Rhythm processing and frequency tracking in gradient frequency nonlinear oscillator networks

摘要

A method for mimicking the auditory system's response to rhythm of an input signal having a time varying structure comprising the steps of receiving a time varying input signal x(t) to a network of n nonlinear oscillators, each oscillator having a different natural frequency of oscillation and obeying a dynamical equation of the form; $$ \stackrel{.}{r}=r\left(\alpha +{\beta }_1{z}^2+\epsilon \frac{{\beta }_2{z}^4}{1-\epsilon {z}^2}\right)+cx\left(t\right)\frac{\cos \varphi -r\sqrt{\epsilon }}{\epsilon r^2-2\sqrt{\epsilon }r\cos \varphi +1}$$ $$ \stackrel{.}{\varphi }=\omega +{\delta }_1{r}^2+\epsilon \frac{{\delta }_2{r}^4}{1-\epsilon r^2}-cx\left(t\right)\frac{\sin \left(\varphi \right)}{\epsilon r^2-2\sqrt{\epsilon }r\cos \left(\varphi \right)+1}\stackrel{.}{\omega }=-kx\left(t\right)\frac{\sin \varphi }{\epsilon r^2-2\sqrt{\epsilon }r\cos \varphi +1}$$wherein ω represents the response frequency, r is the amplitude of the oscillator and φ is the phase of the oscillator. Generating at least one frequency output from said network useful for describing said varying structure.