Aliasing-Truncation Errors in Sampling Approximations of Sub-Gaussian Signals

Yuriy Kozachenko; Andriy Olenko

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Aliasing-Truncation Errors in Sampling Approximations of Sub-Gaussian Signals

机译：次高斯信号采样近似中的混淆截断误差

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摘要

This paper starts with new aliasing-truncation error upper bounds in the sampling theorem for non-bandlimited stochastic signals. Then, it investigates Lp([0, T]) approximations of the sub-Gaussian random signals. Explicit truncation error upper bounds are established. The obtained rate of convergence provides a constructive algorithm for determining the sampling rate and the sample size in the truncated Whittaker-Kotel'nikovShannon expansions to ensure the approximation of the subGaussian signals with given accuracy and reliability. Some numerical examples are presented.

机译：本文从非带限随机信号的采样定理中的新的混叠截断误差上限开始。然后，它研究了次高斯随机信号的Lp（[0，T]）逼近。明确的截断误差上限已确定。所获得的收敛速率为确定截短的Whittaker-Kotel'nikovShannon展开中的采样率和样本大小提供了一个建设性算法，可确保以给定的精度和可靠性近似于高斯信号。给出了一些数值示例。

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来源
《IEEE Transactions on Information Theory》 |2016年第10期|5831-5838|共8页
作者
Yuriy Kozachenko; Andriy Olenko;
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作者单位

Department of Probability Theory, Statistics and Actuarial Mathematics, Kyiv University, Kiev, Ukraine;

School of Engineering and Mathematical Sciences, La Trobe University, Melbourne, VIC, Australia;

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原文格式 PDF
正文语种 eng
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关键词
Random processes; Stochastic processes; Random variables; Upper bound; Finite wordlength effects; Trajectory; Silicon;

机译：随机过程;随机过程;随机变量;上限;有限字长效应;弹道;硅;

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2. Signal recovery algorithm for 2-level amplitude sampling using chromatic signal approximations [J] . Wijenayake Chamith, Scutts Jarryd, Ignjatovic Aleksandar Signal processing . 2018,第DECa期

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3. Bit error rate approximations using Poisson and negative binomial sampling distributions [J] . G.V. Weinberg Electronics Letters . 2008,第3期

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4. SYSTEMATIC STUDY OF ERROR IN APPROXIMATIONS TO THE ONE-SIDED ONE SAMPLE K–S SAMPLING DISTRIBUTION [C] . J. Randall Brown, Milton E. Harvey, Ceyhun Ozgur Annual meeting of the Decision Sciences Institute . 2010

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5. Bounds for the errors in word count distributional approximations. [D] . Huang, Haiyan. 2001

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6. Phase Difference Measurement of Under-Sampled Sinusoidal Signals for InSAR System Phase Error Calibration [O] . Zhihui Yuan, Yice Gu, Xuemin Xing, 2019

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7. Aliasing-truncation Errors in Sampling Approximations of Sub-Gaussian Signals [O] . Kozachenko, Yuriy, Olenko, Andriy 2016

机译：亚高斯分布的采样近似中的混叠截断误差信号

Aliasing-Truncation Errors in Sampling Approximations of Sub-Gaussian Signals

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