Bounding Multivariate Trigonometric Polynomials with Applications to Filter Bank Design

Understand

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 univarite polynomial, these bounds are tighter than existing bounds, and the extension to multivariate polynomials is new.