Two novel ways of averaging waveforms by fourier analysis: the representative and the synchronous averages☆

Abstract Two algorithms are provided which define two new ways of averaging waveforms. The representative average maintains shape, has average d.c. offset, average amplitude and average position of noise-free input signals whose onset varies in time after a trigger pulse. The synchronous average removes random bipolar noise, the amplitude of which is below a critical threshhold, from a randomly occuring waveform. The latter does not require a trigger pulse, maintains its shape, has an average d.c. offset and average amplitude. Its position in the output field is such that the centroid of the waveform is placed in the center of the field. Both methods involve the definition of average phase angle and a quantity called the angular standard deviation.