Modal analysis of the input impedance of wind instruments. Application to the sound synthesis of a clarinet

Abstract

Modal analysis of the input impedance of wind instruments. Application to the sound synthesis of a clarinet. Applied Acoustics, Elsevier, 2018, 141, pp.271 -280 AbstractThis paper investigates the modal analysis of wind instruments as seen from the input of their air column. Beside the treatment of analytical models, a particular emphasis is given to the analysis of measured input impedances. This requires special care because the measurements cover only a limited frequency band and are affected by some unknown errors. This paper describes how the Prony analysis and the Least Squares Complex Exponential (LSCE) classical techniques can be used in this context and how the main pitfalls can be avoided in their application. A physically acceptable method of reconstruction of the low frequency band is proposed. A technique using fictitious points in the high frequency range is described in order to ensure the passivity of the resonator in the whole frequency band. The principles of a real-time synthesis of clarinet sounds based on the modal representation of the resonator is given as an application, with a method to efficiently handle the modal representation during the transition between fingerings. A musically relevant example finally illustrates the possibilities of the modal analysis applied to wind instruments.

Multiple two-step oscillation regimes produced by the alto saxophone

“…where C n are the complex residues and s n the complex poles. These modal parameters are estimated from a measured saxophone input impedance (Taillard et al, 2018). Eq.…”

Woodwind instrument design optimization based on impedance characteristics with geometric constraints

“…These residuals, and this is an essential aspect of this work, are constructed by taking into account the woodwind instrument specificities to assure their continuity and smoothness in the design domain. Resonance frequencies are generally estimated with a global modal analysis [21] or a peak detection approach [15]. However, woodwind instrument toneholes, which can be seen as multiple parallel tubes, impose local and global cutoff frequencies [17].…”

Peak-picking identification technique for modal expansion of input impedance of brass instruments

“…[4,6,7]). In a recent paper dedicated to modal analysis of wind instruments [14], Taillard et al also propose a two-step method, which combines the Least Squares Complex Exponential (LSCE) technique to identify the poles with a fitting procedure to obtain the residues. The proposed method requires a number of preprocessing steps to be applicable to experimental data, possibly noisy and available over a limited frequency range.…”

“…Regarding the last point, the literature review shows that the representation using real modes seems less popular than that using complex modes to approximate a measured input impedance [4,6,14]. The motivation to prefer complex modes is however rarely stated explicitly, except when the dynamics of the resonator is studied in a theoretical framework, where the complex nature of modes results from modeling assumptions (in particular concerning losses) [21].…”