Physical modeling of drums by transfer function methods

Abstract

Multidimensional (MD) physical systems are usually given in terms of partial differential equations (PDEs). Similar to one-dimensional systems, they can also be described by transfer function models (TFMs). In addition to including initial and boundary conditions as well as excitation functions exactly, the TFM can also be discretized in a simple way. This leads to suitable implementations for digital signal processors. Therefore it is possible to implement physics based digital sound synthesis algorithms derived from TFMs in real-time. This paper extends the recently presented solution for vibrating strings with one spatial dimension to two-dimensional drum models.

Turning Vector Partial Differential Equations into Multidimensional Transfer Function Models

“…A more detailed derivation is beyond the scope of this paper. For transfer function models derived from scalar PDEs it is shown in [11,13].…”

“…It holds for any two vectors V and Y and can be shown by performing the differentiation of the product on the right hand side of (13). Furthermore, the expression in brackets on the right hand side of (13) can be expressed in terms of the boundary value operator f b and the associated…”

Wave Field Simulation with the Functional Transformation Method

“…rectangular and circular regions as presented in [1]. The search for the eigenmodes of the model, which are needed for the integral transformations of the FTM, gets very evolved for complex geometries.…”

“…Therefore in this paper a simulation tool for room acoustics based on block based modeling as described in [3] with blocks modeled with the FTM as described in [1] is demonstrated. Focusing on 2D wave fields, a brief review of the approach to block based modeling is given in section 2.…”

“…In doing so, the FTM has so far been successfully applied to physical models of plates and membranes [1], resulting in real-time capable sound synthesis algorithms based on physical modeling.…”