Physically Informed Signal Processing Methods for Piano Sound Synthesis: A Research Overview

EURASIP Journal on Applied Signal Processing 2003:10, 941–952 c 2003 Hindawi Publishing Corporation
Physically Informed Signal Processing Methods for Piano Sound Synthesis: A Research Overview Balázs Bank Department of Measurement and Information Systems, Faculty of Electronical Engineering and Informatics, Budapest University of Technology and Economics, H-111 Budapest, Hungary Email: Federico Avanzini Department of Information Engineering, University of Padova, 35131 Padua, Italy Email: Gianpaolo Borin Dipartimento di Informatica, University of Verona, 37134 Verona, Italy Email: Giovanni De Poli Department of Information Engineering, University of Padova, 35131 Padua, Italy Email: Federico Fontana Department of Information Engineering, University of Padova, 35131 Padua, Italy Email: Davide Rocchesso Dipartimento di Informatica, University of Verona, 37134 Verona, Italy Email: Received 31 May 2002 and in revised form 6 March 2003 This paper reviews recent developments in physics-based synthesis of piano. The paper considers the main components of the instrument, that is, the hammer, the string, and the soundboard. Modeling techniques are discussed for each of these elements, together with implementation strategies. Attention is focused on numerical issues, and each implementation technique is described in light of its efficiency and accuracy properties. As the structured audio coding approach is gaining popularity, the authors argue that the physical modeling approach will have relevant applications in the field of multimedia communication. Keywords and phrases: sound synthesis, audio signal processing, structured audio, physical modeling, digital waveguide, piano. 1. INTRODUCTION Sounds produced by acoustic musical instruments can be described at the signal level, where only the time evolution of the acoustic pressure is considered and no assumptions on the generation mechanism are made. Alternatively, source models, which are based on a physical description of the sound production processes [1, 2], can be developed. Physics-based synthesis algorithms provide semantic sound representations since the control parameters have a straightforward physical interpretation in terms of masses, springs, dimensions, and so on. Consequently, modification of the parameters leads in general to meaningful results and allows more intuitive interaction between the user and the virtual instrument. The importance of sound as a primary vehicle of information is being more and more recognized in the multimedia community. Particularly, source models of sounding objects (not necessarily musical instruments) are being explored due to their high degree of interactivity and the ease in synchronizing audio and visual synthesis [3]. The physical modeling approach also has potential applications in structured audio coding [4, 5], a coding scheme 942 where, in addition to the parameters, the decoding algorithm is transmitted to the user as well. The structured audio orchestral language (SAOL) became a part of the MPEG-4 standard, thus it is widely available for multimedia applications. Known problems in using physical models for coding purposes are primarily concerned with parameter estimation. Since physical models describe specific classes of instruments, automatic estimation of the model parameters from an audio signal is not a straightforward task: the model structure which is best suited for the audio signal has to be chosen before actual parameter estimation. On the other hand, once the model structure is determined, a small set of parameters can describe a specific sound. Casey [6] and Serafin et al. [7] address these issues. In this paper, we review some of the strategies and algorithms of physical modeling, and their applications to piano simulation. The piano is a particularly interesting instrument, both for its prominence in western music and for its complex structure [8]. Also, its control mechanism is simple (it basically reduces to key velocity), and physical control devices (MIDI keyboards) are widely available, which is not the case for other instruments. The source-based approach can be useful not only for synthesis purposes but also for gaining a better insight into the behavior of the instruments. However, as we are interested in efficient algorithms, the features modeled are only those considered to have audible effects. In general, there is a trade-off between the accuracy and the simplicity of the description. The optimal solution may vary depending on the needs of the user. The models described here are all based on digital waveguides. The waveguide paradigm has been found to be the most appropriate for real-time synthesis of a wide range of musical instruments [9, 10, 11]. As early as in 1987, Garnett [12] presented a physical waveguide piano model. In his model, a semiphysical lumped hammer is connected to a digital waveguide string and the soundboard is modeled by a set of waveguides, all connected to the same termination. In 1995, Smith and Van Duyne [13, 14] presented a model based on commuted synthesis. In their approach, the soundboard response is stored in an excitation table and fed into a digital waveguide string model. The hammer is modeled as a linear filter whose parameters depend on the hammer-string collision velocity. The hammer filter parameters have to be precalculated and stored for all notes and hammer velocities. This precalculation can be avoided by running an auxiliary string model connected to a nonlinear hammer model in parallel, and, based on the force response of the auxiliary model, designing the hammer filters in real time [15]. The original motivation for commuted synthesis was to avoid the high-order filter which is needed for high quality soundboard modeling. As low-complexity methods have been developed for soundboard modeling (see Section 5), the advantages of the commuted piano with respect to the direct modeling approach described here are reduced. Also, due to the lack in physical description, some effects, such as the restrike (ribattuto) of the same string, cannot be precisely modeled with the commuted approach. Describing the com- EURASIP Journal on Applied Signal Processing muted synthesis in detail is beyond the scope of this paper, although we would like to mention that it is a comparable alternative to the techniques described here. As part of a collaboration between the University of Padova and Generalmusic, Borin et al. [16] presented a complete real-time piano model in 1997. The hammer was treated as a lumped model, with a mass connected in parallel to a nonlinear spring, and the strings were simulated using digital waveguides, all connected to a single-lumped load. Bank [17] introduced in 2000 a similar physical model, based on the same functional blocks, but with slightly different implementation. An alternative approach was used for the solution of the hammer differential equation. Independent string models wer (...truncated)