Connectionists: Paper: Frequency analysis with oscillators

[Jonas Buchli]

Dear Connectionists, 

we think the following paper might be interesting for some of you: 

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Frequency analysis with coupled nonlinear oscillators

Jonas Buchli, Ludovic Righetti and Auke Jan Ijspeert

Abstract
We present a method to obtain the frequency spectrum of a signal with a
nonlinear dynamical system. The dynamical system is composed of a pool
of adaptive frequency oscillators with negative mean-field coupling. For
the frequency analysis, the synchronization and adaptation properties of
the component oscillators are exploited. The frequency spectrum of the
signal is reflected in the statistics of the intrinsic frequencies of
the oscillators. The frequency analysis is completely embedded in the
dynamics of the system. Thus, no pre-processing or additional
parameters, such as time windows, are needed. Representative results of
the numerical integration of the system are presented. It is shown, that
the oscillators tune to the correct frequencies for both discrete and
continuous spectra. Due to its dynamic nature the system is also capable
to track non-stationary spectra. Further, we show that the system can be
modeled in a probabilistic manner by means of a nonlinear Fokker–Planck
equation. The probabilistic treatment is in good agreement with the
numerical results, and provides a useful tool to understand the
underlying mechanisms leading to convergence. 

Keywords: Frequency analysis; Coupled oscillators; Adaptive frequency
oscillator

available online: http://dx.doi.org/10.1016/j.physd.2008.01.014

If you do not have access to the fulltext please contact me for a
reprint. 

Best regards
Jonas Buchli 


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Jonas Buchli, Dr.sc., MSc EE
Computational Learning and Motor Control Lab
University of Southern California 
http://www-clmc.usc.edu/
+1 (213) 740 67 17
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