On Tue, Nov 2, 2010 at 5:12 PM, <[email protected]> wrote: > On Tue, Nov 02, 2010 at 04:07:40PM -0700, Eric Benjamin wrote: > >> I don't know how to compute the gain factors for 3rd order other than by >> numerical methods. I'm aware that Moreau published the gains of (1.000, >> .862, >> .612, and .305) but I don't know if those are correct or if there was a >> general >> solution published. > > The gain factors provided by Daniel (and Moreau) are a general solution. > For 3D, rE it involves Legendre functions: > > rE = largest root of P_{M+1} > g(m) = P_m(rE) > which also means g(1) = rE
A while back I posted some Maxima code to do this http://www.ai.sri.com/ajh/ambisonics/shelf-gains-example.html For third order, I get 0.861, 0.612, 0.305 which is the same as you and Eric get. However, I have to say that I've never seen the derivation of this result. Moreau gives it in Table 3.5 of his thesis without derivation, citing Daniel's thesis. Page 183 of Daniel's thesis cites Appendix A.4.3 in his 1998 AES paper "Ambisonic Encoding of Other Audio Formats...", which does not appear to have an Appendix 4.3. Aaron <[email protected]> Menlo Park, CA US Aaron _______________________________________________ Sursound mailing list [email protected] https://mail.music.vt.edu/mailman/listinfo/sursound
