On Wed, Nov 07, 2012 at 07:08:59PM +0100, Jörn Nettingsmeier wrote: > On 11/07/2012 10:04 AM, Tommaso Perego wrote:
> >I was wondering how, knowing the diameter of a speaker octagon, > >using 1st or 3rd Order ambisonics, to calculate precisely the dimensions of > >the sweet spot area. > the strict sweet spot is only a function of order and frequency, not > of the array diameter. > r < N/2 * c/f is an approximation i saw mentioned in one of franz > zotter's papers, where N is the order, c is the speed of sound and f > is the frequency. in words, the order N is the number of > zero-crossings of a given frequency which are correctly reproduced. True, this defines the 'radius of reconstruction'. To get an idea of what's happening, have a look at the spherical Bessel functions, e.g. <http://mathworld.wolfram.com/SphericalBesselFunctionoftheFirstKind.html>. These define how the field is reconstructed. At a distance r from the sweet spot, the contribution of the order N spherical harmonic is proportional to the order N spherical Bessel function evaluated at x = 2 * pi * r / wavelength. For example, if x = 2, or r is roughly 1/3 of the wavelength, the contributions of the zero and first orders is more or less equal, and the higher ones contribute significantly less. So this distance is within the 'sweet radius' for first order. The distance at which 3rd order starts to fail is determined by the value at which the 4th and higher order Bessel functions start to contribute a significant part of the field. This also explains why e.g. decoding first order to an octagon is not a good idea. With 8 speakers you can reconstruct up to third order (horizontally), and a decoder for an octagon will actually do that, even if it is just a first order decoder. It wil just force the 2nd and 3th order components (and some higher ones, by aliasing) to be zero. So the field reconstruction will fail for those r where these missing orders contribute most. > in practise, a larger diameter does help, because of two factors: > a) the sound pressure level varies much more slowly in the far field > of a loudspeaker. e.g. the level halves when you move from 2 to 4 > meters (i.e. over 2 meters), and again when you move from 4 to 8 > meters (same drop, but over 4 meters). that means that while the > phase relationships are quite wrong outside the sweet spot, the > intensity ratios of the speakers are more or less correct, which > helps with rE localisation. True. Large diameters to help up to the point where delay effects take over. In summary, Martin Leese's remark is very much to the point: the 'sweet spot' is a fuzzy concept, and much depends on the application. Ciao, -- FA A world of exhaustive, reliable metadata would be an utopia. It's also a pipe-dream, founded on self-delusion, nerd hubris and hysterically inflated market opportunities. (Cory Doctorow) _______________________________________________ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
