2. Information Measures and Spectral Analysis

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.