On the accuracy of first-order numerical derivatives in multidimensional digital waveguide mesh topologies

Digital waveguide mesh (DWM) models are numerical solvers for the wave equation in N-dimensions. They are used for obtaining the traveling-wave solution in practical acoustical modeling applications. Although unstructured meshes can be used with DWMs, regular mesh topologies are traditionally used due to their implementation simplicity. This letter discusses the accuracy of first-order approximations to numerical derivatives on more general unstructured mesh topologies. The results are applied to structured, regular mesh topologies as used in DWM modeling. A comparison of 2-D and 3-D DWM topologies with respect to the accuracy of first-order approximations to numerical derivatives is presented.


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Digital waveguide mesh (DWM) models offer a simple, accurate, time-domain, numerical solution of the wave equation. A specific case where such accurate and computationally simple solutions are needed is the acoustical modeling of open or closed volumes. It is possible to model 3-D propagation of waves in enclosures such as rooms using DWM models. Generally, idealized omnidirectional sources are used for obtaining the impulse response in the DWM. However, real-life sound sources are never completely isotropi...
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Digital waveguide mesh (DWM) models are time-domain numerical methods providing computationally simple solutions for wave propagation problems. They have been used in various acoustical modeling and audio synthesis applications including synthesis of musical instrument sounds and speech, and modeling of room acoustics. A successful model of room acoustics should be able to account for source and receiver directivity. Methods for the simulation of directional sources in DWM models were previously proposed. T...
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Öktem, Sevinç Figen (Institute of Electrical and Electronics Engineers (IEEE), 2009-08-01)
Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier and fractional Fourier transforms are special cases of LCTs. We present the exact relation between continuous and discrete LCTs (which generalizes the corresponding relation for Fourier transforms), and also express it in terms of a new definition of the discrete LCT (DLCT), which is independent of the sampling interval. This p...
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We present a novel receiver structure for the detection and parameter estimation of linear frequency modulated signals. The proposed structure is based on the relations between the fractional Fourier transform and the ambiguity function. It has been shown that the optimal ML receiver, which is the peak detector in the ambiguity plane, can be implemented at a reduced search complexity with the proposed method. The proposed method uses two 1-dimensional search operations in two different fractional Fourier do...
On higher order approximations for hermite-gaussian functions and discrete fractional Fourier transforms
Candan, Çağatay (Institute of Electrical and Electronics Engineers (IEEE), 2007-10-01)
Discrete equivalents of Hermite-Gaussian functions play a critical role in the definition of a discrete fractional Fourier transform. The discrete equivalents are typically calculated through the eigendecomposition of a commutator matrix. In this letter, we first characterize the space of DFT-commuting matrices and then construct matrices approximating the Hermite-Gaussian generating differential equation and use the matrices to accurately generate the discrete equivalents of Hermite-Gaussians.
Citation Formats
H. Hacıhabiboğlu and B. Günel Kılıç, “On the accuracy of first-order numerical derivatives in multidimensional digital waveguide mesh topologies,” IEEE SIGNAL PROCESSING LETTERS, pp. 9–12, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31312.