Download Sound synthesis by physical modelling using the functional transformation method: Efficient implementations with polyphase-filterbanks
The Functional Transformation Method (FTM) is a recently introduced method for sound synthesis by physical modeling. Based on integral transformations, it provides a parallel system description for any linear physical model, usually described by a set of partial differential equations. Such parallel descriptions can be directly implemented by a set of recursive systems in full rate. In this PSfrag replacem paper we present a new and very ef£cient method for this implementation which bene£ts from the spectral decomposition of the system. All recursive systems are working at a subsampled rate and are summed up by the application of a polyphase £lterbank. Performance measurements on a real time implementation show, that a ¤exible and ef£cient realization is achieved. Compared to the direct implementation it is over nine times faster at the cost of nine milliseconds of delay and even faster with more delay.
Download Digital Sound Synthesis of Brass Instruments by Physical Modeling
The Functional Transformation Method (FTM) is an established method for sound synthesis by physical modeling, which has proven its feasibility so far by the application to strings and membranes. Based on integral transformations, it provides a discrete solution for continuous physical problems given in form of initialboundary-value problems. This paper extends the range of applications of the FTM to brass instruments. A full continuous physical model of the instrument, consisting of an air column, a mouthpiece and the player’s lips is introduced and solved in the discrete domain. It is shown, that the FTM is a suitable method also for sound synthesis of brass instruments.
Download Implementation of Arbitrary Linear Sound Synthesis Algorithms by Digital Wave Guide Structures
The Digital Wave Guide (DWG) method is one of the most popular techniques for digital sound synthesis via physical modeling. Due to the inherent solution of the wave equation by the structure of the DWG method, it provides a highly efficient algorithm for typical physical modeling problems. In this paper it will be shown, that it is possible to use this efficient structure for any existing linear sound synthesis algorithm. By a consequent description of discrete implementations with State Space Structures (SSSs), suitable linear state space transformations can be used to achieve the typical DWG structure from any given system. The proposed approach is demonstrated with two case studies, where a modal solution achieved with the Functional Transformation Method (FTM) is transformed to a DWG implementation. In the first example the solution of the lossless wave equation is transformed to a DWG structure, yielding an arbitrary size fractional delay filter. In another example a more elaborated model with dispersion and damping terms is transformed, resulting in a DWG model with parameter morphing features.
Download Adjustable Boundary Conditions for Multidimensional Transfer Function Models
Block based physical modeling requires to provide a library of modeling blocks for standard components of real or virtual musical instruments. Complex synthesis models are built by connecting standard components in a physically meaningful way. These connections are investigated for modeling a resonating structure as a distributed parameter system. The dependence of a resonator’s spectral structure on the termination of its ports is analyzed. It is shown that the boundary conditions of a distributed parameter system can be adjusted by proper termination only. Examples show the corresponding variation of the resonator’s spectral structure in response to variations of the external termination.
Download Physical Modeling for Spatial Sound Synthesis
This contribution combines techniques for sound synthesis and spatial reproduction for a joint synthesis of the sound production and sound propagation properties of virtual string instruments. The generated sound field is reproduced on a massive multichannel loudspeaker system using wave field synthesis techniques. From physical descriptions of string vibrations and sound waves by partial differential equations follows an algorithmic procedure for synthesis-driven wave field reproduction. Its processing steps are derived by mathematical analysis and signal processing principles. Three different building blocks are addressed: The simulation of string vibrations, a model for the radiation pattern of the generated acoustical waves, and the determination of the driving signals for the multichannel loudspeaker array. The proposed method allows the spatial reproduction of synthetic spatial sound without the need for pre-recorded or pre-synthesized source tracks.
Download Spatial Sound Synthesis for Circular Membranes
Physical models of real or virtual instruments are usually only exploited for the generation of wave forms. However, models of twoand three-dimensional vibrating structures contain also information about the sound radiation into the free field. This contribution presents a model for a membrane from which the required driving functions for a multichannel loudspeaker array are derived. The resulting sound field reproduces not only the musical timbre of the sounding body but also its spatial radiation characteristics. It is suitable for real-time synthesis without pre-recorded or presynthesized source tracks.
Download A Csound Opcode for a Triode Stage of a Vacuum Tube Amplifier
The Csound audio programming language adheres to the inputoutput paradigm and provides a large number of specialized commands (called opcodes) for processing output signals from input signals. Therefore it is not directly suitable for component modeling of analog circuitry. This contribution describes an attempt to virtual analog modeling and presents a Csound opcode for a triode stage of a vacuum tube amplifier. Externally it communicates with other opcodes via input and output signals at the sample rate. Internally it uses an established wave digital filter model of a standard triode. The opcode is available as library module.
Download Soliton Sonification - Experiments with the Kortweg-deVries Equation
Solitons are special solutions of certain nonlinear partial differential equations of mathematical physics. They exhibit properties that are partly similar to the solutions of the linear wave equation and partly similar to the behaviour of colliding particles. Their characteristic features are well-known in the mathematical literature but few closed-form solutions are available. This contribution derives algorithmic structures for the computation of solitons in a dimensionless space-time domain which can be scaled to the audio frequency range. The investigations are confined to first and second order solutions of the Korteweg-de Vries equation. Sound examples show that the effects of wave propagation and soliton interaction can be represented by audible events.
Download A Physical String Model with Adjustable Boundary Conditions
The vibration of strings in musical instruments depends not only on their geometry and material but also on their fixing at the ends of the string. In physical terms it is described by impedance boundary conditions. This contribution presents a functional transformation model for a vibrating string which is coupled to an external boundary circuit. Delay-free loops in the synthesis algorithm are avoided by a state-space formulation. The value of the boundary impedance can be adjusted without altering the core synthesis algorithm.
Download A Continuous Frequency Domain Description of Adjustable Boundary Conditions for Multidimensional Transfer Function Models
Physical modeling of string vibrations strongly depends on the conditions at the system boundaries. The more complex the boundary conditions are the more complex is the process of physical modeling. Based on prior works, this contribution derives a general concept for the incorporation of complex boundary conditions into a transfer function model designed with simple boundary conditions. The concept is related to control theory and separates the treatment of the boundary conditions from the design of the string model.