Description

For upper-level undergraduate courses in deterministic and stochastic signals and system engineering

An Integrative Approach to Signals, Systems and Inference

Signals, Systems and Inference is a comprehensive text that builds on introductory courses in time- and frequency-domain analysis of signals and systems, and in probability. Directed primarily to upper-level undergraduates and beginning graduate students in engineering and applied science branches, this new textbook pioneers a novel course of study. Instead of the usual leap from broad introductory subjects to highly specialised advanced subjects, this engaging and inclusive text creates a study track for a transitional course.

Properties and representations of deterministic signals and systems are reviewed and elaborated on, including group delay and the structure and behavior of state-space models. The text also introduces and interprets correlation functions and power spectral densities for describing and processing random signals. Application contexts include pulse amplitude modulation, observer-based feedback control, optimum linear filters for minimum mean-square-error estimation, and matched filtering for signal detection. Model-based approaches to inference are emphasised, in particular for state estimation, signal estimation, and signal detection.

Features

Signals, Systems and Inference facilitates learning with the following features.

A text structure that is highly organised and easy to navigate

• The text is divided into four major parts:
• Chapters 1-3 present a review of the assumed prerequisite notions in signals and systems, and apply these to digital communication by pulse amplitude modulation.
• Chapters 4-6 treat space-state models,
  • concentrating on the single-input single-output LTI case;
  • introducing the idea of model-based inference;
  • examining associated feedback control strategies.
• Chapters 7-9 provide a review of assumed prerequisites in probability, including estimation and hypothesis testing for static random variables.
• Chapters 10-13 explore wide-sense stationary random signals and their processing by LTI systems for various applications.
  • The properties and interpretations of correlation functions and power spectral densities are developed in Chapters 10-11,and used in the remaining chapters to study canonical inference problems in signal estimation and signal detection.
  • Chapter 12 focuses on Wiener filtering, or linear minimum mean square error signal estimation.
  • Chapter 13 emphasises signal detection problems for which the optimum solutions involve matched filtering.

Thorough and interesting chapters full of information

• An exploration of fundamental material in an interesting and engaging manner.
• Further Reading sections at the end of each chapter help students gain further knowledge of the subject matter.
• Basic, Advanced, and Extension problems that review chapter material and ask the students to test and apply their knowledge of the subject.

A flexible approach to a broad course of study

• Since there is more material in this text than can comfortably be taught in a one-semester course, the text allows for different routes of instruction that emphasise various paths of study.
• Chapters 4-6 can be omitted or only briefly addressed in courses oriented towards communication and signal processing.
• Chapters 3, 9 and 13 can be considered optional for courses with more of a control orientation.

A course that includes core material from every chapter can be taught with two weekly lectures and associated small group discussions over an approximately 13-week semester.

Table of Contents

Preface

The Cover

Acknowledgments

Prologue

 

1. Signals and Systems

1.1 Signals, Systems, Models, and Properties

   1.1.1 System Properties

1.2 Linear, Time-Invariant Systems

   1.2.1 Impulse-Response Representation of LTI Systems

   1.2.2 Eigenfunction and Transform Representation of LTI Systems

   1.2.3 Fourier Transforms

1.3 Deterministic Signals and Their Fourier Transforms

   1.3.1 Signal Classes and Their Fourier Transforms

   1.3.2 Parseval’s Identity, Energy Spectral Density, and Deterministic Autocorrelation

1.4 Bilateral Laplace and Z-Transforms

   1.4.1 The Bilateral z-Transform

   1.4.2 The Bilateral Laplace Transform

1.5 Discrete-Time Processing of Continuous-Time Signals

   1.5.1 Basic Structure for DT Processing of CT Signals

   1.5.2 DT Filtering and Overall CT Response

   1.5.3 Nonideal D/C Converters

1.6 Further Reading

Problems

   Basic Problems

   Advanced Problems

   Extension Problems

 

2. Amplitude, Phase, and Group Delay

2.1 Fourier Transform Magnitude and Phase

2.2 Group Delay and the Effect of Nonlinear Phase

   2.2.1 Narrowband Input Signals

   2.2.2 Broadband Input Signals

2.3 All-Pass and Minimum-Phase Systems

   2.3.1 All-Pass Systems

   2.3.2 Minimum-Phase Systems

   2.3.3 The Group Delay of Minimum-Phase Systems

2.4 Spectral Factorization

2.5 Further Reading

Problems

   Basic Problems

   Advanced Problems

   Extension Problems

 

3. Pulse-Amplitude Modulation

3.1 Baseband Pulse-Amplitude Modulation

   3.1.1 The Transmitted Signal

   3.1.2 The Received Signal

   3.1.3 Frequency-Domain Characterizations

   3.1.4 Intersymbol Interference at the Receiver

3.2 Nyquist Pulses

3.3 Passband Pulse-Amplitude Modulation

   3.3.1 Frequency-Shift Keying (FSK)

   3.3.2 Phase-Shift Keying (PSK)

   3.3.3 Quadrature-Amplitude Modulation (QAM)

3.4 Further Reading

Problems

   Basic Problems

   Advanced Problems

   Extension Problems

 

4. State-Space Models

4.1 System Memory

4.2 Illustrative Examples

4.3 State-Space Models

   4.3.1 DT State-Space Models

   4.3.2 CT State-Space Models

   4.3.3 Defining Properties of State-Space Models

4.4 State-Space Models from LTI Input-Output Models

4.5 Equilibria and Linearization of Nonlinear State-Space Models

   4.5.1 Equilibrium

   4.5.2 Linearization

4.6 Further Reading

Problems

   Basic Problems

   Advanced Problems

   Extension Problems

 

5. LTI State-Space Models

5.1 Continuous-Time and Discrete-Time LTI Models

5.2 Zero-Input Response and Modal Representation

   5.2.1 Undriven CT Systems

   5.2.2 Undriven DT Systems

   5.2.3 Asymptotic Stability of LTI Systems

5.3 General Response in Modal Coordinates

   5.3.1 Driven CT Systems

   5.3.2 Driven DT Systems

   5.3.3 Similarity Transformations and Diagonalization

5.4 Transfer Functions, Hidden Modes, Reachability, and Observability

   5.4.1 Input-State-Output Structure of CT Systems

   5.4.2 Input-State-Output Structure of DT Systems

5.5 Further Reading