By Jens Ahrens
This booklet places the focal point on serving human listeners within the sound box synthesis even though the procedure might be additionally exploited in different functions equivalent to underwater acoustics or ultrasonics. the writer derives a basic formula in keeping with normal quintessential equations and the single-layer strength strategy is pointed out as a useful gizmo for you to derive a normal resolution. He additionally proposes extensions to the single-layer capability strategy which permit for a derivation of particular ideas for round, planar, and linear distributions of secondary resources. in response to above defined formula it truly is proven that the 2 tested analytical ways of Wave box Synthesis and Near-field Compensated larger Order Ambisonics represent particular recommendations to the final challenge that are coated through the single-layer power resolution and its extensions.
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Additional info for Analytic Methods of Sound Field Synthesis
1) are outlined below exemplarily for the x and k x -dimensions respectively. The frequency variable in the time Fourier transform is the radian time frequency ω, which is related to the time frequency f via ω = 2π f. In practice, the time-frequency scale (not the radian frequency scale) is used in order to refer to specific values. The frequency variable in the spatial Fourier transform is the wavenumber in x-direction k x . k x can thus be interpreted as the spatial radian frequency and is of unit rad/m.
By combinations of monopoles located at infinitesimal distance from each other (Gumerov and Duraiswami 2004, p. 71). Lower order multipoles are also referred to as monopoles, dipoles, quadrupoles, octopoles, etc. Multipole expansions are closely related to spherical harmonics expansions with the fundamental difference that the former are not unique and thus do not form a basis in the strict sense. Multipole expansions will only play a marginal role in the context of this book and are therefore not treated in detail but only their existence is mentioned.
The according transforms for decomposition and recomposition are outlined in the respective sections. From above considerations, the meaning of the term spatial bandlimitation becomes clear: Spatial bandlimitation constitutes a recomposition of a given signal using only a subset of the corresponding spectral coefficients and basis functions. 39). , by modifying the boundaries of the integral of the inverse transforms accordingly. The reader might have an intuitive understanding of the effect of bandlimiting a time-domain signal in terms of the way the timbre of the signal changes.