Discrete Entropic Uncertainty Relations Associated with FRFT

• 作者: Guanlei Xu Lijia Zhou Limin Shao Xiaogang Xu Xiaotong Wang
• 来源期刊: 信号与信息处理(英文)
• 学科: 数学
• 关键词: DISCRETE FRACTIONAL FOURIER TRANSFORM (DFRFT) Uncertainty PRINCIPLE Rényi ENTROPY Shannon ENTROPY
• 年，卷（期）: 2013,（3）
• 页码范围: 120-124
• 页数: 5页
• 分类号: O1

摘要

Based on the definition and properties of discrete fractional Fourier transform (DFRFT), we introduced the discrete Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discrete Rényi entropic uncertainty relation were explored. Also, the condition of equality via Lagrange optimization was developed, as shows that if the two conjugate variables have constant amplitudes that are the inverse of the square root of numbers of non-zero elements, then the uncertainty relations reach their lowest bounds. In addition, the resolution analysis via the uncertainty is discussed as well.