Adaptive Wavetable Oscillators
An adaptive oscillator is a system that can lock on to a time-varying input signal, synchronizing its output to both the frequency and phase of the input. A wavetable oscillator generates a periodic output by indexing into a lookup table that stores a single period of the waveform. An adaptive wavetable oscillator (AWO) combines these two ideas in a technique which separates the periodic output waveform from the parameters that control the adaptation of the frequency and phase of the waveform. This separation is advantageous because it decouples the state of the oscillator from the dynamics of the adaptation, allowing the process of synchronization to be interpreted as a simple gradient optimization on a cost function. The oscillations remain stable over a large and easily described range of parameter values, and analysis of the synchronization can proceed along lines familiar from standard adaptive systems. Key issues in the design of AWOs are: the class of admissible inputs, the shape of the wavetable, the parameters that will be controlled, and the adaptive algorithm that adjusts the parameters. This paper examines these issues through analysis and simulation, focusing on conditions that achieve the desired synchronization between output and input.