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Analogical model for mechanical vibrations in flue organ pipes inferred by independent component analysis

Several experiments have been performed to investigate the mechanical vibrations associated with an organ pipe. The measurements have been made by using laser Doppler vibrometry, a well-known not-invasive optical measurement technique that is very widely used in structural dynamics. The recorded signals are analyzed by using a well-established decomposition method in time domain, i.e., independent component analysis. Asymptotic dynamics methods to recognize low-dimensional dynamic system associated with this wave field is then considered. The full-toned recorded signals appear decomposed into three independent components. The independent components are nonlinear due to the fractal dimension of the attractor. These results for the mechanic vibrational field are compared with those of the acoustic one. It is interesting to note that the two fields have many common characteristics. Finally, a low-dimensional dynamic system that reproduces the main characteristics of the mechanical wave field in the time and frequency domains is introduced.

ICA based identification of dynamical systems generating synthetic and real world time series

Independent Component Analysis (ICA) is a recent and well known technique used to separate mixtures of signals. While in general the researchers put their attention on the type of signals and of mixing, we focus our attention on a quite general class of models which act as sources of the time series, the dynamical systems. In this paper we focus our attention on the general problem to understand the behaviour of ICA methods with respect to the time series deriving from a specific dynamical system, selecting large classes of them, and using ICA to make separation. This study gives some interesting results that are very useful both to highlight some properties related to dynamical systems and to clarify some general aspects of ICA, by using both synthetic and real data.From one hand we study the features of the linear (simple and coupled) and non-linear (single and coupled) dynamical systems, stochastic resonances, chaotic and real dynamical systems. We have to stress that we obtain information about the separation of these systems and substantially how from the entropy of the complete system we can obtain the entropies of the single dynamical systems (so that we also could obtain a more realistic analogic circuit).On the other hand these results show the high capability of the ICA method to recognize the dynamical systems independently from their complexity and in the case of stochastic series ICA perfectly recognizes the different dynamical systems also where the Fourier Transform is irresolute.We also note that in the case of real dynamical systems we showed that ICA permits to recognize the information connected to the sources and to associate to it a phenomenological dynamical system that reproduce it (i.e. Organ Pipe, Stromboli Volcano, Aerosol Index).

ANALOGICAL MODEL INFERRED FROM TIME DOMAIN ANALYSIS AND GENERATING ORGAN PIPES SELF SUSTAINED-TONE

We have recorded acoustic signals emitted by organ pipes in a variety of experimental framework. We have analyzed the recorded sounds with nonlinear techniques in time domain. Starting from this analysis we have extracted their relevant characteristics. Finally, we have constructed simple and suitable analogical model, able to reproduce the registered waveform and sound in listening.

Modeling and Generating Organ Pipes Self-Sustained Tones by Using ICA

Aim of this work is to analyze and to synthesize acoustic signals emitted by organ pipes. An Independent Component Analysis technique is applied to study the behavior of single notes or chords obtained in real and simulated environments. These analyses suggest that the pipe acoustic signals can be described by a mixture of nonlinear oscillations obtained by a self-sustained feedback system (i.e., Andronov oscillator). This system allows to obtain a realistic pipe waveform with features very similar to the sound produced by the pipe and to propose an additive synthesis model. Moreover, suitable analogical and integrate circuit models, able to reproduce the registered waveforms and sound, have been designed. A comparison between real and reconstructed acoustic signals is provided.

Modelization of mechanical vibrations in organ pipes by independent component analysis

Several experiments have been carried out to investigate the mechanical vibrations generated by an organ pipe. Measurements were made by using Laser Doppler Vibrometry. It is a not-invasive optical measurement technique which allows to detect pipe-wall vibrations. The mechanical vibration field is compared with the acoustic field. Namely, we study the behaviour of these fields when they are excited by different levels of pressure. Strong analogies have been evidenced by using techniques in time e frequency domain supporting the assumption that the pipe is not a passive resonator. The challenge is to understand the complex mechanism of coupling between modes of air and eigen-modes of pipe that produces the sound. Here, we present, in first approximation, a low dimensional dynamical system which describes the main characteristics of pipe-wall vibrations. What is interesting is that the same low dimensional dynamical system is able to reproduce also the recorded acoustic field, implying that wall vibrations and acoustic pressure field are strictly related one to each other.