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

Angelo Ciaramella, Enza De Lauro, Salvatore De Martino, Mariarosaria Falanga, Roberto Tagliaferri

.

DOI: 10.4236/jsip.2011.23018                

Abstract

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.

Keywords

Independent Component Analysis, Sound Synthesis, Non-Linear Oscillators, Integrate Circuits

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. Gorges, “Programming Synthesizers,” Wizoobooks, Bremen, 2005.
[2]	N. H. Fletcher and T. D. Rossing, “The Physics of Musical Instruments,” II Edition, Springer, New York, 1998.
[3]	N. H. Fletcher, “The Nonlinear Physics of Musical Instruments,” Reports on Progress in Physics, Vol. 62, No. 5, 1999, pp. 723-764. doi:10.1088/0034-4885/62/5/202
[4]	S. A. Elder, “On the Mechanism of Sound Production in Organ Pipes,” Journal of Acoustical Society of America, Vol. 54, No. 6, 1973, pp. 1554-1564. doi:10.1121/1.1914453
[5]	A. Hyvarinen, J. Karhunen and E. Oja, “Independent Component Analysis,” Wiley-So Inc., Hoboken, 2001. doi:10.1002/0471221317
[6]	S. Osowski, A. Majkowski and A. Cichocki, “Robust PCA Neural Networks for Random Noise Reduction of the Data,” IEEE International Conference on Acoustic, Speech, and Signal Processing, Vol. 5, 2000, pp. 3152-3155.
[7]	H. D. I. Abarbanel, “Analysis of Observed Chaotic Data,” Springer-Verlag, New York, 1995.
[8]	E. De Lauro, S. De Martino, E. Del Pezzo, M. Falanga, M. Palo and R. Scarpa, “Model for High-Frequency Strombolian Tremor Inferred by Wavefield Decomposition and Reconstruction of Asymptotic Dynamics,” Journal of Geophysical Research, Vol. 113, 2008, 16 Pages.
[9]	F. Takens, “Detecting Strange Attractors in Turbolence,” Dynamical Systems and Turbulence Warwick, Lectures Notes in Mathematics, Vol. 898, 1981, pp. 366-381.
[10]	A. Ciaramella, E. De Lauro, S. De Martino, M. Falanga and R. Tagliaferri, “ICA Based Identification of Dynamical Systems Generating Synthetic and Real World Time Series,” Soft Computing, Vol. 10, 2006, pp. 587-606. doi:10.1007/s00500-005-0515-7
[11]	M. Covell, M. Withgott, and M. Slaney, “Mach1: Nonuniform Timescale Modification of Speech,” Proceedings of IEEE International Conference on Acoustic, Speech, Signal Processing (ICASSP), Seattle, 1998, pp. 349-352.
[12]	E. De Lauro, S. De Martino, E. Esposito, M. Falanga and E. P. Tomasini, “Analogical Model for Mechanical Vibrations in Flue Organ Pipes Inferred by Independent Component Analysis,” Journal of Acoustical Society of America, Vol. 122, No. 4, 2007, pp. 2413-2424. doi:10.1121/1.2772225
[13]	F. Acernese, A. Ciaramella, S. De Martino, R. De Rosa, M. Falanga and R. Tagliaferri, “Neural Networks for Blind Source Separation of Stromboli Explosion Quakes,” IEEE Transactions on Neural Networks, Vol. 14, No. 1, 2003, pp. 167-175. doi:10.1109/TNN.2002.806649
[14]	A. Ciaramella, C. Bongardo, H. D. Aller, M. F. Aller, G. De Zotti, A. Lahteenmaki, G. Longo, L. Milano, R. Tagliaferri, H. Terasranta, M. Tornikoski and S. Urpo, “A Multifrequency Analysis of Radio Variability of Blazars,” Astronomy & Astrophysics Journal, Vol. 419, 2004, pp. 485-500.
[15]	A. Ciaramella, “Single Channel Polyphonic Music Transcription,” Frontiers in Artificial Intelligence and Applications, New Directions in Neural Networks—18th Italian Workshop on Neural Networks: WIRN 2008, Vol. 193, 2009, pp. 99-108.
[16]	E. De Lauro, S. De Martino, M. Falanga, A. Ciaramella and R. Tagliaferri, “Complexity of Time Series Associated to Dynamical Systems Inferred from Independent Component Analysis,” Physical Review E, Vol. 72, 2005, pp. 1-14.
[17]	A. Ciaramella, M. Funaro and R. Tagliaferri, “Separation of Convolved Mixtures in Frequency Domain ICA,” International Journal of Contemporary Mathematical Sciences, Vol. 1, No. 16, 2006, pp. 769-795.
[18]	A. Ciaramella and R. Tagliaferri, “Amplitude and Permutation Indeterminacies in Frequency Domain Convolved ICA,” Proceedings of the IEEE International Joint Conference on Neural Networks 2003, Vol. 1, 2003, pp. 708-713.
[19]	B. Natarajan, “Filtering Random Noise from Deterministic Signals via Data Compression,” IEEE Transactions on Signal Processing, Vol. 43, 1995, pp. 2595-2605. doi:10.1109/78.482110
[20]	P. Grassberger and I. Procaccia, “Measuring the Strangeness of Strange Attractors,” Physica D: Nonlinear Phenomena, Vol. 9, No. 1-2, 1983, pp. 189-208.
[21]	L. D. Landau and E. M. Lifshitz, “Fluid Mechanics,” Pergamon Press, Oxford, 1959.
[22]	A. A. Andronov, A. A. Vitt and S. E. Khaikin, “Theory of Oscillators,” Republished Dover Publications, Inc., 1966.