Two algorithms for periodic extension on uniform grids

Nira Gruberger, David Levin

Research output: Contribution to journalArticlepeer-review

Abstract

Given function values on a uniform grid in a domain Ω in ℝd, one is often interested in extending the values to a larger grid on a box B containing Ω. In particular, we are interested in “periodic extensions.” For such extensions the discrete Fourier transform (DFT) of the resulting grid values on B is expected to provide good efficient approximation to the underlying function on Ω. This paper presents two different extension algorithms. The first method is a natural approach to this problem, aiming at achieving the fastest decay of the DFT coefficients of the extended data.The second is a fast algorithm which is appropriate for the univariate case and for limited cases of multivariate scenarios. It is shown that if a “good” periodic extension exists, the proposed method will find an extension with similar properties.

Original languageEnglish
Pages (from-to)475-494
Number of pages20
JournalNumerical Algorithms
Volume86
Issue number2
DOIs
StatePublished - Feb 2021

Keywords

  • Decay rate
  • Extension
  • Fourier coefficients
  • Periodic
  • Uniform grid

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