By Jens Ahrens

ISBN-10: 3642257437

ISBN-13: 9783642257438

This publication places the point of interest on serving human listeners within the sound box synthesis even though the strategy might be additionally exploited in different purposes equivalent to underwater acoustics or ultrasonics. the writer derives a primary formula according to ordinary necessary equations and the single-layer power strategy is pointed out as a great tool to be able to derive a basic answer. He additionally proposes extensions to the single-layer capability strategy which permit for a derivation of specific options for round, planar, and linear distributions of secondary assets. in line with above defined formula it really is proven that the 2 proven analytical methods of Wave box Synthesis and Near-field Compensated better Order Ambisonics represent particular suggestions to the overall challenge that are lined via the single-layer capability resolution and its extensions.

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K is termed wavenumber (although it is rather a coefficient than a number) and is of unit rad/m. It is related to the radian frequency ω via k2 = ω c 2 . 3) The radian frequency ω is related to the time frequency f via ω = 2π f and is of unit rad/s. The wavelength λ, measured in m, is given by λ= c 2π = . , lossless) media is considered throughout this book. 2) assume that the medium, which is air in the present case, is perfectly linear. , x1 (t) and x2 (t), leads to an according linear combination of the output signals y1 (t) and y2 (t) of the individual input signals as (Girod et al.

30) is exploited. 2). , any sound field) can thus be expressed by its according expansion coefficients S˚nm (r, ω) as (Arfken and Weber 2005, p. 790) ∞ n S˚nm (r, ω)Ynm (β, α). 31) n = 0 m = −n The representation of a function S(x, ω) as such a double series is a generalized Fourier series known as a Laplace series (Arfken and Weber 2005, p. 790). It can be shown that interior and exterior problems have to be considered separately (Williams 1999, p. 207, 217). , all sound sources and 30 2 Physical Fundamentals of Sound Fields (b) (a) sound source sound source Fig.

In the following the most basic properties of spatially bandlimited expansions that are important in the context of this book are summarized. Note that the properties presented below can not be seen as general. They are valid only if the stated assumptions are met. , the origin of the coordinate system), and higher orders describe the represented sound field at locations at far distances from the expansion center. 34 2 Physical Fundamentals of Sound Fields This circumstance is directly reflected by the properties of the spherical Bessel functions jn (·) (refer to Fig.

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