Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications (Hardcover)

An engineering perspective on probability and random processes

Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background.

The book has the following features:

• Several appendices include related material on integration, important inequalities and identities, frequency-domain transforms, and linear algebra. These topics have been included so that the book is relatively self-contained. One appendix contains an extensive summary of 33 random variables and their properties such as moments, characteristic functions, and entropy.
• Unlike most books on probability, numerous figures have been included to clarify and expand upon important points. Over 600 illustrations and MATLAB® plots have been designed to reinforce the material and illustrate the various characterizations and properties of random quantities.
• Sufficient statistics are covered in detail, as is their connection to parameter estimation techniques. These include classical Bayesian estimation and several optimality criteria: mean-square error, mean-absolute error, maximum likelihood, method of moments, and least squares.
• The last four chapters provide an introduction to several topics usually studied in subsequent engineering courses: communication systems and information theory; optimal filtering (Wiener and Kalman); adaptive filtering (FIR and IIR); and antenna beamforming, channel equalization, and direction finding. This material is available electronically at the companion website.

Probability, Random Variables, and Random Processes is the only textbook on probability for engineers that includes relevant background material, provides extensive summaries of key results, and extends various statistical techniques to a range of applications in signal processing.

《概率和隨機過程的工程觀點》

《概率、隨機變量和隨機過程》是一本針對工程師的概率理論綜合教材，提供了比大學本科課程中通常遇到的更嚴謹的數學框架。它適用於有一定概率和隨機變量知識的研究生一年級學生，雖然不一定熟悉隨機過程和作用於隨機信號的系統。它也適用於具有強大數學背景的高年級本科生。

本書具有以下特點：
- 包含多個附錄，其中包括有關積分、重要不等式和恆等式、頻域變換以及線性代數的相關材料。這些主題被包含在內，以使本書相對自成一體。其中一個附錄包含了對33個隨機變量及其特性（如矩、特徵函數和熵）的廣泛摘要。
- 與大多數概率書籍不同，本書包含了大量圖示，以澄清和擴展重要觀點。超過600個插圖和MATLAB®繪圖被設計用於加強材料並說明隨機量的各種特性和性質。
- 詳細介紹了充分統計量及其與參數估計技術的聯繫。這些包括傳統的貝葉斯估計和幾個最優性準則：均方誤差、平均絕對誤差、最大似然、矩法和最小二乘法。
- 最後四章介紹了通常在後續工程課程中學習的幾個主題：通信系統和信息理論；最優濾波（Wiener和Kalman）；自適應濾波（FIR和IIR）；以及天線波束成形、信道均衡和方向尋找。這些材料可以在配套網站上以電子形式獲得。

《概率、隨機變量和隨機過程》是唯一一本針對工程師的概率教材，包含相關背景材料，提供了重要結果的廣泛摘要，並將各種統計技術擴展到信號處理的各種應用中。