By Jens Ahrens
This ebook places the point of interest on serving human listeners within the sound box synthesis even though the process may be additionally exploited in different purposes resembling underwater acoustics or ultrasonics. the writer derives a basic formula according to ordinary fundamental equations and the single-layer power procedure is pointed out as a great tool which will derive a basic answer. He additionally proposes extensions to the single-layer power technique which enable for a derivation of specific options for round, planar, and linear distributions of secondary assets. in line with above defined formula it truly is proven that the 2 verified analytical ways of Wave box Synthesis and Near-field Compensated greater Order Ambisonics represent particular ideas to the overall challenge that are coated by way of the single-layer strength answer and its extensions.
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Additional info for Analytic Methods of Sound Field Synthesis
Consider now a sound field carrying a signal that is broadband with respect to the time frequency. When the spatial bandwidth of the sound field is constant over the entire time-frequency range, then the sound field has a larger “extent” at low frequencies than at high frequencies. At positions closer to the expansion center more energy is apparent at higher time frequencies than at farther positions. This circumstance is illustrated in Fig. 9, which shows the amplitude of a 5-th order plane wave (N = 6), which propagates inside the horizontal plane.
17) and (Gumerov and Duraiswami 2004, Eq. 18) (2) whereby f n can be any of jn , yn , h n or h n . The prime denotes differentiation with respect to the argument. In certain situations the large-argument approximation of the spherical Hankel functions given by (Williams 1999, Eq. 68), p. 19) will be employed in order to simplify problems. 19) constitutes a far-field/high-frequency approximation. 14) are given by the complex exponential functions eimα with m ∈ Z and the colatitudinal solutions Φ(β) are given by the associated Legendre functions Pnm (cos β).
The soundscape renderer: A unified spatial audio reproduction framework for arbitrary rendering methods. In 124th Convention of the AES. , & Spors, S. (2010, May). Perceptual evaluation of focused sources in wave field synthesis. In 128th Convention of the AES (p. 8069). Gerzon, M. A. (1973). Periphony: With-height sound reproduction. JAES, 21, 2–10. Gerzon, M. A. (1980, February). Practical periphony: The reproduction of full-sphere sound. In 65th Convention of the AES (p. 1571). Gerzon, M. A.
Analytic Methods of Sound Field Synthesis by Jens Ahrens