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Abstract
The paper presents a method to obtain the modal expansion of the measured input impedance of a brass instrument. The method operates as a peak-picking procedure, which makes it particularly intuitive for users who are not experts in modal analysis. To bypass the limitation of usual peak-picking approaches, which are valid only for well separated resonances, the present method is based on a semi-local optimization problem. It consists in adjusting the frequency and damping of one mode at a time while taking into account the presence of all other modes in the basis. The practical application of the method involves four elementary actions, which can be chained in different ways to progressively approximate a measured input impedance. This procedure is illustrated through the approximation of the input impedance of a bass trombone. The supervised nature of the method allows the user to favour modes that have a physical meaning, i.e. that can be associated with a resonance peak. A single spurious mode can however be deliberately introduced to approximate the input impedance curve beyond the last visible peak. The method applies directly to the frequency-domain data provided by an impedance sensor and does not require any preprocessing. Nevertheless, it is fairly robust to noisy data. Since the method allows a reconstruction of the input impedance using either complex modes or real modes, results obtained with each approximation are critically compared.
Highlights
The input impedance of a wind instrument can be mathematically represented using a modal expansion [1]
By carrying out modal identification from a measured input impedance, it is possible to model the resonator of an existing instrument by a set of ordinary differential equations which can be directly plugged into numerical methods for analysing the emergence of self-sustained oscillations, such as time-domain simulations [2], linear stability analysis [3,4,5] or numerical continuation [6,7,8]
Modal identification techniques are commonly classified into two categories: single degree of freedom (SDOF) and multiple degrees of freedom (MDOF) methods
Summary
The input impedance of a wind instrument can be mathematically represented using a modal expansion [1]. By carrying out modal identification from a measured input impedance, it is possible to model the resonator of an existing instrument by a set of ordinary differential equations which can be directly plugged into numerical methods for analysing the emergence of self-sustained oscillations, such as time-domain simulations [2], linear stability analysis [3,4,5] or numerical continuation [6,7,8]. This approach is facilitated by the fact that well-established experimental devices and procedures exist for measuring the input impedance of wind instruments [9, 10].
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