Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2011, Article ID 151436, 13 pages doi:10.1155/2011/151436 Research Article Trombone Synthesis by Model and Measurement Tamara Smyth and Frederick S. Scott School of Computing Science, Simon Fraser University, Surrey, BC, Canada V3T 0A3 Correspondence should be addressed to Tamara Smyth, tamaras@cs.sfu.ca Received 29 August 2010; Revised 15 December 2010; Accepted 24 January 2011 Academic Editor: Vesa Valimaki Copyright © 2011 T. Smyth and F. S. Scott. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A physics-based synthesis model of a trombone is developed using filter elements that are both theoretically-based and estimated from measurement. The model consists of two trombone instrument transfer functions: one at the position of the mouthpiece enabling coupling to a lip-valve model and one at the outside of the bell for sound production. The focus of this work is on extending a previously presented measurement technique used to obtain acoustic characterizations of waveguide elements for cylindrical and conical elements, with further development allowing for the estimation of the flared trombone bell reflection and transmission functions for which no one-parameter traveling wave solution exists. A one-dimensional bell model is developed providing an approximate theoretical expectation to which estimation results may be compared. Dynamic trombone model elements, such as those dependent on the bore length, are theoretically and parametrically modeled. As a result, the trombone model focuses on accuracy, interactivity, and efficiency, making it suitable for a number of real-time computer music applications. 1. Introduction Instrument synthesis involving real-time interactive sound often faces trade-offs between accuracy and computational efficiency to provide both parametric control and quality sound production. It is often the case that a more playable model, one that is more responsive to human gestural input, is a better sounding virtual musical instrument than one that prioritizes acoustic precision. That is, the more the sound production can be effectively controlled in the hands of a musician employing phrasing, nuances, and other musical subtleties, the more the perceived sound quality will approach that of an actual acoustic instrument. Nevertheless, producing a model that is as acoustically accurate as resources will allow requires knowledge of the instrument’s acoustic characteristics, properties that may be effectively obtained by measurement. Acoustic accuracy becomes increasingly important if the focus of the model’s application is less on interactive sound production and more on model validation, inverse modeling, and parameter estimation. For example, if the goal is to extract physical parameter values from an instrument during performance, the model’s produced sound when played with proper parameter values will likely require a higher degree of actual (over perceived) similarity to the instrument being modeled. In this application, which is gaining increasing attention in the physical modeling community [1–8], the virtual model must often also account for the frequency characteristics of any variables involved in the acquisition of data, such as instrument radiation, mic placement, or inclusion of any measurement device/apparatus that may also alter the acoustic behaviour of the instrument being modeled. In this work, a physics-based synthesis model of a trom- bone is presented, suitable for applications mentioned above. That is, the aim is for high-quality real-time sound production, with highly intuitive and interactive control parameters, yet with a sufficiently accurate acoustic model of the trombone instrument that its inverse transfer function may be applied during real-time performance. Deconvolving the effects of the bore and bell in the instrument’s produced sound allows for the estimation of the dynamic effects of the lip-valve signal, a signal related to the valve’s volume velocity holding the primary sound control information for most wind instruments such as blowing pressure, embouchure, and more advanced playing techniques. The instrument’s