Read e-book online Analytic Methods of Sound Field Synthesis PDF

By Jens Ahrens

This e-book places the focal point on serving human listeners within the sound box synthesis even though the strategy could be additionally exploited in different functions corresponding to underwater acoustics or ultrasonics. the writer derives a primary formula according to commonplace indispensable equations and the single-layer capability technique is pointed out as a useful gizmo with a view to derive a normal resolution. He additionally proposes extensions to the single-layer strength technique which permit for a derivation of particular suggestions for round, planar, and linear distributions of secondary resources. in line with above defined formula it truly is proven that the 2 verified analytical methods of Wave box Synthesis and Near-field Compensated better Order Ambisonics represent particular strategies to the final challenge that are coated by means of the single-layer strength resolution and its extensions.

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A cross-section through the horizontal plane is shown. a N = 13; the dotted line bounds the r 12 -region; the dashed line bounds the domain of validity of the interior expansion; the arrows indicate the local propagation direction. 5 cm). An (N − 1)-th order sound field is described by N 2 coefficients S˘nm (ω), which are 136 coefficients in the present case. The situation can be different for other types of sound fields. Spherical waves the origin of which is far away from the expansion center behave similarly as shown in Fig.

8 ms. 9 ms. 9 ms. e large scale, t = 0 ms. , 20 log10 | {sS (x, t}| . 32a). 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.

7) and thus constitute plane waves. 8) is fulfilled. Thus, the wavenumber k represents the length of the propagation vector k = [k x k y k z ]T . 8) can be rearranged to read k 2y = k 2 − k x2 − k z2 . 9) provided that they are real (Williams 1999, p. 21). 10) ⎩ ±i k 2 + k 2 − k 2 for k 2 + k 2 ≥ k 2 x z x z since k is non-negative. 10) represents a propagating or homogeneous plane wave. The vector k points into the direction of propagation. Refer to Fig. 1a for a simulation. 10) (with complex k y ) represents an evanescent or inhomogeneous wave.

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