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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...

An extremely efficient method for modeling wave propagation in a membrane is provided by the multidimensional extension of the digital waveguide. The 2-D digital waveguide mesh is constructed out of bidirectional delay units and scattering junctions. We show that it coincides with the standard finite difference approximation scheme for the 2-D wave equation, and we derive the dispersion error. Applications may be found in physical models of drums, soundboards, cymbals, gongs, small-box reverberators, and other acoustic constructs where a one-dimensional model is less desirable. 1 Background Theory There are many musical applications of the onedimensional digital waveguide ranging from the generation of wind and string instrument tones, to flanging effects [Van Duyne and Smith, 1992], to reverberation [Smith, 1987]. We review the theoretical derivation of one-dimensional traveling waves as a basis for development of the twodimensional digital waveguide mesh. 1.1 The 1-D Wave Equation...

Abstract—The spatialization of the sound field in a room is studied, in particular the evolution of room impulse responses as a function of their spatial positions. It was observed that the multidimensional spectrum of the solution of the wave equation has an almost bandlimited character. Therefore, sampling and interpolation can easily be applied using signals on an array. The decay of the spectrum is studied on both temporal and spatial frequency axes. The influence of the decay on the performance of the interpolation is analyzed. Based on the support of the spectrum, the number and the spacing between the microphones is determined for the reconstruction of the sound pressure field up to a certain temporal frequency and with a certain reconstruction quality. The optimal sampling pattern for the microphone positions is given for the linear, planar and three-dimensional case. Existing techniques usually make use of room models to recreate the sound field present at some point in the space. The presented technique simply starts from the measurements of the sound pressure field in a finite number of positions and with this information the sound pressure field can be recreated at any spatial position. Finally, simulations and experimental results are presented and compared with the theory. Index Terms—Interpolation, plenoptic function, room impulse response, sampling, sound pressure field sampling. I.

Sonification is the use of non-speech audio to convey information. We are developing tools for interactive data exploration, which make use of sonification for data presentation. In this paper, model-based sonification is presented as a concept to design auditory displays. Two designs are described: (1) particle trajectories in a "data potential" is a sonification model to reveal information about the clustering of vectorial data and (2) "data-sonograms" is a sonification for data from a classification problem to reveal information about the mixing of distinct classes.

this paper, many of the saxophone mouthpiece facing designs prevalent in the 1920's were such that the reed frequency could not be raised much above the playing frequency of notes in the top of the second register. The notes written at about D6 could be achieved as reed regimes, but it was not possible to play many notes in the third register of the instrument. It was also not possible to play the second register without opening the register hole, because the reed frequency was too low to add energy to the oscillation at a higher component. More recent mouthpiece facing designs have allowed the reed frequency to be raised to a range analogous to that of the clarinet so that the third register is possible and the second register can be played without the register hole (Thompson, 1979). Given the fact that Adolphe Sax demonstrated a three octave range on the saxophone in the 1840's (Rascher, 1970), the validity of this example is unlikely. Further, this author has performed on saxophone mouthpieces (and instruments) from the 1920's and has never had difficulty achieving a range of at least three and a half octaves. Performers of reed woodwinds are typically affected by instrument response problems when they CHAPTER 2. ACOUSTICAL ASPECTS OF WOODWIND DESIGN & PERFORMANCE 87 travel to locations of significant elevation difference from their normal place of practice. By considering the reed's role as a pressure-dependent air valve, it is reasonable to expect variations in reed response between different elevations. At high elevations, the ambient air pressure is lower. Thus, the pressure variations within the air column will oscillate about a lower ambient pressure value. Because the reed functions properly for a particular range of pressure differences across it and becaus...

In this paper, a nonlinear discrete-time model that simulates a vibrating string exhibiting tension modulation nonlinearity is developed. The tension modulation phenomenon is caused by string elongation during transversal vibration. Fundamental frequency variation and coupling of harmonic modes are among the perceptually most important effects of this nonlinearity. The proposed model extends the linear bidirectional digital waveguide model of a string. It is also formulated as a computationally more efficient single-delay-loop structure. A method of reducing the computational load of the string elongation approximation is described, and a technique of obtaining the tension modulation parameter from recorded plucked string instrument tones is presented. The performance of the model is demonstrated with analysis /synthesis experiments and with examples of synthetic tones available at http://www.acoustics.hut.fi/~ttolonen/tmstr_SAP/. Index Terms---Acoustic signal processing, modeling, mu...

This paper presents a method for relocation of a mobile robot using sonar data. The process of determining the pose of a mobile robot with respect to a global reference frame in situations where no a priori estimate of the robot's location is available is cast as a problem of searching for correspondences between measurements and an a priori map of the environment. A physically-based sonar sensor model is used to characterize the geometric constraints provided by echolocation measurements of different types of objects. Individual range returns are used as data features in a constraint-based search to determine the robot's position. A hypothesize and test technique is employed in which positions of the robot are calculated from all possible combinations of two range returns that satisfy the measurement model. The algorithm determines the positions which provide the best match between the range returns and the environment model. The performance of the approach is demonstrated using data from both a single scanning Polaroid sonar and from a ring of Polaroid sonar sensors.

This thesis proposes banded waveguide synthesis as an approach to real-time sound synthesis based on the underlying physics. So far three main approaches have been widely used: digital waveguide synthesis, modal synthesis and finite element methods. Digital waveguide synthesis is efficient and realistic and captures the complete dynamics of the underlying physics but is restricted to instruments that are well-described by the one-dimensional string equation. Modal synthesis is efficient and realistic yet abandons complete dynamical description and hence cannot used for certain types of performance interactions like bowing. Finite element methods are realistic and capture the behavior of the constituent physical equations but on current commodity hardware does not perform in real-time. Banded waveguides offer efficient simulations for cases for which modal synthesis is appropriate but traditional digital waveguide synthesis is not applicable. The key realization is that the dynamic behavior of traveling waves, which is being used in waveg-uide synthesis, can be applied to individual modes and that the efficient computational

Abstract. A computational theory for classification of natural biosonar targets is developed based on the properties of an example stimulus ensemble. An extensive set of echoes (84 800) from four different foliages was transcribed into a spike code using a parsimonious model (linear filtering, half-wave rectification, thresholding). The spike code is assumed to consist of time differences (interspike intervals) between threshold crossings. Among the elementary interspike intervals flanked by exceedances of adjacent thresholds, a few intervals triggered by disjoint half-cycles of the carrier oscillation stand out in terms of resolvability, visibility across resolution scales and a simple stochastic structure (uncorrelatedness). They are therefore argued to be a stochastic analogue to edges in vision. A three-dimensional feature vector representing these interspike intervals sustained a reliable target classification performance (0.06% classification error) in a sequential probability ratio test, which models sequential processing of echo trains by biological sonar systems. The dimensions of the representation are the first moments of duration and amplitude location of these interspike intervals as well as their number. All three quantities are readily reconciled with known principles of neural signal representation, since they correspond to the center of gravity of excitation on a neural map and the total amount of excitation.