Introduction to Random Signals and Noise (PDF)

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

Wim C. van Etten, University of Twente, Department of
Electrical Engineering, Enschede, Netherlands

Wim Van Etten was appointed as a Full Professor of
Telecommunications at the University of Twente, Enschede, the
Netherlands, in 1994, where he heads a group on telecommunication
engineering.

He is author or co-author of over eighty papers in international
journals, conferences and symposia and his current interests
comprise of optical communications, mobile communications,
communication networks, detection, and simulation of communication
systems.

He is also past-president of the NERG (Dutch Institute of
Electronic and Radio Engineers) and Chairman of the executive
committee of the IEEE Benelux joint Chapter on Communications and
Vehicular Technology.

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