Theoretical Research On Sound Synthesis Technique Based On Physical Model

Sound synthesis techniques for physical model are research subjetcs based on acoustics and elastic dynamics and mathematics and signal process. They start from a continuous model for the vibrating body, given by partial differential equation dependent on elastic dynamics, and take its initial and boundary conditions, as well as excitation functions into account. Physical model methods are able to preserve not only the inherent physical stability, but also natural frequencies of the oscillating body. They are different from other sonud synthesis methods presenting characteristic of body with respect to time and frequency domain.In term of physical principles, wind and string and flute instruments, and so on, can be described by their One-dimensional PDE. And then, drums and gongs and cymbals, and etc, can be described by their two-dimensional PDE. The physical models for those sound synthesis methods can exactly describe musical instruments's fundamental and harmonious and inharmonious frequencyies, as well as their nautral sounding process. They can be played like real musical instruments, representing players's strength, velocity and pattern, as well as emotion. So, the methods are playing very important roles within the sound synthesis domain currently, with MPEG4 published and improvement of computer's computational efficiency.However, they have been developing for a relatively shorter time as excellent methods, since 1970's when they were proposed. Nowadays, they still have several imperfects in princilpes and applications. One of those is that fundamental model of one or multi-dimensional PDE have disadvantages in some degree, another is that it is difficult to construct maths equations of irregular boundary conditions and excition functions.Firstly, a brief overview of the popular sound synthesis techniques is provided in this paper. And then, the features of the partial string and membrane instruments are described. Finally, some of the disadvantages of existing physical model methods are discussed. However, the key problems to be solved in the paper are to testify limitations of the most famous PDE existing in one and two-dimensional vibrating system, and construct their new models. So, the most important research achievements in this paper are summarized as follow.1. We testify limitations of the most famous one-dimensional PDE for sound synthesis from its princilpes to application based on string instrument.2. We establish a new one-dimensional vibrating PDE dependent on elastic dynamics, and prove the PDE is correct according to its principles and applications baesd on string instrument.3. We testify limitations of the most famous two-dimensional PDE for sound synthesis in its princilpes for rectangle and circle membrances.4. We establish a new two-dimensional vibrating PDE dependent on elastic dynamics, and prove the PDE is correct according to its principles for rectangle and circle membrances.