Spectral analysis with short data batches (photon correlation spectroscopy)

Abstract

This paper studies the limiting accuracy with which power spectra and the values of spectral parameters for random signals can be achieved from short batches of data. Initially, general expressions for arbitrary data are derived; these are then restricted for simplicity to wide-band signals. In addition, comparison is made with computer simulation for two well defined models, namely, photodetection of light of constant intensity and heterodyne photodetection of narrow-band Gaussian-Lorentzian light. It is shown that there is no analytical difference between operation in time or frequency space for batch data, and also that long data sets can be analysed at least as well, in terms of the accuracy with which spectral parameters can be determined by fitting, by averaging over many short batches as by processing the set as a whole.