Computing circular auto-correlation of randomly sampled sequences

Being related to the power density spectrum of a data sequence, auto-correlation provides useful information in digital signal processing. With regular sampling, the size of each shift (step size) for computing an auto-correlation of a sequence is necessarily the same as the sampling period. When random sampling is adopted, there is no such natural choice and the step size must be determined according to other criteria. This paper suggests to choose a step size that can accommodate the highest frequency component of interest contained in a sequence. The techniques developed for solving the problems in finding overlaps and speeding up computation are described. Although the discussion is confined to circular auto-correlation, the computation techniques proposed can apply equally well to cross-correlation and convolution of randomly sampled sequences.