Abstract
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 language | English (US) |
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Article number | 8552451 |
Pages (from-to) | 700-707 |
Number of pages | 8 |
Journal | IEEE Transactions on Signal Processing |
Volume | 67 |
Issue number | 3 |
DOIs | |
State | Published - Feb 1 2019 |
Keywords
- Multivariate polynomials
- Oversampling
- Positive trigonometric polynomials
- Trigonometric interpolation
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering