Nonuniform sampling: Bandwidth and aliasing

G. Larry Bretthorst

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


For spectroscopic measurements, there are good reasons why one might consider using nonuniformly nonsimultaneously sampled complex data. The primary one is that the effective bandwidth, the largest spectral window free of aliases, can be much wider than with uniformly sampled data. In this article, we discuss nonuniformly nonsimultaneously sampled data, describe how these data are traditionally analyzed, analyze them using probability theory, and show how probability theory generalizes the discrete Fourier transform: first for uniformly sampled data, then for nonuniformly sampled data, and finally for nonuniformly nonsimultaneously sampled data. These generalizations demonstrate that aliases are not so much removed by nonuniform nonsimultaneous sampling as they are moved to much higher frequencies.

Original languageEnglish
Pages (from-to)417-435
Number of pages19
JournalConcepts in Magnetic Resonance Part A: Bridging Education and Research
Issue number6
StatePublished - Nov 2008


  • Aliasing
  • Bandwidth
  • Bayesian probability theory
  • Frequency estimation
  • Nonuniform sampling


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