Error measures for resampled irregular data

With resampling, a regularly sampled signal is extracted from observations which are irregularly spaced in time, Resampling methods can be divided into simple and complex methods, Simple methods such as Sample&Hold (S&H) and Nearest Neighbor Resampling (NNR) use only one irregular sample for one resampled observation. A theoretical analysis of the simple methods is given. The various resampling methods are compared using the new error measure SDT: the spectral distortion at interval T, SDT is zero when the time domain properties of the signal are conserved. Using the time domain approach, an antialiasing filter is no longer necessary: the best possible estimates are obtained by using the data themselves. In the frequency domain approach, both allowing aliasing and applying antialiasing leads to distortions in the spectrum. The error measure SDT has been compared to the reconstruction error. A small reconstruction error does not necessarily result in an accurate estimate of the statistical signal properties as expressed by SDT.