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Virtual Strings Based on a 1-D FDTD Waveguide Model: Stability, Losses, and Traveling Waves

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The one-dimensional digital waveguide structures based on finite difference time domain (FDTD) formulations provide a flexible approach for real-time sound synthesis of simple one-dimensional (1-D) structures, such as a vibrating string. This paper summarizes the basic 1-D FDTD waveguide theory, carries out the stability analysis of the model, and presents a sufficient condition for the stability. The simulation of frequency-independent losses has also been covered. The formation of the traveling waves and initialization of the 1-D FDTD waveguides are investigated. The methods shown in the paper may be used to interconnect the 1-D FDTD waveguides to other model-based sound synthesis structures, such as digital waveguides that are based on the traveling wave solution of the wave equation.

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