一类Nyquist滤波器的过冲与$L^1$ -范数
Overshooting and $L^1$-Norms of a Class of Nyquist Filters
摘要：
为了严格控制信号包络，估计FFT样本之间的峰值再生是多载波通信中的一个重要子问题。虽然三角多项式（即OFDM）的问题是很好的研究，非周期性发射滤波器的影响也很重要，通常在峰值再生分析中被忽略。在本文中，我们提供了新的界限一般多载波信号的样本之间的过冲改善小过采样因子的可用界限。特别地，我们推广了[1，定理4.10]的一个结果.我们的结果也将被推广到一类奈奎斯特滤波器的界超调。最后，结果是相关的一些各自的$L^1$ -这些过滤器与应用程序的过滤器设计的属性。
英文摘要：
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.
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