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Dept. of Measurement and Information Systems, Budapest University of Technology and Economics


Digital Signal Processing Laboratory

 

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DSP25
Organ · String instruments · Nonlinear strings · Bells

 

Sound Synthesis

 

 

Sound synthesis is about reproducing the sound of musical instruments by means of signal processing algorithms. From this point of view, this is similar to modeling of any other system: first a model has to be constructed, then the parameters of the model has to be determined (similarly to system identification). Finally, the model has to be implemented on DSP or PC.

 

The sound synthesis research in the DSP laboratory has started by the synthesis of organ sounds in 1998 as a student work (Project Laboratory and M.Sc. thesis). The organ sound was modeled by a signal model, composed of a set of sinusoids and filtered noise. The parameters of the model were identified from recorded organ sounds.

 

For the synthesis of string instruments the physics-based approach has been used. In this approach the target of model development is not the sound, but the instrument itself. Therefore, the method simulates the sound production mechanism (the vibration) of the instrument. An advantage of the model is that the interaction between the different parts of the instrument (e.g., the coupled vibration of strings) can be easily taken into account. The synthesis of piano sounds has been started as a student work and resulted in several publications, and a Ph.D. dissertation. Through these years we have gained internationally recognized experience in modeling string instruments, and particularly, the piano. Besides piano synthesis, various types of physics-based guitar and violin synthesisers has been or are being developed in the form of student work (e.g. M.Sc. thesis).

Our newest field of research is about modeling the geometric nonlinearity of musical instrument strings. Geometric nonlinearity comes from the geometry of the string, thus, it will act also in the case of a perfectly elastic string, if the amplitude of vibration is large enough. In this case the transverse and longitudinal vibration of the string become nonlinearly coupled. The most widely used linear string models cannot take this effect into account, therefore they are not capable of reproducing some important aspects of the sounds. Particularly, the metallic sound of low piano tones is produced by the nonlinear coupling of the longitudinal and transverse polarization, which has to be modeled for good sound quality.

 

For the synthesis of bell sounds, a source-filter model has been used, which is in between signal modeling and the physics based approach: the modes of the bell are modeled by complex resonators, which are excited by the output of a signal model (the model of the hammer excitation). The research has been started as a student work and now the algorithm has found an industrial application: the digital carillon has been installed in many places around the country.

 

Besides the above mentioned topics, our colleagues and students has also dealt with the development in virtual analog synthesizers and musical effects (e.g. pitch shift). As for physics based sound synthesis, the modeling of membranes and plates is also under research.

 
 

 

 

Signal model based synthesis of organ pipe sounds

The synthesis of organ sound as a combination of sinusoidal components and noise filtered by a set of second-order resonators. The envelopes of the sinusoids are modeled by the step response of low-roder IIR filters.

Physics-based sound synthesis of string instruments

The application of digital waveguides for string instruments, with an emphasis on the piano. Here only the linear transverse vibration of the string is modeled.

Modeling the nonlinear vibrations of strings

The vibration of strings cannot be described by linear theory above a certain amplitude of vibration, as in this case the tension of the string cannot be assumed constant. This leads to the nonlinear excitation of longitudinal vibration.

Modeling of bell sounds by a source-filter model

The bell is modeled by a set of complex resonators are excited by the output of a signal model.