Papers by Rudolf Rabenstein
arXiv (Cornell University), Mar 28, 2018
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. ... more This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or magnetism. The dynamics of the diffusion process are modeled by multi-dimensional transfer functions in a spatio-temporal frequency domain. Realistic boundary conditions are incorporated by the design of a feedback loop. The result is a discretetime semi-analytical model for the particle concentration in the channel. The model is validated by comparison to particlebased simulations. These numerical experiments reveal that the particle concentration of the proposed semi-analytical model and the particle-based model are in excellent agreement. The analytical form of the proposed solution provides several benefits over purely numerical models, e.g. high flexibility, existence of low run-time algorithms, extendability to several kinds of boundary conditions, and analytical connection to parameters from communication theory.
International Journal of Applied Mathematics and Computer Science, Sep 1, 2008
Block-based physical modeling is a methodology for modeling physical systems with different subsy... more Block-based physical modeling is a methodology for modeling physical systems with different subsystems. Each subsystem may be modeled according to a different paradigm. Connecting systems of diverse nature in the discrete-time domain requires a unified interconnection strategy. Such a strategy is provided by the well-known wave digital principle, which had been introduced initially for the design of digital filters. It serves as a starting point for the more general idea of blockbased physical modeling, where arbitrary discrete-time state space representations can communicate via wave variables. An example in musical acoustics shows the application of block-based modeling to multidimensional physical systems.
EURASIP Journal on Advances in Signal Processing, Jun 27, 2004
The functional transformation method (FTM) is a well-established mathematical method for accurate... more The functional transformation method (FTM) is a well-established mathematical method for accurate simulations of multidimensional physical systems from various fields of science, including optics, heat and mass transfer, electrical engineering, and acoustics. This paper applies the FTM to real-time simulations of transversal vibrating strings. First, a physical model of a transversal vibrating lossy and dispersive string is derived. Afterwards, this model is solved with the FTM for two cases: the ideally linearly vibrating string and the string interacting nonlinearly with the frets. It is shown that accurate and stable simulations can be achieved with the discretization of the continuous solution at audio rate. Both simulations can also be performed with a multirate approach with only minor degradations of the simulation accuracy but with preservation of stability. This saves almost 80% of the computational cost for the simulation of a six-string guitar and therefore it is in the range of the computational cost for digital waveguide simulations.
Block based physical modeling requires to provide a library of modeling blocks for standard compo... more 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.
arXiv (Cornell University), Mar 28, 2018
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. ... more This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or magnetism. The dynamics of the diffusion process are modeled by multi-dimensional transfer functions in a spatio-temporal frequency domain. Realistic boundary conditions are incorporated by the design of a feedback loop. The result is a discretetime semi-analytical model for the particle concentration in the channel. The model is validated by comparison to particlebased simulations. These numerical experiments reveal that the particle concentration of the proposed semi-analytical model and the particle-based model are in excellent agreement. The analytical form of the proposed solution provides several benefits over purely numerical models, e.g. high flexibility, existence of low run-time algorithms, extendability to several kinds of boundary conditions, and analytical connection to parameters from communication theory.
The derivation of suitable analytical models is an important step for the design and analysis of ... more The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications (e.g., assumption of an unbounded environment). In this paper, we develop a realistic model for particle diffusion in a bounded sphere and particle transport through a semi-permeable boundary. This model can be used for various applications, such as modeling of inter-/intra-cell communication or the release process of drug carriers. The proposed analytical model is based on a transfer function approach, which allows for fast numerical evaluation and provides insights into the impact of the relevant molecular communication system parameters. The proposed solution of the bounded spherical diffusion problem is formulated in terms of a state-space description and the semi-permeable boundary is accounted for by a feedback loop. Particle-based simulations verify the proposed modeling approach.
European Signal Processing Conference, Sep 1, 2005
Tension modulated nonlinearities for the modeling of string instruments are well known to increas... more Tension modulated nonlinearities for the modeling of string instruments are well known to increase the quality of synthesized sounds significantly. These models consider the nonlinear feedback from the string's deflection to one of its physical parameters, the string tension. Obviously this effect occurs for two dimensional models, drums or plates for instance, too, however so far only non real-time implementations are available. Therefore in this paper a new approach is presented, where the functional transformation method (FTM) is applied. The mathematical model of a dispersive and damped membrane is set up including an additional term for the tension modulated nonlinearity. Using some slight simplification this model is solved with the FTM and, thanks to the scalability of the FTM, implemented in real-time.
Publication in the conference proceedings of EUSIPCO, Antalya, Turkey, 2005
Publication in the conference proceedings of EUSIPCO, Tampere, Finland, 2000
ISPA 2001. Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis. In conjunction with 23rd International Conference on Information Technology Interfaces (IEEE Cat. No.01EX480)
After recent advances in coding of natural speech and audio signals, also the synthetic creation ... more After recent advances in coding of natural speech and audio signals, also the synthetic creation of musical sounds is gaining importance. Various methods for waveform synthesis are currently used in digital instruments and software synthesizers. A family of new synthesis methods is based on physical models of vibrating structures (string, drum, etc.) rather than on descriptions of the resulting waveforms. This article describes various approaches to digital sound synthesis in general and discusses physical modelling methods in particular: Physical models in the form of partial differential equations are presented. Then it is shown, how to derive discrete-time models which are suitable for real-time DSP implementation. Applications to computer music are given as examples.
ICC 2020 - 2020 IEEE International Conference on Communications (ICC), 2020
The derivation of suitable analytical models is an important step for the design and analysis of ... more The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications (e.g., assumption of an unbounded environment). In this paper, we develop a realistic model for particle diffusion in a bounded sphere and particle transport through a semi-permeable boundary. This model can be used for various applications, such as modeling of inter-/intra-cell communication or the release process of drug carriers. The proposed analytical model is based on a transfer function approach, which allows for fast numerical evaluation and provides insights into the impact of the relevant molecular communication system parameters. The proposed solution of the bounded spherical diffusion problem is formulated in terms of a state-space description and the semi-permeable boundary is accounted for by a feedback loop. Particle-based simulations verify the proposed modeling approach.
2002 11th European Signal Processing Conference, 2002
This paper presents a multidimensional state-space approach for the numerical simulation of sound... more This paper presents a multidimensional state-space approach for the numerical simulation of sound propagation in enclosures. The simulation algorithm is essentially based on the wave digital filter principle however we will give a more direct access to the numerical solution of the wave equation here. To simulate sound propagation in enclosures, a detailed treatment of the boundary conditions is necessary. We focus in this paper on the treatment of memoryless boundary conditions in the new simulation algorithm.
2007 15th European Signal Processing Conference, 2007
For the simulation of multi-dimensional systems, currently so called block based methods are unde... more For the simulation of multi-dimensional systems, currently so called block based methods are under investigation. A physical model is split into a number of blocks, each corresponding to a specific spatial region, which are modeled and realized separately. The correct interaction of these blocks is guaranteed by interaction laws, which can be derived from the assumption of a global model. In doing so, this paper presents an application of mixed modeling strategies for the 2D wave equation, where different blocks are realized with different methods. On the one hand the Finite Difference Time Domain (FDTD) approach can model arbitrary geometries, but suffers from numerical dispersion. The Functional Transformation Method (FTM) on the other hand, is completely free of numerical dispersion, but is restricted to simple geometries. Via a combination of both methods, it is possible to model arbitrary geometries, while large parts of the modeling region are realized free of dispersion with ...
Proceedings of the 1999 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics. WASPAA'99 (Cat. No.99TH8452)
Various methods for sound synthesis based on physical models have been presented. They start from... more Various methods for sound synthesis based on physical models have been presented. They start from a continuous model for the vibrating body, given by partial differential equations (PDEs), and employ proper discretization in time and space. Examples are wave guide models or finite difference models. A different approach is presented here. It is based on a multidimensional transfer function model derived by suitable functional transformations in time and space. Physical effects modeled by the PDE like longitudinal and transversal oscillations, loss and dispersion are treated with this method in an exact fashion. Moreover, the transfer function models explicitely take initial and boundary conditions, as well as excitation functions into account. The discretization based on analog-to-discrete transformations preserves not only the inherent physical stability, but also the natural frequencies of the oscillating body. The resulting algorithms are suitable for real-time implementation on digital signal processors. This paper shows the new method on the linear example of a transversal oscillating tightened string with frequency dependent loss terms.
The Functional Transformation Method (FTM) is a recently introduced method for sound synthesis by... more 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 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.
Block based physical modeling requires to provide a library of modeling blocks for standard compo... more 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.
2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221), 2001
Multidimensional (MD) physical systems are usually given in terms of partial differential equatio... more Multidimensional (MD) physical systems are usually given in terms of partial differential equations (PDEs). Similar to one-dimensional systems, they can also be described by transfer function models (TFMs). In addition to including initial and boundary conditions as well as excitation functions exactly, the TFM can also be discretized in a simple way. This leads to suitable implementations for digital signal processors. Therefore it is possible to implement physics based digital sound synthesis algorithms derived from TFMs in real-time. This paper extends the recently presented solution for vibrating strings with one spatial dimension to two-dimensional drum models.
IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 2005.
An application of block-based physical modeling for the simulation of room acoustics with the Fun... more An application of block-based physical modeling for the simulation of room acoustics with the Functional Transformation Method (FTM) is presented in this paper. In doing so, an analytic solution of the two-dimensional wave equation for rectangular regions achieved with the FTM is employed as a simple block element of the entire model. Due to a recently introduced approach to block-based modeling, it is possible to apply arbitrary boundary conditions for this block, including the connection to other blocks and the simulation of openings. By the connection of several block elements, it is possible to construct and simulate complex regions with complex boundaries. In result a new wave field simulation technique is achieved, that avoids the disadvantages of the FTM, the restriction to simple regions, while preserving its advantages like dispersion-free simulation and exact source and receiver positioning.
International Journal of Applied Mathematics and Computer Science, 2008
Block-Based Physical Modeling with Applications in Musical AcousticsBlock-based physical modeling... more Block-Based Physical Modeling with Applications in Musical AcousticsBlock-based physical modeling is a methodology for modeling physical systems with different subsystems. Each subsystem may be modeled according to a different paradigm. Connecting systems of diverse nature in the discrete-time domain requires a unified interconnection strategy. Such a strategy is provided by the well-known wave digital principle, which had been introduced initially for the design of digital filters. It serves as a starting point for the more general idea of block-based physical modeling, where arbitrary discrete-time state space representations can communicate via wave variables. An example in musical acoustics shows the application of block-based modeling to multidimensional physical systems.
International Journal of Applied Mathematics and Computer Science
Continuous multidimensional systems described by partial differential equations can be represente... more Continuous multidimensional systems described by partial differential equations can be represented by discrete systems in a number of ways. However, the relations between the various forms of continuous, semi-continuous, and discrete multidimensional systems do not fit into an established framework like in the case of one-dimensional systems. This paper contributes to the development of such a framework in the case of multidimensional systems. First, different forms of partial differential equations of physics-based systems are presented. Secondly, it is shown how the different forms of continuous multidimensional systems lead to certain discrete models in current use (finite-difference models, multidimensional wave digital filters, transfer function models). The links between these discrete models are established on the basis of the respective continuous descriptions. The presentation is based on three examples of physical systems (heat flow, transmission of electrical signals, acoustic wave propagation).
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Papers by Rudolf Rabenstein