title: An introduction to the Fourier transform: relationship to MRI.
abstract: OBJECTIVE
  The Fourier transform, a fundamental mathematic tool widely used in signal analysis, is ubiquitous in radiology and integral to modern MR image formation. Understanding MRI techniques requires a basic understanding of what the Fourier transform accomplishes. MR image encoding, filling of k-space, and a wide spectrum of artifacts are all rooted in the Fourier transform.
  
  
  CONCLUSIONS
  This article illustrates these basic Fourier principles and their relationship to MRI.
authors.affiliation: Department of Radiology, Loyola University Medical Center, 2160 S First Ave., Maywood, IL 60153, USA. tgalla1@lumc.edu
authors.forename: Thomas A
authors.initials: TA
authors.lastname: Gallagher
authors.forename: Alexander J
authors.initials: AJ
authors.lastname: Nemeth
authors.forename: Lotfi
authors.initials: L
authors.lastname: Hacein-Bey
mesh_terms: D016477:Artifacts; D005583:Fourier Analysis; D006801:Humans; D008279:Magnetic Resonance Imaging