Complex waveform estimation using adaptive frequency oscillators

Abstract

Automatic learning and emulation of a complex periodic waveform is demonstrated using a nonlinear dynamical system containing a single adaptive frequency oscillator (AFO) with feedback. The AFO uses a phase-lock loop (PLL) to match the fundamental frequency and phase of a periodic input signal. Nonlinear functions of the AFO state provide an extended basis to represent the waveform shape, and amplitudes for the extended basis are automatically estimated using feedback. Significantly, the approach also works if the AFO state is not sinusoidal but is itself complex shaped. Numerical simulations demonstrate successful estimation of a triangle wave and a complex waveform constructed with multiple harmonics using both Hopf and van der Pol AFOs.