Statistical Signal Processing

Modern information systems must handle huge amounts of data having varied natural or technological origins. Automated processing of these increasing loads of signals requires training specialists capable of formalising the problems encountered. This book aims at supplying a formalised, concise presentation of the basis of statistical signal processing. Similar interest is directed to aspects related to signal modelling and to signal estimation. So, in order to supply the reader with the desirable theoretical bases and to allow him to make progress in the discipline, most of the results presented here are carefully justified. First, the representation of random signals in the Fourier domain and their filtering are considered. These tools enable linear prediction theory and related classical filtering techniques to be addressed in a simple way. Then the spectrum identification problem is presented as a first step toward spectrum estimation, which is studied in the non-parametric and in the parametric frameworks. The last chapters introduce synthetically further advanced techniques that will enable the reader to solve signal processing problems of a general nature. Rather than supplying an exhaustive description of existing techniques, this book is designed for students, scientists and research engineers interested in statistical signal processing who need to acquire the necessary bases to address the specific problems that they may be faced with, as well as the corresponding literature. The CD-ROM contains MATLABÊ<ha programs in HTML format and is intended to provide simulation examples (program listings + simulation results) In addition, it also presents some basics of probability.

Contents

Introduction.- Random Processes.- Power Spectrum.- Spectral Representation.- Filtering.- Important Particular Processes.- Non-linear Transforms of Processes.- Linear Prediction.- Particular Filtering Techniques.- Rational Spectral Densities.- Spectral Identification.- Non-parametric Spectral Estimation.- Parametric Spectral Estimation.- Higher-order Statistics.- Bayesian and MCMC Methods.- Adaptive Estimation.- Appendices A-Z.

現代資訊系統必須處理來自不同自然或技術來源的大量數據。自動處理這些不斷增加的信號負載需要訓練有素的專家，能夠形式化遇到的問題。本書旨在提供統計信號處理基礎的形式化、簡潔介紹。同樣的興趣也集中在與信號建模和信號估計相關的方面。為了為讀者提供理想的理論基礎，並使其在這個學科上取得進展，這裡介紹的大部分結果都經過了仔細的證明。首先，考慮了在傅立葉域中隨機信號的表示和濾波。這些工具使得能夠以簡單的方式討論線性預測理論和相關的經典濾波技術。然後，將譜識別問題作為譜估計的第一步進行介紹，並在非參數和參數框架下進行研究。最後幾章簡要介紹了進一步的高級技術，這將使讀者能夠解決一般性的信號處理問題。本書不僅提供現有技術的詳盡描述，還針對對統計信號處理感興趣的學生、科學家和研究工程師，提供了必要的基礎，以應對可能遇到的特定問題，以及相應的文獻。CD-ROM包含以HTML格式呈現的MATLAB程式，旨在提供模擬示例（程式清單+模擬結果）。此外，它還介紹了一些概率基礎知識。

目錄：
- 引言
- 隨機過程
- 功率譜
- 頻譜表示
- 濾波
- 重要的特殊過程
- 非線性過程變換
- 線性預測
- 特殊的濾波技術
- 有理譜密度
- 譜識別
- 非參數譜估計
- 參數譜估計
- 高階統計
- 貝葉斯和MCMC方法
- 自適應估計
- 附錄A-Z