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

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.