High-Resolution Alignment of Sampled Waveforms

Waveforms are often sampled faster than the Nyquist rate to obtain desired temporal resolution, even though, theoretically, oversampling adds no information and should not be necessary. This paper shows how high resolution can be achieved efficiently from data sampled at the Nyquist rate by working with coefficients of the Fourier-series expansion of the continuous interpolating waveform. Practical algorithms are presented for aligning and comparing waveforms, locating peaks, resolving superimpositions, and averaging overlapping waveforms. The algorithms prove to be more accurate, and to require fewer computations and less storage than techniques which employ continuous oversampling in many signal-processing applications, particularly template matching.