Geometric View of Aliasing via ℝ/ℤ

Samples of a periodic signal at N equally spaced points cannot distinguish frequencies that differ by a multiple of N. This note explains why, using the group ℝ/ℤ: the sampling points form a finite subgroup isomorphic to ℤ/Nℤ, while the distinguishable frequencies form the quotient group ℤ/Nℤ of the integers.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-07
DOI
https://doi.org/10.5281/zenodo.24044288
Citations
1
Primary Topic
Mathematical Analysis and Transform Methods
Type
article
Field-Weighted Citation Impact
2.17
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article

Geometric View of Aliasing via ℝ/ℤ

Dan Vassilev
1 citations
Zenodo (CERN European Organization for Nuclear Research)
Mathematical Analysis and Transform Methods
2.17
article

Geometric View of Aliasing via ℝ/ℤ

Dan Vassilev
article en
1 citations

Abstract

Samples of a periodic signal at N equally spaced points cannot distinguish frequencies that differ by a multiple of N. This note explains why, using the group ℝ/ℤ: the sampling points form a finite subgroup isomorphic to ℤ/Nℤ, while the distinguishable frequencies form the quotient group ℤ/Nℤ of the integers.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 10%
Mathematical Analysis and Transform Methods
2.17
DOIOpen Access PDFOpenAlex
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