic Average Complex” : Quadratic average or RMS in complex values.

“Arithmetic Average Magnitude” : Arithmetic mean in real values in dB, with phase zeroed.

USER GUIDE CROSSOLITE REV 1.1

Does the magnitude average change with trace offset? Yes. It appears that trace offset in Crosslite is the same as a gain change.

Does the magnitude average change with phase offset? Yes, except for Arithmetic Average Magnitude.

In this test I averaged the response of two microphone cables with a second order APF inserted on one of them at 1kHz.

Se deseja saber a média de fontes separadas coerentes ou de uma curva polar, é bom utilizar a aritmética complexa.

Se é média para curvas de equalização, melhor a de magnitude em dB.

Escolhi os tipos que estão mais presentes na maioria dos softwares que possuem funções de média.

Francisco Monteiro

If you want to know the average of separate coherent sources or a polar curve, it’s a good idea to use complex arithmetic.

If it’s an average for equalization, better the magnitude in dB.

[For Crosslite] I chose to offer the types that are most present in most software that have averaging functions.

Francisco Monteiro

L-Acoustics M1

M1 offers a single kind of average, which appears to be a simple average with phase zeroed.

Does the magnitude average change with trace offset? No. There is no trace offset option.

Does the magnitude average change with phase offset? No.

OpenSound Meter v1.0.5

Open Sound Meter offers vector and polar averaging.

Does the magnitude average change with trace offset? Yes, the results are the same for a measured gain change.

Does the magnitude average change with phase offset? Yes for vector. No for polar.

For in-space averaging I use polar method. For vector (complex) you need to have very close phase responses.

Pavel Smokotnin

REW v5.20

REW offers two options for averaging.

Vector average, which averages the currently selected traces taking into account both magnitude and phase. It can only be applied to measurements that have an impulse response.

RMS average, which calculates an rms average of the SPL values of those traces which are selected when the button is pressed. Phase is not taken into account, measurements are treated as incoherent. This does the same as the Average The Responses button. If the measurements were made at different positions (spatial averaging) it may be helpful to first use the Align SPL… feature to remove overall level differences due to different source distances.

REW Help

Does the magnitude average change with trace offset? Yes, but only after the data is permanently changed with the Add offset to data button.

Does the magnitude average change with phase offset? Yes for vector. No for RMS.

RiTA

RiTA offers a single options for averaging traces: Arithmetic Average Complex

Does the magnitude average change with trace offset? Yes.

Does the magnitude average change with phase offset? Yes.

The next version of RiTA will include three options for averaging.

Complex AVG: magnitude estimation is greatly affected when complex averaging is performed. It is useful when you are interested, in close measurements, in knowing the constructive and destructive interference of the sound system.

ABS AVG and dB AVG are intended for spatial averaging of several microphones. Abs AVG tends to give priority to good data and less to data affected by reflections. dB AVG gives equal weight to all data.

By default, RiTA 2.5 uses ABS AVG

Pepe Ferrer

SATlive

SATlive offers a three options for averaging: Create Sum Trace, Complex Add, and Weighted Average.

Does the magnitude average change with trace offset? No

Does the magnitude average change with phase offset? Yes for Complex Add. No for Sum Trace.

SATlive offers 3 different approaches for averaging different measurements.

1. Complex averaging: Will calculate the sum using the amplitude values of each trace and the phase relation between the traces. It is intended to average measurements taken at the same mic position, like Sub/Top time align or interference of different sources. (quick traces -> sum trace complex averaging).

2. Amplitude based averaging: Will calculate the sum by normalizing (center at 0 dB) each trace and afterwards adding the amplitude values only. This is helpful when you want to average traces taken at different mic locations (and in most cases, using the same source).  (quick traces -> sum trace Create Sum Trace).

3. Weighted averaging: This is a special version of 2. where you can assign a weighting factor to each trace (three configurable settings). This was inspired by the Primary/Secondary/Tertiary measurement approach, which I first heard about during my SIM II seminar. In fact, it does not make much sense to add tertiary traces to the result, but it would be possible. (Trace Manager)

Hint: There is a Valid only if all traces valid option for 1. and 2. where you can define wether just one valid result at a certain frequency will be sufficient for a valid result or all traces averaged must contain a valid value to create a valid result.

Which of the options do you recommend to your users for judgement of tonality and EQ operations?

Only option 2. and 3. will make sense here. I rarely work with averaged measurements during EQing. Normally I’d use the Primary Location trace as the base for EQ while the other traces help me to distinguish if the problem is global or just local.

Big differences between the different mic-locations (primary/secondary) indicate a problem that you should fix before applying the eq (redirecting the speaker, additional speaker, speaker with a different directivity pattern).

For overall tonality I’d go for 2 and for Eq-ing for 3

Thomas Neumann

Smaart v8.5.0.2

Smaart offers two options of averaging with the second including built-in proprietary pre-processing.

Decibel spatial averaging, sometimes called arithmetic averaging, is a simple average of decibel magnitudes at each frequency. Spatial power averaging is the average of squared linear magnitudes at each frequency with the result converted to decibels.

Unweighted dB averaging works exactly the same way both transfer function magnitude and spectrum averages. When you select Power averaging for transfer function measurements, however, Smaart automatically adjusts the overall level of all individual measurements going into the average according to their average decibel magnitudes in the range of 225 Hz to 8.8 kHz so that they are all approximately equal in level throughout that range.

Rational Acoustics Smaart v8 User Guide, Release 8.3

Does the magnitude average change with trace offset? No.

Does the magnitude average change with phase offset? No.

Our data is in dB, so we have to decide whether to average linearly or logarithmically, whether to normalize first, whether to weight by coherence (does it make sense that poor-quality data gets as much “say” in the final result as high-quality data?) and of course remembering that FFT math spits out complex data points, not simple integers.

So you can end up with a lot of approaches that are all valid from a mathematical standpoint, but the question becomes “which method gives us the most useful result?” (I could average together the number of socks in my drawer and the number of tires on my car, and even if my math was correct, it’s a meaningless answer for all practical purposes.) So at the end of the day, we want averaging that produces information that’s helpful to the user. If you have a bunch of traces and you average them, we have an expectation of what that final averaged response should look like. How well does it highlight the trends indicated by the individual traces? That’s what we’re looking for when we take an average, and so our averaging is designed with that in mind.

In terms of which to use, just like everywhere else in Smaart: if you’re not sure which setting you need, use the defaults. They’ve been carefully chosen over many years to give good results without the user having to tweak around. I actually reset the software to default configuration every time I use it, and I pretty rarely need to go in and change a bunch of things from that state. The primary advantage of power averaging would be if you’re averaging together a bunch of traces that have severe comb filtering (which hopefully doesn’t happen all that often). The math will give more weight to the peaks and less to the dips, so you end up with something that can be more representative of the overall response in that area and what your ear might tell you. But – in most circumstances, the differences between coherence-weighted dB average and power average end up being very small. If you create both types of average from the same dataset, and lay the two averages traces on top of each other, you’ll see they tend to agree very well. I think you’d have to come up with a pretty contrived situation or have pretty bad-quality measurement data to get a result where the power averaging and the dB averaging disagree.

Michael Lawrence

All together now

Here’s an overview of the different averages being discussed in high contrast. All of these are my own estimations since the math is not exposed and is in some cases proprietary.

Which one should I use?

Please follow the manufacturer guidelines and in most cases stick with the default settings.

The demos in this post average electrical measurements of symmetrical EQ filters in order to clearly expose the calculations being used. I want to be able to see clearly if the average of +6 and -6 is 0 or something else. Measurements of speakers in rooms will feature many wide peaks and narrow valleys instead of this symmetrical behavior.

As I worked through each demo I found myself wondering why I might use one average over another. Being visually inclined and looking at a graph, at first the simple magnitude average made the most sense.

(-6 + 6) / 2 = 0

M1 offers this as its only option and it is the default option in Smaart and SATlive.

Why do the other options exist?

If you had one subwoofer and I gave you another, how much would that be in decibels? You would add 0dB + 0dB to get 6dB.

If I gave you another half a sub you would have 8dB because 20 * log10(1 + 1 + 0.5) = 8.

Following the same process of linear to log conversion, we should calculate the decibel average of -6dB and 6dB like this:

20 * log10((0.5 + 2) / 2) = 1.9dB

Maybe it makes more sense now why some audio analyzers like REW, RiTA, and Open Sound Meter show an average of 1.9dB instead of 0dB.

Interestingly, Bob McCarthy finds even this form of average to be lacking since it does not take psychophysics into account.

Studying summation revealed that 20–40 dB dips are likely to stay down in only a small area, whereas 6 dB peaks may spread over a wide area. Studying perception revealed greater tonal sensitivity to wide peaks over narrow dips. Therefore we should be wary of accepting 0 dB as the best representative here. When samples agree, the averaging builds confidence. When samples differ, the average is suspect. There’s safety in numbers when math averaging is used: get a lot of samples.

McCarthy, Bob. Sound Systems: Design and Optimization: Modern Techniques and Tools for Sound System Design and Alignment (p. 453). Taylor and Francis. Kindle Edition.

In this case “0 dB” refers to the average of a 6dB peak and a -40dB valley.

My takeaway from all of this is that more measurements combined with optical averaging (looking at them all at once) is more important than the specific form of mathematical averaging you choose.

What do you think?