Rudolf Rabenstein

• Prof. Dr.-Ing. habil.
• Professor at Friedrich-Alexander-University Erlangen-Nürnberg

The image-source method is widely applied to compute room impulse responses (RIRs) of shoebox rooms with arbitrary damping. However, with increasing RIR lengths, the number of image sources grows rapidly, leading to slow computation. We propose a method to estimate the damping density of a damped shoebox room, which in turn can provide the energy d...

This book covers the theory of multidimensional signals and systems and related practical aspects. It extends the properties and mathematical tools of one-dimensional signals and systems to multiple dimensions and covers relevant timeless topics including multidimensional transformations, multidimensional sampling as well as discrete multidimension...

This chapter builds upon established knowledge on one-dimensional signals and extends it to multiple dimensions. Indeed, many operations on multidimensional signals are similar to the one-dimensional case but there are new aspects and new possibilities. The presentation focusses on two-dimensional signals but the extension to three or more dimensio...

Signals are functions or sequences of numbers which represent information. They show the variation of physical or abstract quantities in dependence on one or more independent variables, like time, space, frequency, or others. This chapter serves as a first introduction to the rich world of different kinds of multidimensional signals. It gives an ov...

This chapter provides a short introduction to selected elements of one-dimensional signals and systems. It serves to provide a foundation for reference in the following chapters. No complete coverage is intended since readers are assumed to have some previous knowledge on signals and systems. Instead, emphasis is placed on signal spaces and signal...

Hilbert spaces of square-integrable functions or square-summable sequences provide a mathematically rigorous framework for many engineering calculations including signal processing. They possess well-structured mathematical properties of highly practical relevance. However, signals and systems deal also with signals which are not square-integrable...

Sampling in two dimensions provides far more possibilities to choose the sampling points than in one dimension. The presentation starts with rectangular sampling and proceeds to general sampling grids based on lattice theory. Then aliasing in two dimensions is investigated before some frequently used sampling lattices are discussed.

This chapter takes a turn into the discrete world. While continuous multidimensional systems are and will be of practical importance, their modelling and simulation is accomplished by digital means. Therefore the description of continuous multidimensional systems is at first cast into a state space representation. Then the continuous-time represent...

This chapter revisits the topic of multidimensional transformations and applies it to initial-boundary-value problems. Some basic notions are first discussed by an introductory example. Then the spatial differentiation operators involved in initial-boundary-value problems are investigated further as a prerequisite to the introduction of a suitable...

The Sturm-Liouville transformation for initial-boundary-value problems requires the solution of eigenvalue problems for the involved spatial differentiation operators. The key problem, the calculation of a matrix exponential, is discussed in detail for problems with one space variable. The presented method is extended to problems with two or three...

Linear discrete multidimensional systems are classified in the same way as one-dimensional systems: there are finite impulse response systems (FIR-systems) and infinite impulse response systems (IIR-systems). FIR-systems are widely applied in image processing and in processing of sampled volume data. IIR-systems in multiple dimensions are more comp...

Multidimensional systems with continuous variables result from the description of natural or technical systems by differential equations. Whenever not only the time evolution but also the spatial extension has to be considered, then the mathematical description comprises partial derivatives with respect to time and also partial derivatives with res...

This chapter presents examples of two- and three-dimensional transformations which are extensions of their 1D counterparts. At first, the two-dimensional Fourier transformation in Cartesian coordinates is introduced and its properties are derived by affine mappings. Then follows the Fourier transformation in polar coordinates, Hankel and Radon tran...

Molecular communications is a promising framework for the design of controlled-release drug delivery systems. Under this framework, drug carriers, diseased cells, and the channel in between are modeled as transmitters, absorbing receivers, and diffusive channel, respectively. However, existing works on drug delivery systems consider only simple dru...

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or partial differential equations, using established techniques. Recent work has applied the techniques of machine-lea...

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or partial differential equations, using established techniques. Recent work has applied the techniques of machine-lea...

Kurzfassung Mit Hilfe von im kontinuierlichen oder im diskreten Zeitbereich formulierten Systemmodellen können Gleich-stromnetze nachgebildet werden, um die Auswirkungen von Ereignissen im Normalbetrieb und von Fehlersitua-tionen auf die Signale an den Strom-und Spannungsmessstellen abzuschätzen. Dabei kann durch Integration von spezifischen Fehler...

For the purpose of refined fault detection in DC grids, linear models of components, cabling and possible faults can be applied in order to model the first milliseconds after a possible sudden event. Using a semi-analytical model, a factorial analysis of signals at voltage and current sensors is set up – specific signal patterns representing either...

Molecular communications is a promising framework for the design of controlled-release drug delivery systems. Under this framework, drug carriers, diseased cells, and the channel in between are modeled as transmitters, absorbing receivers, and diffusive channel, respectively. However, existing works on drug delivery systems consider only simple dru...

The analysis and design of advection-diffusion based molecular communication (MC) systems in cylindrical environments is of particular interest for applications such as micro-fluidics and targeted drug delivery in blood vessels. Therefore, the accurate modeling of the corresponding MC channel is of high importance. The propagation of particles in t...

Physical accuracy of virtual acoustics receives increasing attention due to renewed interest in virtual and augmented reality applications. So far, the modeling of vibrating objects as point sources is a common simplification which neglects effects caused by their spatial extent. In this contribution, we propose a technique for the interconnection...

The analysis and design of advection-diffusion based molecular communication (MC) systems in cylindrical environments is of particular interest for applications such as micro-fluidics and targeted drug delivery in blood vessels. Therefore, the accurate modeling of the corresponding MC channel is of high importance. The propagation of particles in t...

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 diff...

The attachment of feedback loops to physical or musical systems enables a large variety of possibilities for the modification of the system behavior. Feedback loops may enrich the echo density of feedback delay networks (FDN), or enable the realization of complex boundary conditions in physical simulation models for sound synthesis. Inspired by con...

The behavior of a distributed parameter system can be represented by an expansion into eigenfunctions. It allows to calculate the output signal in dependence on the parameters of the system. This contribution considers the inverse problem: Estimate the system parameters from noisy measurements of the output. To this end, an eigenfunction expansion...

A specific refinement of fault detection in LVDCmicrogrids requires model-based knowledge about the system due to possible variations in topology, component parameters and line lengths. In order to gain this information, passive system identification methods based on current and voltage measurement data are applied. Further using machine learning t...

Physical modeling leads to efficient and scalable simulation algorithms in the discrete time domain, which are used in real-time music applications. Many percussive instruments are physically described by Kirchhoff’s thin plate equation. Considering a complete system, e.g. the single plates of a xylophone, the oscillation behavior can be describe...

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-t...

Modern DC distribution grids and DC systems of renewable energy production require more elaborated safety concepts than AC applications. Due to the stability of DC arcs for system voltages above 20V, a short fault detection time is essential for circuit protection devices. In many applications, the implementation of overcurrent and overvoltage prot...

Kurzfassung Klein-und Niederspannungsgleichstromnetze erfordern Schutzkonzepte, die gezielt für die jeweilige Applikation und Systemspannung ausgelegt sind. Mit Hilfe von Methoden der Systemidentifikation und des maschinellen Lernens kann dabei eine Identifikation und Zuordnung von Fehlerereignissen verfeinert werden. Nichtrekursive und rekursive G...

Specific system protection is needed for direct current microgrids in the low voltage range. Model-based analysis of transient events applying system identification and machine learning procedures provides additional knowledge on system topology and components. Using this information, refined model-based fault detection and discrimination methodolo...

Direct current microgrids in the low voltage range require specific system protection. In addition to the basic functionality of conventional protective devices, a refined and model-based analysis of measured current and voltage signals is necessary. Signal processing, system identification and machine learning methods are helpful to identify, clas...

Low end extra low voltage direct current grids require selective fault protection designed for the specific application and system voltage. System identification and machine learning methods are helpful to identify, to localize and to classify occurring fault events. A category of non-recursive large-signal methods in the time domain for system ide...

Fault detection in DC grids requires new concepts for the design of protection devices. A promising concept for predictive circuit protection is model based learning, e.g. Kalman estimation. It requires detailed system models of electrical circuits. An established modeling technique in circuit theory is the wave digital principle which preserves ci...

This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the sa...

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-t...

This script is intended as supplementary material for the manuscript ”Approximation of Enzyme Kinetics For High Enzyme Concentarion by a First Order Perturbation Approach” by Sebastian Kram, Maximilian Schäfer and Rudolf Rabenstein. submitted to the Journal of Mathematical Chemistry, Springer International Publishing AG.

A transfer function description is derived for a general class of linear distributed parameter systems dependent on time and one spatial variable. Suitable functional transformations are the Laplace transformation for the time variable and the Sturm-Liouville transformation for the space variable. A practical problem is the determination of the eig...

The rich literature on acoustic source localization mostly relies on the assumption of a constant value for the speed of sound. This hypothesis allows establishing simple relations between range differences and time differences and leads to effective estimation algorithms. However, it must be challenged for certain applications of wireless acoustic...

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 d...

Various fault scenarios have been analyzed by running a number of differently combined 380 VDC microgrid tests.These tests represented a common grid topology with low systemimpedance at grid resonance points within the single- or lowerdouble-digit kHz range. At serial arc faults, self-excited resonantmodes of the arc plasma column have been observe...

Measurements of the input impedance of electrical transmission lines indicate a frequency dependency of the line parameters. This behavior can be simulated by adjustments to a suitable transfer function model for frequency independent parameters. To this end, functional transformations in time and space set up a transfer function model as a decompo...

Keynote presentation at the International Workshop on Acoustic Signal Enhancement (IWAENC) in Xi’an, China, September 2016

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....

The analysis of the quantization error in fixed-point arithmetic is usually based on simplifying assumptions. The quantization error is modelled as a random variable which is independent of the quantized variable. This contribution investigates the wordlength reduction of a digital multiplier in greater detail. The power spectrum of the quantizatio...

DC grids of system voltages above 20V demand different safety concepts compared to conventional AC grids. More elaborate protection devices have to be developed to detectnot only high-power, but also low-power faults. The discrimination between faults and load variations can be supported by model-based machine learning methods. For this purpose,thi...

Molecular communication channels transmit information by the release and detection of chemical substances. Single information bits can be encoded as individual releases of certain amounts of molecules. Intersymbol interference between successive releases can be minimized by enforcing a decay of the substrate concentration through enzyme reactions....

This paper introduces a method for localizing reflectors in one dominant direction of a three-dimensional acoustic enclosure. The method is based on the response of the acoustic environment to an acoustic excitation. Only a single sound source and a single microphone are required. A two-step algorithm is proposed. In the first step, the distance be...

The propagating speed of waves depends on the physical properties of the transmitting material. Since these properties can vary along the propagation path, they cannot be determined from local measurements. However, mean values of the propagation speed can be obtained from time measurements, either between distributed sources and sensors (Time Of A...

Transmission electron microscopes (TEMs) are the tools of choice in materials science, semiconductor, and biological research and it is expected that they will be increasingly used to autonomously perform high-volume, repetitive, nano-measurements in ...

Acoustic source localization using microphone arrays is often based on the Time Difference of Arrivals (TDOA). The estimation of Time Differences of Arrivals (TDOAs) relies on the detection of the peak in suitable cross-correlations between microphone signals. Unfortunately, in real environments a number of spurious peaks occur in the cross-correla...

The article: "New Entries to the SPL EDICS for Audio and Acoustic Signal Processing," by Christensen and Rabenstein et al. (DOI: 10.1109/LSP.2013.2271353) will not be published in an upcoming issue of the Signal Processing Letters as it was previously published under the DOI: 10.1109/LSP.2012.2224516 in the December 2012 issue of Signal Processing...

This letter describes some of the new entries to the Signal Processing Letters (SPL) Editor's Information Classification Scheme (EDICS) for the topic Audio and Acoustic Signal Processing.

Spatially distributed acoustic sensors find increasingly many new applications in speech-based humanmachine interfaces. One well researched topic is the localization of sound sources from Time Differences Of Arrival (TDOAs) measurements. Typically, the propagation speed of sound is considered a known constant. However due to temperature variations...

Solitons are special solutions of certain nonlinear partial differen-tial 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 litera-ture but few clo...

Implicit schemes are a popular approach to the discretization of linear partial differential equations by finite differences. They require to solve a set of linear equations in each time step. Since finite difference discretizations lead to a local coupling, these systems of equations are sparse and can be effectively solved by iterative methods. N...

Geometric inference is an approach for localizing reflectors in a closed acoustic space. It is based on a simple observation that turns time differences of arrival (TDOA) or time of arrival (TOA) measurements from the signals of a microphone array into a geometric constraint. The reflector localization methodology relies on accurate TDOA which is d...

Spatially distributed acoustic sensors find increasingly new ap-plications in speech-based human-machine interfaces. One well researched topic is the localisation of an emitting source from Time-Difference-Of-Arrival (TDOA) measurements. This manuscript shows how to exploit the source localization framework and its state of the art techniques to ac...

Available methods for room-related sound presentation are introduced and evaluated. A focus is put on the synthesis side rather than on complete transmission systems. Different methods compared using common, though quite general criteria. The methods selected for comparison are: INTENSITY STERLOPHONY after Blumlein, vector-base amplitude panning (V...

The application of the Functional Transformation Method (FTM) for the simulation of acoustical wave fields has been recently extended to complex room geometries by the usage of so called "block-based" modeling techniques. The complete model is split into several elementary blocks with simple geometry, which are solved separately with the FTM and re...

In this paper we propose a method for the estimation of the propagation speed of sound waves from Time Of Arrivals (TOAs) observed at a sensor array. In our previous work we presented a speed estimation method based on Time Differences of Arrival (TDOAs), here we show that the same approach may be applied successfully to the TOA-based problem. The...

SCENIC is an EC-funded project aimed at developing a harmonized corpus of methodologies for environmentaware acoustic sensing and rendering. The project focusses on space-time acoustic processing solutions that do not just accommodate the environment in the modeling process but that make the environment help towards achieving the goal at hand. The...

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 prese...

Recent applications of iterative learning control and repetitive processes lead to implicit second order finite difference schemes which require practical stability testing. A von Neumann type stability analysis is employed to reduce the problem to a second order polynomial. The conditions under which its zeros lie within the unit circle can be rec...

Spatial sound rendering techniques are based on established theoretical frameworks. The theoretical wave field predicted by the underlying of a specific rendering technique is an ap-proximation of the desired ideal wave field. Moreover the practical implementations require often compromises which cause an additional deviation of the rendered wave f...

The SCENIC project is aimed at making the environment become an integral part of the acoustic system. The goal is to boost the performance of arrays of speakers and microphones and, in some cases, to enable applications that would not be possible otherwise. This paper describes how this can be achieved.

In this paper we propose a novel technique to localize planar obstacles through the measurement of the Direction of Arrival by a microphone array. The measurement of the Direction of Arrival of the reflected path is turned into a quadratic constraint where the unknowns are the line parameters of the reflector. A cost function that combines multiple...

In this paper we propose a methodology for assessing the accuracy of techniques of wave field rendering through loudspeaker arrays. In order to measure the rendered wave field we adopt a solution based on a circular harmonic analysis of the sound field captured by a virtual microphone array. As a result of this analysis stage, we are able to compar...

The two main approaches for the description of sound fields are methods derived from solutions of the wave equation and geometric methods based on analogies to ray optics. Their mathematical representations are reviewed and it is shown that representations by projective geometry and descriptions by Fourier acoustics lead to similar para-metric repr...

In the context of acoustic source localization, knowing the actual propagation speed is crucial especially in uncontrolled environments where the temperature is subject to significant changes that influence the sound speed. In a recent paper we showed the effects of the assumed propagation speed on the localization performance of two closed-form lo...

Time-differences-of-arrival measurements play a relevant role in localizing and tracking of acoustic sources. Though a huge literature has been devoted to this topic the influence of the propagation speed on the localization accuracy has been largely disregarded. The sound speed is usually supposed to be exactly known, but actually this information...

Wave field analysis of stationary sound fields can be performed with high spatial resolution when sequential measurements on a circle are employed. Applying a circular harmonics decomposition to wideband audio data requires a careful setup of the measurement process to avoid noise amplification at certain frequencies. To this end, measurements with...

Pre-equalization of MIMO systems is required for a wide variety of applications, e. g. in channel equalization and spatial sound repro-duction. However, traditional adaptive algorithms fail for channel numbers of some ten or more. It is shown that the problem becomes tractable by decoupling of the MIMO adaptation problem, e. g. by a generalized sin...

Wave Field Synthesis is a technique for spatial sound reproduction that overcomes the limitations of classical stereophonic techniques. A thorough analysis of acoustic wave propagation prinicples delivers the technical description in terms of loudspeaker array technology. Suitable signal processing methods convert the source signals into driving si...

Implicit schemes are a popular approach to the discretization of linear partial differential equations by finite differences. They require to solve a linear set of equations in each time step. Since finite difference discretizations lead to a local coupling, these systems of equations are sparse and can be effectively solved by iterative procedures...

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 typ- ical physical modeling problems. In this paper it will be shown, that it is possible to u...

Multidimensional wave digital yield robust algorithms for the computer simulation of certain distributed parameter systems described by par-tial diierential equations. Here, a multidimen-sional wave digital algorithm for the space-time discretization of the physical laws of acou-stics is discussed. Its implementation by state equations is presented...

Processing of one-dimensional signals for all kinds of appli-cations is based on the mature theory of signals and systems. On the other hand, processing methods for acoustical signals have been developed in quite diverse application fields like seismic engineering, sonar, audio engineering, and commu-nication acoustics. Similar techniques and algor...

This contribution describes an implementation of near fieldcoding higher order Ambisonics on an existing circular array of 48 loudspeakers. Static and moving source s can be reproduced with a variable Ambisonics order and variable number of loudspeakers. Informal listening testswere performed to evaluate the influence of Ambisonics order and loudsp...

This contribution combines techniques for sound synthesis and spatial reproduction for a joint synthesis of the sound prod uction and sound propagation properties of virtual string instruments. The generated sound field is reproduced on a massive multichanne l loudspeaker system using wave field synthesis techniques. F rom physical descriptions of...

Block-based physical modeling is a recently introduced method for digital sound synthesis via the simulation of physical models. The method follows a "divide-and-conquer" approach, where the elements are individu- ally modeled and discretized, while their interaction topology is separately implemented. In this paper the application of this approach...

Block-Based Physical Modeling with Applications in Musical Acoustics 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. Su...

A variety of methods for physical modeling sound synthesis has been developed so far, mostly for single sound objects like strings, plates, etc. However, complex virtual musical instruments require not only advanced models but also methods for combining one or more sound objects with excitation mechanisms and resonating structures. This presentatio...

This paper demonstrates the analysis of complex acoustic environments using high-resolution circular measurements and complementary 3D simulations. The possibilities and limitations of room acoustic analysis using either measurements or simulations are discussed. An exemplary study is presented on the sound propagation in a complex shaped room: The...

The digital synthesis of musical sounds is a field with many applications in digital audio, computer music, and virtual environments. One family of sound synthesis methods is physical modeling, which is based on digital implementations of vibrating bodies. The physical model is expressed by partial differential equations which describe the dynamic...

Wave field synthesis is a spatial sound field reproduction technique aiming at authentic reproduction of auditory scenes. Its theoretical foundation has been developed almost 20 years ago and has been improved considerably since then. Most of the original work on wave field synthesis is restricted to the reproduction in a planar listening area usin...

The sound quality for acoustical communication, information, and entertainment is often subject to impairments by room reflections and undesired noise sources. As a remedy, various signal processing techniques have been developed for different applications, like acoustic echo cancelation and active noise control. Starting from the single channel ca...

Multichannel sound field reproduction aims at the physically correct synthesis of acoustical wave fields with a large number of loudspeakers. It goes beyond stereophony by extending or eliminating the so-called sweet spot. This chapter presents the physical and mathematical description of various methods for this purpose and presents the physical...

The acoustic theory for multichannel sound reproduction systems usually assumes free-field conditions for the listening environment. However, their performance in real-world listening environments may be impaired by reflections at the walls. This impairment can be reduced by suitable compensation measures. For systems with many channels, active com...

The stability of two-step repetitive processes will be considered. We assume signals depending on two spatial variables and the pass-number. In all cases of interest the pass lengths will be finite. Since all known approaches to the stability problem do not take this fact into account, the resulting statements concerning stability are of little hel...

Almost everybody uses sound synthesis in their daily lives, although many may not know it.

Block-based physical modeling is a methodology for modeling physical systems with different subsystems. It is an important concept for the physical modeling of real or virtual musical instruments where different components may be modeled according to different paradigms. Connecting systems of diverse nature in the discrete-time domain requires a co...

Still, music synthesizers and related equipment, such as digital pianos, are popular, and they are continuously culti- vated. Old sound synthesis technology does not disappear but is brought back to life with the help of new signal process- ing: take, for example, virtual analog syn- thesis, a methodology that emulates the oscillators and filters o...

Dieses Lehrbuch bietet eine leicht zugängliche Einführung in die Systemtheorie für Studierende der Elektrotechnik, Elektronik, Informationstechnik und verwandter Gebiete. Es legt die Grundlagen für das Studium anwendungsorientierter Fächer wie Multimediakommunikation, Nachrichtenübertragung und Signalverarbeitung. Der Schwerpunkt liegt auf der Verm...