Combining Digital Waveguide and Functional Transformation Methods for Physical Modeling of Musical Instruments
Digital sound synthesis based on physical models is realized in real-time applications mostly with the well known digital waveguide method (DWG). It approximates the underlying physical behavior of a vibrating structure in a computationally efficient way. Due to these computational efficient approximations, the waveguide method looses the direct connection to the parameters of the underlying physical model. The recently introduced functional transformation method (FTM) on the other hand solves the underlying physical model analytically. Thus, the physical parameters are explicitly given in the discrete realization of the FTM. But due to this 'physicality' the computational cost of synthesis using FTM is larger than using DWG. This paper compares the DWG with the FTM and shows that for linear vibrating strings it is always possible to design an acoustically indistinguishable DWG approximation with the parameters obtained from the FTM. In that way, a computationally efficient and physically meaningful synthesis method is obtained. Furthermore, this paper shows the limits of this new synthesis method.
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