Equilibria of Adaptive Wavetable Oscillators with Applications to Beat Tracking
William A. Sethares, Raman Arora · 2007
An adaptive oscillator is a system that can lock onto 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. The key issues in the design of AWOs are: the kind of oscillator to use, the class of admissible inputs, the shape of the wavetable, the control parameters, and the adaptive algorithm that adjusts the parameters. Wavetable oscillators can be applied to track the beat in MIDI signals, or, after an appropriate psycho-acoustical data reduction, to the tracking of audio signals. This paper examines these issues through analysis and simulation, focusing on conditions that achieve the desired entrainment between output and input. Sound examples demonstrate the application to beat tracking.