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On Polynomials with Low Peak Signal to Power (L∞toL2Norm) Ratios and Theorems of Kashin and Spencer

机译:关于具有低峰值信功率比 (L∞toL2Norm) 的多项式以及 Kashin 和 Spencer 定理

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摘要

In many engineering problems such as optical communications, radar and sonar problems, the electronic synthesis of speech, etc., as well as mathematical applications, a problem that arises is that of finding a waveform (trigonometric polynomial) with a specified spectrum, such that its crest factor is minimum, where the crest factor is the ratio of the peak signal energy (L∞norm) to the power (L2norm) of the waveform. The mathematical formulation of the problem is as follows: Given 1 ≤m1
机译:在许多工程问题中,如光通信、雷达和声纳问题、语音的电子合成等,以及数学应用中,出现的问题是找到具有指定频谱的波形(三角多项式),使其波峰因数最小,其中波峰因数是峰值信号能量(L∞范数)与波形的功率(L2范数)之比。问题的数学公式如下:给定 1 ≤m1

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