Nonuniform fast Fourier transforms using min-max interpolation

Jeffrey A. Fessler, Bradley P. Sutton

Research output: Contribution to journalArticlepeer-review


The fast Fourier transform (FFT) is used widely in signal processing for efficient computation of the FT of finite-length signals over a set of uniformly spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e., a nonuniform FT. Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The rain-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function.

Original languageEnglish (US)
Pages (from-to)560-574
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number2
StatePublished - Feb 2003
Externally publishedYes


  • Discrete Fourier transform
  • Gridding
  • Imaging
  • Magnetic resonance
  • Min-max interpolation
  • Tomography

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


Dive into the research topics of 'Nonuniform fast Fourier transforms using min-max interpolation'. Together they form a unique fingerprint.

Cite this