An examination of frequency indexes used in the non-uniform DFT

Discrete data with random spacing between sample instances presents unique signal processing challenges. The spectrum of non-uniformly sampled data is computed via the non-uniform discrete Fourier transform (NUDFT). While similar to the discrete Fourier transform (DFT), there is a significant difference in frequency indexing. An important restriction on indexing must be included in the definition of the NUDFT, otherwise computations are useless. This restriction is generally not emphasized, and often completely ignored, in the existing literature on non-uniform sampling.