Introduction to Random Signals and Noise (Hardcover)

Description:

Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal.

With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals.

Key features:

• Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains.
• Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver.
• Examines optimal filtering methods and their consequences.
• Presents a detailed discussion of the topic of Poisson processes and shot noise.

An excellent resource for professional engineers developing communication systems, semiconductor devices, and audio and video equipment, this book is also ideal for senior undergraduate and graduate students in Electronic and Electrical Engineering.

 

Table of Contents:

Preface.

1 Introduction.

1.1 Random Signals and Noise.

1.2 Modelling.

1.3 The Concept of a Stochastic Process.

1.4 Summary.

2 Stochastic Processes.

2.1 Stationary Processes.

2.2 Correlation Functions.

2.3 Gaussian Processes.

2.4 Complex Processes.

2.5 Discrete-Time Processes.

2.6 Summary.

2.7 Problems.

3 Spectra of Stochastic Processes.

3.1 The Power Spectrum.

3.2 The Bandwidth of a Stochastic Process.

3.3 The Cross-Power Spectrum.

3.4 Modulation of Stochastic Processes.

3.5 Sampling and Analogue-To-Digital Conversion.

3.6 Spectrum of Discrete-Time Processes.

3.7 Summary.

3.8 Problems.

4. Linear Filtering of Stochastic Processes.

4.1 Basics of Linear Time-Invariant Filtering.

4.2 Time Domain Description of Filtering of Stochastic Processes.

4.3 Spectra of the Filter Output.

4.4 Noise Bandwidth.

4.5 Spectrum of a Random Data Signal.

4.6 Principles of Discrete-Time Signals and Systems.

4.7 Discrete-Time Filtering of Random Sequences.

4.8 Summary.

4.9 Problems.

5 Bandpass Processes.

5.1 Description of Deterministic Bandpass Signals.

5.2 Quadrature Components of Bandpass Processes.

5.3 Probability Density Functions of the Envelope and Phase of Bandpass Noise.

5.4 Measurement of Spectra.

5.5 Sampling of Bandpass Processes.

5.6 Summary.

5.7 Problems.

6 Noise in Networks and Systems.

6.1 White and Coloured Noise.

6.2 Thermal Noise in Resistors.

6.3 Thermal Noise in Passive Networks.

6.4 System Noise.

6.5 Summary.

6.6 Problems.

7 Detection and Optimal Filtering.

7.1 Signal Detection.

7.2 Filters that Maximize the Signal-to-Noise Ratio.

7.3 The Correlation Receiver.

7.4 Filters that Minimize the Mean-Squared Error.

7.5 Summary.

7.6 Problems.

8 Poisson Processes and Shot Noise.

8.1 Introduction.

8.2 The Poisson Distribution.

8.3 The Homogeneous Poisson Process.

8.4 Inhomogeneous Poisson Processes.

8.5 The Random-Pulse Process.

8.6 Summary.

8.7 Problems.

References.

Further Reading.

Appendices.

A. Representation of Signals in a Signal Space.

A.1 Linear Vector Spaces.

A.2 The Signal Space Concept.

A.3 Gram–Schmidt Orthogonalization.

A.4 The Representation of Noise in Signal Space.

A.5 Signal Constellations.

A.6 Problems.

B. Attenuation, Phase Shift and Decibels.

C. Mathematical Relations.

C.1 Trigonometric Relations.

C.2 Derivatives.

C.3 Indefinite Integrals.

C.4 Definite Integrals.

C.5 Series.

C.6 Logarithms.

D. Summary of Probability Theory.

E. Definition of a Few Special Functions.

F. The Q(.) and erfc Function.

G. Fourier Transforms.

H. Mathematical and Physical Constants.

Index.

描述：

在許多工程系統和網絡中，隨機信號和噪音是存在的。信號處理技術使工程師能夠區分音頻、視頻或通信設備中的有用信號和干擾干擾所帶來的期望信號的干擾。

憑藉堅實的數學基礎，本書清晰地介紹了隨機過程的基礎知識及其在隨機信號和噪音中的實際應用。通過實例、問題和詳細的附錄，隨機信號和噪音導論使讀者獲得設計最佳系統以有效應對不需要的信號的知識。

主要特點：

• 考慮了各種信號和噪音，包括模擬、離散時間和帶通信號在時間和頻率域中的情況。
  


• 分析了使用匹配濾波、信號空間表示和相關接收器的數字信號檢測的基礎。
  


• 研究了最優濾波方法及其結果。
  


• 詳細討論了泊松過程和脈沖噪音的主題。

對於開發通信系統、半導體設備和音頻視頻設備的專業工程師來說，這是一個很好的資源，同時也非常適合電子和電氣工程的高年級本科生和研究生。

 

目錄：

前言。

1 引言。

1.1 隨機信號和噪音。

1.2 建模。

1.3 隨機過程的概念。

1.4 概要。

2 隨機過程。

2.1 靜態過程。

2.2 相關函數。

2.3 高斯過程。

2.4 複雜過程。

2.5 離散時間過程。

2.6 概要。

2.7 問題。

3 隨機過程的頻譜。

3.1 功率譜。

3.2 隨機過程的帶寬。

3.3 交叉功率譜。

3.4 隨機過程的調製。

3.5 取樣和類比到數字轉換。

3.6 離散時間過程的頻譜。

3.7 概要。

3.8 問題。