Analytic Methods of Sound Field Synthesis (T-Labs Series in by Jens Ahrens
By Jens Ahrens
This booklet specializes in serving human listeners in sound box synthesis. comprises extensions to the single-layer capability strategy which permit for a derivation of particular recommendations for round, planar, and linear distributions of secondary resources.
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Extra info for Analytic Methods of Sound Field Synthesis (T-Labs Series in Telecommunication Services)
34 2 Physical Fundamentals of Sound Fields This circumstance is directly reflected by the properties of the spherical Bessel functions jn (·) (refer to Fig. 2a in Sect. 3): The higher the order n of the Bessel function, the higher is the argument (ω/c) r at which the maximum value is reached (Abramowitz and Stegun 1968). Typically, the domain inside which a bandlimited sound field description is considered to be comparable to its full-band analog is assumed to be inside the region where the argument (ω/c) r of the spherical Bessel function jn (·) is smaller than the highest order (N − 1) contained in the expansion (Gumerov and Duraiswami 2004, p.
43) and thus employs only 0-th order. N ! (N or or −n−1)! Yn 0 ∀n ≤ N −1 . , its nominal orientation. 44) represents a purely real spatial transfer function. Refer to Fig. 5 −2 −2 −1 0 1 2 x (m) Fig. 12 Sound fields the horizontal plane and far-field signature functions (see Sect. 44). a N = 4, f = 1000 Hz. b Normalized far-field signature function, N = 4. c N = 21, f = 1000 Hz. d Normalized far-field signature function, N = 21 respectively. The far-field directivities of the two sound sources are also depicted (refer to Sect.
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. , its wave form is less intuitive. A spatial bandlimitation applied to a sound field affects the spatial structure of the latter. The way this spatial structure changes depends heavily on the fact with respect to which representation of the spatial spectrum the signal is bandlimited.