Overshooting and $L^1$-Norms of a Class of Nyquist Filters

TL;DR

This paper derives new bounds on overshooting for multicarrier signals with aperiodic filters, extending existing results for trigonometric polynomials and relating overshoot to $L^1$-norm properties of Nyquist filters, aiding in filter design.

Contribution

It provides novel bounds on overshoot for general multicarrier signals with aperiodic filters, extending previous results and connecting overshoot analysis to $L^1$-norm properties of Nyquist filters.

Findings

Improved bounds on overshooting for small oversampling factors.

Extension of overshoot bounds to a class of Nyquist filters.

Relation of overshoot bounds to $L^1$-properties of filters.

Abstract

To tightly control the signal envelope, estimating the peak regrowth between FFT samples is an important sub-problem in multicarrier communications. While the problem is well-investigated for trigonometric polynomials (i.e. OFDM), the impact of an aperiodic transmit filter is important too and typically neglected in the peak regrowth analysis. In this paper, we provide new bounds on the overshooting between samples for general multicarrier signals improving on available bounds for small oversampling factors. In particular, we generalize a result of [1, Theorem 4.10]. Our results will be extended to bound overshooting of a class of Nyquist filters as well. Eventually, results are related to some respective $L^1$-properties of these filters with application to filter design.