Bounding multivariate trigonometric polynomials

Luke Pfister, Yoram Bresler

Research output: Contribution to journalArticlepeer-review


The extremal values of multivariate trigonometric polynomials are of interest in fields ranging from control theory to filter design, but finding the extremal values of such a polynomial is generally NP-Hard. In this paper, we develop simple and efficiently computable estimates of the extremal values of a multivariate trigonometric polynomial directly from its samples. We provide an upper bound on the modulus of a complex trigonometric polynomial, and develop upper and lower bounds for real trigonometric polynomials. For a univariate polynomial, these bounds are tighter than existing bounds, and the extension to multivariate polynomials is new. As an application, the lower bound provides a sufficient condition to certify global positivity of a real trigonometric polynomial.

Original languageEnglish (US)
Article number8552451
Pages (from-to)700-707
Number of pages8
JournalIEEE Transactions on Signal Processing
Issue number3
StatePublished - Feb 1 2019


  • Multivariate polynomials
  • Oversampling
  • Positive trigonometric polynomials
  • Trigonometric interpolation

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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