Analytic Methods of Sound Field Synthesis
This book puts the focus on serving human listeners in the sound field synthesis although the approach can be also exploited in other applications such as underwater acoustics or ultrasonics. The author derives a fundamental formulation based on standard integral equations and the single-layer potential approach is identified as a useful tool in order to derive a general solution. He also proposes extensions to the single-layer potential approach which allow for a derivation of explicit solutions for circular, planar, and linear distributions of secondary sources. Based on above described formulation it is shown that the two established analytical approaches of Wave Field Synthesis and Near-field Compensated Higher Order Ambisonics constitute specific solutions to the general problem which are covered by the single-layer potential solution and its extensions.
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2 Physical Fundamentals of Sound Fields
3 Continuous Secondary Source Distributions
4 Discrete Secondary Source Distributions
5 Applications of Sound Field Synthesis
A Coordinate Systems
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Acoustics Ahrens and Spors Ambisonics amplitude approximation assumed audio bandlimited boundary circular secondary source coefficients Convention coordinate system denotes depicted in Fig desired sound field discretization artifacts domain driving function Duraiswami 2004 emitted Equation Fazi ﬁeld filter focused source Fourier series Fourier transform frequency fullband synthesis Girod given Gumerov and Duraiswami Hankel function Helmholtz equation horizontal plane illustrated in Fig impulse response integral linear secondary source listener located loudspeaker narrowband narrowband synthesis perception propagation direction properties radiation Refer to Fig representation reproduction respect secondary source distribution setup signature function sound field S(x sound field synthesis sound pressure sound reproduction spatial bandwidth spatial discretization spatial transfer function spectral repetitions spherical harmonics spherical secondary source spherical wave Stereophony synthesized sound field synthesizing a virtual time-domain time-frequency virtual plane wave virtual sound field virtual sound sources wave field synthesis wave front wavenumber Weisstein 2002