The Crest factor for trigonometric polynomials. Part I: Approximation theoretical estimates

Abstract

The Chebyshev norm of a degree n trigonometric polynomial is estimated against a discrete maximum norm based on equidistant sampling points where, typically, oversampling rather than critical sampling is used. The bounds are derived from various methods known from classical Approximation Theory. These estimates are of fundamental importance for the design of efficient OFDM in communication systems.