Nonuniform sampling specifically for finite-length data

This article discusses nonuniform sampling specifically for the case of finite-length sets of data. The approach exploits the features of a finite interval and this restriction makes it possible to obtain the results presented using very simple analytical techniques. Much more complex methods have been used previously when the problem was treated over an infinite domain, followed by windowing to introduce the finite data length requirement. The emphasis is on the properties of the spectra of nonuniformly sampled data, particularly in relationship to the results obtained with uniform sampling. In this form of representation the uniform sampling appears as a highly degenerate and very fortuitous special case of nonuniform sampling. The results obtained are also used to develop approximate methods of inverting such spectra including an approximate interpolation function. The theory is illustrated using simulation examples relating to oblique incidence measurement of surface profiles.