Clearly there's no magic here -- this scheme isn't going to let you play third-order recordings on a cube or something as irregular as The Morning Line. As Fons has pointed out on the Linux audio list, decoder design for irregular arrays is still a bit of a black art. Even if there were a definition of optimal we could all agree upon, I wouldn't claim that AllRAD produces optimal decoders. An interesting example to study is the trirectangle, as we do know how to make optimal decoders for that, so any deviation shows the compromises in the AllRAD approach. I can post some performance graphs if anyone would like to see them.
It does offer a deterministic solution for some speaker configurations that are difficult to handle with conventional techniques, specifically partial-coverage rigs, like a dome, which seem to be a fairy common configuration, and it produces useable decoders quickly. The AllRAD decoder we did for the 24-speaker dome at Bing Concert Hall needed no manual tuning and the improvement over the previous (hand-tuned!) decoder I'd designed was immediately obvious to everyone. Bing is a fairly reverberant hall, so perhaps some artifacts were masked, but we also did some careful full-sphere and upper-hemisphere decoder comparisons in CCRMA's listening room, which is pretty dead, with quite favorable results. One nice feature is that it gives you a easy-to-understand way to control the reproduction of sources that are from directions where you don't have adequate coverage. This is essentially the same problem as doing something reasonable to play material with overhead sources, say an airplane flyover, on a horizontal array. Frankly, I was skeptical too, as it takes just a bit of math to see that VBAP interpolation is not correct for Ambisonics. However, once you start designing decoders for irregular arrays, you have to trade off uniform energy (loudness) for correct angular direction. Numerical optimization schemes let you make those trade offs explicitly by adjusting the weights in the objective function, but my experience is that it gets unwieldy once you have more than a 100 or so variables; for reference, a 3rd-order decoder for a 24-speaker array has 384 variables per frequency band. One approach we mention in our LAC2012 paper is to optimize each order successively, freezing lower orders as you go, except for an overall gain. We found that that tends to create decoders that have a lower average rE than optimizing all orders simultaneously, but it makes the process quicker and more tractable. In contrast, AllRAD starts with uniform energy distribution and tries to preserve that by using a much larger number of virtual loudspeakers than real ones, so that the signals for each triangle of speakers are derived from 10 to 20 virtual speakers. I did take a detailed look at rE in third-order AllRAD decoders. Over regions with adequate loudspeaker coverage, maximum angular errors tend to be a bit larger than the decoders produced by my optimizer when angular accuracy is favored (~5-7 vs 1 degree), but I get good-sounding decoders for large arrays in a few seconds vs a few hours. I'd like to think that these decoders would be a good starting point for the optimizer, but haven't experimented with that yet. I also spent some time trying understand why variations in magnitude and direction of rE are not symmetric despite symmetric speaker arrays, and finally realized that it is because the triangulation of the convex hull is not necessarily symmetric. One aspect of the manual tuning that Dave and Fons allude to is what to do when there are large gaps in coverage of the speaker array, such as the bottom of a dome, or a missing speaker from the 5th-order 12-speaker ring Fons mentions. Conventional advice is don't use arrays like that for ambisonic playback, but often that is not an option, as placement of loudspeakers is typically constrained by architecture, rigging, aesthetics, time, budget, especially in temporary arrays, such as those CCRMA installs at Bing or in their courtyard. The solution Zotter proposes is to insert imaginary loudspeakers into the array to fill large gaps. There are a couple of things one can do with the signals intended for those imaginary speakers: decorrelate and mix into the other speakers or simply discard. My toolbox currently does the latter so it can produce presets for AmbDec, but it would not be difficult to implement the former with a different decoding engine. When used with a dome, the effect is that as a signal is panned down in elevation, it sticks at the equator and then fades out. Adjusting the placement of the imaginary speaker controls how quickly it fades, close to the center gives quick fades, farther down slower ones. Finally, lots of people seem to have thought about or tried hybrid ambi/vbap schemes (even me -- the other day I stumbled across a long forgotten email to Eric Benjamin where I described such a scheme). Zotter and colleagues at IEM get credit for publishing a succinct description of what they did and the results of their analysis. If you don't want to download and install a couple thousand lines of MATLAB code, spend me some speaker coordinates in a CSV file and I'll send you some decoders to try out. My only request is that they be for real arrays you have access to (vs. pathological examples), so you can listen and report back on what you hear. Aaron Heller (hel...@ai.sri.com) Menlo Park, CA US -------------- next part -------------- An HTML attachment was scrubbed... URL: <https://mail.music.vt.edu/mailman/private/sursound/attachments/20130423/2df0a9dd/attachment.html> _______________________________________________ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
