Information Measures and Spectral Analysis

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• 刊名：Lecture Notes in Control and Information Sciences
• 出版年：2017
• 出版时间：2017
• 年：2017
• 卷：465
• 期：1
• 页码：15-37
• 全文大小：233 KB
• 作者单位：Song Fang (6)
  Jie Chen (6)
  Hideaki Ishii (7)
  
  6. Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong
  7. Department of Computer Science, Tokyo Institute of Technology, Yokohama, Japan
  
• 丛书名：Towards Integrating Control and Information Theories
• ISBN：978-3-319-49289-6
• 刊物类别：Engineering
• 刊物主题：Control Engineering
  Vibration, Dynamical Systems and Control
  
• 出版者：Springer Berlin / Heidelberg
• 卷排序：465

文摘

In this chapter we introduce the notations and background knowledge that will be used in this book. In particular, the key notions from information theory and stochastic processes, e.g., entropy, mutual information, channel capacity, “water-filling” power allocation, stationarity and asymptotic stationarity, are exposed concisely together with discussions on their properties. In addition, we propose a measure of how Gaussian and white an asymptotically stationary stochastic process is, which is therefore termed Gaussianity-whiteness. Towards this end, we first introduce the notion of negentropy rate, which provides a measure of non-Gaussianity for asymptotically stationary stochastic processes. Then, by combining negentropy rate with spectral flatness in a non-trivial way, the Gaussianity-whiteness is defined. Properties of the notions are also analyzed.