The formation of templates from natural data patterns

Signal averaging procedures used to create virtually noise-free templates from sets of natural data patterns are presented. It is assumed that a large number of data patterns are available that consist of replicas of a basic underlying waveform, the signal of interest. These replicas vary in time alignment, time stretch, amplitude bias, and amplitude stretch. It is further assumed that the data waveforms are corrupted with zero-mean white additive noise. The procedures adjust the alignment, bias, and stretch of the data waveforms to obtain a best fit to matching reference, then average the data waveforms to reduce the additive noise. Noise-induced residual misalignments and misadjustments of the data waveforms introduced a distortion in the averaged template; the analysis focuses on the nature and magnitude of this distortion.