By Jens Ahrens
This booklet places the point of interest on serving human listeners within the sound box synthesis even supposing the strategy will be additionally exploited in different purposes resembling underwater acoustics or ultrasonics. the writer derives a basic formula in response to commonplace essential equations and the single-layer capability technique is pointed out as a great tool with a view to derive a common resolution. He additionally proposes extensions to the single-layer capability strategy which enable for a derivation of particular strategies for round, planar, and linear distributions of secondary assets. in line with above defined formula it truly is proven that the 2 demonstrated analytical ways of Wave box Synthesis and Near-field Compensated better Order Ambisonics represent particular options to the final challenge that are coated via the single-layer strength answer and its extensions.
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3. An extensive treatment can be found in (Gumerov and Duraiswami 2004). 2. 2 Selected Properties of Bandlimited Spherical Harmonics Series Consider a bandlimited series N −1 n S˚nm (r, ω)Ynm (β, α). 39) converges uniformly for given r and ω (Kennedy et al. 2007; Gumerov and Duraiswami 2004) so that any such bandlimited series constitutes an approximation of S(x, ω) the error of which decreases with increasing N > Nmin . , S˚nm (r, ω) = 0 ∀ n > N − 1, one speaks of an N-truncated sum (Gumerov and Duraiswami 2004, p.
82). , it covers evanescent components. 4. The most important relation in the context of this book is S¯i (φ, θ, ω) = ∞ n n = 0 m = −n m i n S˘n,i (ω)Ynm (φ, θ ). 5 Far-Field Radiation As outlined in Sect. 32b). 19) (Williams 1999) can be applied resulting in (Gumerov and Duraiswami 2004, Eq. 39), p. 47) m i n S˘n,e (ω) Ynm (β, α) . 43) whereby the angular dependency of the transfer function is given by the far-field signature function S¯e (β, α, ω) (Gumerov and Duraiswami 2004, p. 296). The latter is given by an m (ω) respectively.
Text in French. Daniel, J. (2003, May). Spatial sound encoding including near field effect: Introducing distance coding filters and a viable, new ambisonic format. In 23rd International Conference of the AES. de Vries, D. (2009). Wave field synthesis. AES monograph. New York: AES. du Moncel, T. (1881, December). The telephone at the Paris opera. Scientific American, pp. 422–423. Dutton, G. F. (1962). The assessment of two-channel stereophonic reproduction performance in studio monitor rooms, living rooms and small theatres.
Analytic Methods of Sound Field Synthesis by Jens Ahrens