Techniques are described for reducing complexity in stringed instrument simulation for purposes of digital synthesis. These include commuting losses and dispersion to consolidate them into a single lter, replacing body resonators by look-up tables, simplied bow-string interaction, and single-lter, multiply-free coupled strings implementation. Contents 1 Digital Waveguide Theory 2 2 The Terminated String 4 3 Simplied Body Filters 5 4 Simplied Bowed Strings 8 5 Coupled Strings 10 6 Summary 14 7 Appendix 14 1 Page 2 1 Digital Waveguide Theory This section summarizes the digital waveguide model for vibrating strings. Further details can be found in [Smith 1992]. Position y (t,x) 0 x . . . . . . 0 K String Tension e = Mass/Length Figure 1: The ideal vibrating string. The wave equation for the ideal (lossless, linear, exible) vibrating string, depicted in Fig. 1, is given by Ky 00 = y where K = string tension y = y(t; x) = linear mass density _ y...

This paper discusses the analysis of large linear electrical networks consisting of passive components, such as resistors, capacitors, inductors, and trans-formers. Such networks admit a symmetric formula-tion of their circuit equations. We introduce SyPVL, an eficient and numerically stable algorithm for the computation of reduced-order models of large, linear, passive networks. SyPVL represents the specializa-tion of the more general PVL algorithm, to symmetric problems. Besides the gain in eficiency over PVL, SyPVL also preserves the symmetry of the problem, and, as a consequence, can often guarantee the sta-bility of the resulting reduced-order models. Moreover, these reduced-order models can be synthesized as actual physical circuits, thus facilitating compatibility with existing analysis tools. The application of SyPVL is illustrated with two interconnect-analysis examples. 1

Increases in delay due to coupling can have a dramatic impact on IC performance for deep submicron technologies. To achieve maximum performance there is a need for analyzing logic stages with large complex coupled interconnects. In timing analysis, the worst-case delay of gates along a critical path must include the effect of noise due to switching of nearby aggressor gates. In this paper, we propose a new waveform iteration strategy to compute the delay in the presence of coupling and to align aggressor inputs to determine the worst-case victim delay. We demonstrate the application of our methodology at both the transistor-level and celllevel. In addition, we prove that the waveforms generated in our methodology converge under typical timing analysis conditions. 1.

We present methods for velocity estimation from discrete and quantized position samples using adaptive windowing. Previous methods necessitate tradeoffs between noise reduction, control delay, estimate accuracy, reliability, computational load, transient preservation, and difficulties with tuning. In contrast, a first-order adaptive windowing method is shown to be optimal in the sense that it minimizes the velocity error variance while maximizes the accuracy of the estimates, requiring no tradeoff. Variants of this method are also discussed. The effectiveness of the proposed technique is verified in simulation and by experiments on the control of a haptic device.

An eigenvalue-based characterization of positive realness of transfer functions of singleinput single-output time-invariant linear systems is derived. Based on this characterization, we propose efficient computational procedures to determine if a given transfer function is positive real. The input for these eigenvalue-based tests is any given, not necessarily minimal, state-space representation of the linear system. Furthermore, the tests only involve standard matrix computations, such as computing eigenvalues of a matrix or a matrix pencil. Results of numerical experiments with these eigenvalue-based tests for positive realness are reported. Key words: linear system, state-space representation, transfer function, passivity, positive realness 1 Introduction Passivity is an important concept in control and circuit theory. Roughly speaking, a (linear or nonlinear) system is strictly passive if it "consumes" energy, and it is passive if it does not "deliver" energy. The concept was firs...

The classical Lanczos process can be used to efficiently generate Pad'e approximants of the transfer function of a given single-input single-output time-invariant linear dynamical system. Unfortunately, in general, the resulting reduced-order models based on Pad'e approximation do not preserve the stability, and possibly passivity, of the original linear dynamical system. In this paper, we describe the use of partial Pad'e approximation for reduced-order modeling. Partial Pad'e approximants have a number of prescribed poles and zeros, while the remaining degrees of freedom are used to match the Taylor expansion of the original transfer function in as many leading coefficients as possible. We present an algorithm for computing partial Pad'e approximants via suitable rank-1 updates of the tridiagonal matrices generated by the Lanczos process. Numerical results for two circuit examples are reported. Key words: Lanczos algorithm; Linear dynamical system; Transfer function; Stability; Passi...

Abstract-An iterative procedure is presented which permits the determination of a rational transfer function in the Laplace trans-form variable s which is optimal with respect to given input and output time-functions. The optimal system of a particular order is defined as the one whose output when subjected to the known input function is nearest in the time integral square sense to the desired output function. The method is thus applicable to a number of problems involving the minimization of an integral square error. To illustrate the technique, a set of optimal lumped-parameter delay lines is synthesized and their characteristics investigated; the behavior and convergence of the iteration in these problems is also studied. A comparison of other iterative methods applicable to the same problems leads to the conclusion that the proposed procedure has real advantages in computational simplicity and speed of conver-

In this paper, we present new methods for velocity estimation from discrete and quantized position samples. The proposed methods are based on adaptive windowing and address the shortcomings of the previous methods which necessitate tradeoffs between noise reduction, control delay, estimate accuracy, reliability, computational load, transient preservation, and difficulties with tuning. In particular, first order adaptive windowing method is shown to be optimal in the sense that it minimizes the velocity error variance while maximizes the accuracy of the estimates. The effectiveness of the proposed techniques are verified by simulation results and also by experimental results in the control of a haptic interface. 1 Introduction Numerous control systems require on-line velocity estimation from discrete-time position signal. Examples include velocity control of manipulators [3], [14], visual servoing [7], implementation of stiff virtual walls for force reflecting interfaces [4], and mos...

Contents 1 Introduction 2 2 Positive Real Functions 2 2.1 Relation to Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Relation to Schur Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Relation to functions positive real in the right-half plane . . . . . . . . . . . . . . . . . . . . . 6 2.4 Special cases and examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.1 Minimum Phase (MP) polynomials in z . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Conjectured Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Introduction to Digital Filter Theory 9 3.1 Linearity and Time-Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Dierence Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.1 Convolution Representation . . . . . . . . . ....

An amplifier has been designed for optimal use of position sensitive thermal neutron detectors using the principle of resistive charge division. The important points in this optimization are: high counting rates and good spatial resolution. This amplifier is built as a hybrid circuit and is now used on several new instruments at the ILL. It consists of a fast low noise current pre-amplifier, a gaussian shaping circuit based on a 4th order active filter and an essentially noiseless baseline reconstruction. In this paper, we present a rather complete theoretical analysis of the problem that lead us to the choices made above, and allows for an optimal adaptation to other situations. An analysis of unwanted, secondary effects is also worked out. 1 Introduction. The original motivation for the design of this electronics was given by a project called SANS-2MHZ, in the framework of the Millennium program at the Institut