Reducing the dispersion error in the digital waveguide mesh using interpolation and frequency-warping techniques
Reducing the dispersion error in the digital waveguide mesh using interpolation and frequency-warping techniques
复制标题
使用插值和频率扭曲技术减少数字波导网格中的色散误差
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
V. Välimäki
中科院分区：
文献类型：
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作者：
Lauri Savioja;V. Välimäki
数字波导网是一维数字波导技术的扩展。该网格可用于模拟乐器和声学空间中的二维和三维（3-D）波传播。原始的矩形数字波导网格算法受到方向相关色散的影响。替代的几何形状，如三角形网格，以前已经提出，以提高网格的性能。在本文中，我们表明，分散的问题可以减少使用各种其他技术。这些方法包括多维插值，优化的点扩展函数，和频率弯曲。我们比较了这些技术在二维（2-D）的情况下的准确性和计算复杂性，并进行数值模拟的膜。采用二阶拉格朗日插值的矩形网格可以在没有乘法的情况下实现，但其精度比其他增强结构差。就相对频率误差而言，最准确的技术是变形三角形网格，其最大误差为0.6%。具有优化加权系数的扭曲矩形网格不那么精确，但仍提供1.2%的准确度。
The digital waveguide mesh is an extension of the one-dimensional (1-D) digital waveguide technique. The mesh can be used for simulation of two- and three-dimensional (3-D) wave propagation in musical instruments and acoustic spaces. The original rectangular digital waveguide mesh algorithm suffers from direction-dependent dispersion. Alternative geometries, such as the triangular mesh, have been proposed previously to improve the performance of the mesh. In this paper, we show that the dispersion problem may be reduced using various other techniques. These methods include multidimensional interpolation, optimization of the point-spreading function, and frequency warping. We compare the accuracy and computational complexity of these techniques in the two-dimensional (2-D) case and conduct numerical simulations of a membrane. A rectangular mesh using second-order Lagrange interpolation can be implemented without multiplications, but its accuracy is worse than that of other enhanced structures. The most accurate technique in terms of the relative frequency error is the warped triangular mesh whose maximum error is 0.6%. The warped rectangular mesh with optimized weighting coefficients is not as exact, but still offers a 1.2% accuracy.