The digital waveguide (DWG) mesh is a method for simulating wave propagation in multiple dimensions. Boundary conditions are needed for modeling changes in wave propagation media such as walls and furniture in a room or boundaries of a resonating membrane of a musical instrument. The boundary conditions have been solved for a one-dimensional DWG structure, but there is no known exact solution for the multi-dimensional mesh. In this work, a new boundary structure is introduced for modeling reflection coefficient values −1 ≤ r ≤ 1 in two dimensions. The new method gives remarkably more accurate results than the earlier approximations, especially at the low absolute values of r. At incident angles of Θ < 60o , the absolute error of reflection coefficient r is below 0.1 at frequencies 0.004 < f < 0.222 relative to the sampling frequency and at 60o ≤ Θ ≤ 80o the same result is reached at 0.005 < f < 0.114.

Download

The three-dimensional digital waveguide mesh is a method for modeling the propagation of sound waves in space. It provides a simulation of the state of the whole soundfield at discrete timesteps. The updating functions of the mesh can be formulated either using physical values of sound pressure or particle velocity, also called the Kirchhoff values, or using a wave decomposition of these instead. Computation in homogenous media is significantly lighter using Kirchhoff variables, but frequency-dependent boundary conditions are more easily defined with wave variables. In this paper a conversion method between these two variable types has been further simplified. Using the resulting structure, a novel method for defining the mesh boundaries with digital filters is introduced. With this new method, the reflection coefficients can be defined in a frequency-dependent manner at the boundaries of a Kirchhoff variable mesh. This leads to computationally lighter and more realistic simulations than previous solutions.

Download

Characteristics of digital waveguide meshes with more than three physical dimensions are studied. Especially, the properties of a 4-D mesh are analyzed and compared to waveguide structures of lower dimensionalities. The hypermesh produces a response with a dense and irregular modal pattern at high frequencies, which is beneficial in modeling the reverberation of rooms or musical instrument bodies. In addition, it offers a high degree of decorrelation between output points selected at different locations, which is advantageous for multi-channel reverberation. The frequencydependent decay of the hypermesh response can be controlled using boundary filters introduced recently by one of the authors. Several hypermeshes can be effectively combined in a multirate system, in which each mesh produces reverberation on a finite frequency band. The paper presents two hypermesh application examples: the modeling of the impulse response of a lecture hall and the simulation of the response of a clavichord soundbox.

Download