Allow me some general consideration on the topic Spatial Average. Obviously I am not referring to a particular method but to general considerations.

So…SPATIAL AVERAGES.

Thirst of all..they are just MATH.

No one hears a “GLOBALLY” or “MUST RAPPRESENTATIVE” average response.

Meaningful EQ could be applied to a loudspeaker based on a spatial average of positions that were free of phase interference, and these are determined by the relative physical positions of the loudspeakers. The method suggested that subtle improvement could be achieved for a device that was already well-designed and acoustically symmetrical.

Some modal phenomena could be considered global and improved via equalization.

Multi-mic spatial averaging satisfies the logic that “there must be a common-denominator fix” for this system’s problems, when in fact the response at each and every listener position is unique. The suggested EQ curve, no matter how sophisticated or expensive the analyzer, will be completely dependent on which group of seats you pick, and unique for different choices. I don’t see where the benefits can extend beyond the psychological.

Now, allow me to express a series of more specific notes, which I have assimilated over the years. I still remember a very old discussion, somewhere, in which this topic was addressed. I do not remember with who I had this discussion, nor the authors of the various thoughts (many in the years), but i certainly made them mine and pinned them. I report them to you below.

Assuming we can acquire a correct average response for a sound system of any size we should acknowledge a few facts about that response:

- How many listeners will ever hear it? ZERO!
- The average response contains no information about the position-dependent response variations. it does not tell us what is best and what is worst and does not reflect, for each session, all the possible gradations between these two scenarios.
- Average smooth out position-dependent problems, without telling us anything about their meaning and about their audible effects.
- What we ear of the sound phenomenon is an envelope for the frequency response and a sort of Leq, RSM AVG, of sound pressure level variations over time. Peaks of a response tend also to be more objectionable than notches. Any type of averaging can provide a reliable means for making such distinctions.Having acknowledged the above, we need to examine the challenge of actually acquiring an average response:
- When we take response data at discrete mic positions, we are “spatially sampling” the response. Just as with temporal sampling, we are subject to the Nyquist criterion with respect to periodicity and sampling interval. We’re guessing, and the response picture we generate may be affected by “spatial aliasing”.
- Even taking it for granted the previous point, we must be sure that we have chosen a representative sample of points at which to take the system response. Otherwise, the response we will not represent the system’s average response. This is impossible in a real-world equalization scenario. Exceptions to this might include systems with some periodicity, like distributed systems, in which a sufficiently dense sampling of the response in one area could safely be assumed to represent the response in other similar areas.
- Talking about “spatial averaging” implicitly assumes that the issues which cannot be equalized have already been identified and, where possible, addressed. On this point, if the identification of non-equalizable issues it is not addressed, it is totally out of place to talk about “equalization” and spatial averaging.

If instead we are to the point that we can make equalization choices, rather than worrying about acquiring an average, we need to identify best/worst case responses and to have an idea of the distribution of audience members between those two extremes. This identification process

is best initiated by examining the sound system design and choosing candidate locations for each scenario. It cannot be reliably achieved by any sampling technique that we will have time to complete while we’re all still above ambient temperature.

Done this, my suggestion is to pursue the “least worst”. Do your best to ameliorate the worst case while minimizing the compromise to sound quality elsewhere. In this process, human is the protagonist.

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