Abstract: Systems, methods, and non-transitory computer-readable storage media for determining when to wirelessly communicatively couple together a pair of untethered wireless audio output devices and for determining when to erase a connection history stored on one or both of the wireless audio output devices.

Abstract: The synthesising of a waveform which upon integration will approximate a sinusoid of controllable frequency and amplitude is disclosed. Any desired amplitude may be programmed for a particular frequency. The synthesiser is suitable as a variable speed AC motor drive. The output waveform is synthesised by chopping a square wave using a variable width chop. To obtain lower harmonic content, a chopped square wave is Walsh multiplied with another square wave of different frequency to produce a pulse width modulated waveform having a frequency equal to the frequency difference between the square waves. Methods for accurately controlling the difference frequency using variable digital dividers are disclosed.