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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. 75), an expansion with spatial bandwidth N − 1, or an (N − 1)-th order expansion. When simulations are presented in this book that depict quantities of infinite order, the order of the simulations is chosen such that the result becomes indistinguishable from the exact representation.

Close to center, the wave fronts are indeed as desired, whereby the accuracy of the bandlimited sound field description rises for source for positions closer to the expansion center. A distances far from the expansion center, the wave fronts tend to be smeared with respect to time, which is a consequence of the lack of energy at high frequencies at these locations. Note that an r N −1 -region (Sect. 1) can not be indicated here since it is frequency dependent. Inspecting Fig. 11 thoroughly reveals that not all energy is propagating in the same direction like the plane wave.

2005, May). 2 multichannel sound system and its application. In 118th Convention of the AES (p. 6406). , & Møller, H. (2002). Methods for binaural recording and reproduction. Acustica, 88(3), 303–311. , & Donohue, K. D. (2008). Virtual sound source rendering using a multipoleexpansion and method-of-moments approach. JAES, 56(6), 473–481. Ise, S. (1999). A principle of sound field control based on the Kirchhoff–Helmholtz integral equation and the theory of inverse systems. Acta Acustica United with Acustica, 85, 78–87.

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