Linear systems and signals : a primer / JC Olivier.

Format:

Book

Author/Creator:

Olivier, J. C. (Jan Corné), author.

Series:

Artech House radar library.

Artech House radar series

Language:

English

Subjects (All):

Signal processing--Mathematics.

Signal processing.

Linear time invariant systems.

Physical Description:

1 online resource (304 pages)

Edition:

1st ed.

Place of Publication:

Norwood, Massachusetts : Artech House, (c)2019.

Summary:

This new resource covers a wide range of content by focusing on theorems and examples to explain key concepts of signals and linear systems theory in fewer than 300 pages. Readers will learn how to compute the impulse response of an electronic circuit, design a filter in the presence of colored noise, and use the Z transform to design a digital filter. The book covers transform theory and statespace analysis and design. Stochastic systems and signals, a topic that has become important recently with the advent of renewable energy, is also presented. The Ergodic theorem is discussed in detail, with specific, real world examples of its application to renewable power and energy systems as well as signal processing systems. The book also provides a self-contained introduction to the theory of probability. Written for the practicing engineer and the student new to the subject, this comprehensive guide includes links to literature and online resources for the reader who wants additional information. In addition to numerous worked examples, this primer includes MATLABª source code to assist readers with their projects in the field. Publisher description.

Contents:

Intro

Linear Systems and Signals: A Primer

Contents

Preface

Part I Time Domain Analysis

Chapter 1 Introduction to Signals and Systems

1.1 Signals and Their Classification

1.2 Discrete Time Signals

1.2.1 Discrete Time Simulation of Analog Systems

1.3 Periodic Signals

1.4 Power and Energy in Signals

1.4.1 Energy and Power Signal Examples

References

Chapter 2 Special Functions and a System Point of View

2.1 The Unit Step or Heaviside Function

2.2 Dirac's Delta Function d(t)

2.3 The Complex Exponential Function

2.4 Kronecker Delta Function

2.5 A System Point of View

2.5.1 Systems With Memory and Causality

2.5.2 Linear Systems

2.5.3 Time Invariant Systems

2.5.4 Stable Systems

2.6 Summary

Chapter 3 The Continuous Time Convolution Theorem

3.1 Introduction

3.2 The System Step Response

3.2.1 A System at Rest

3.2.2 Step Response s(t)

3.3 The System Impulse Response h(t)

3.4 Continuous Time Convolution Theorem

3.5 Summary

Chapter 4 Examples and Applications of the Convolution Theorem

4.1 A First Example

4.2 A Second Example: Convolving with an Impulse Train

4.3 A Third Example: Cascaded Systems

4.4 Systems and Linear Di˛erential Equations

4.4.1 Example: A Second Order System

4.5 Continuous Time LTI System Not at Rest

4.6 Matched Filter Theorem

4.6.1 Monte Carlo Computer Simulation

4.7 Summary

Chapter 5 Discrete Time Convolution Theorem

5.1 Discrete Time IR

5.2 Discrete Time Convolution Theorem

5.3 Example: Discrete Convolution

5.4 Discrete Convolution Using a Matrix

5.5 Discrete Time Di˛erence Equations

5.5.1 Example: A Discrete Time Model of the RL Circuit

5.5.2 Example: The Step Response of a RL Circuit

5.5.3 Example: The Impulse Response of the RL Circuit.

5.5.4 Example: Application of the Convolution Theorem to Compute the Step Response

5.6 Generalizing the Results: Discrete TimeSystem of Order N

5.6.1 Constant-Coe˝cient Di˛erence Equation of Order N

5.6.2 Recursive Formulation of the Response y[n]

5.6.3 Computing the Impulse Response h[n]

5.7 Summary

Chapter 6 Examples: Discrete Time Systems

6.1 Example: Second Order System

6.2 Numerical Analysis of a Discrete System

6.3 Summary

Chapter 7 Discrete LTI Systems: State Space Analysis

7.1 Eigenanalysis of a Discrete System

7.2 State Space Representation and Analysis

7.3 Solution of the State Space Equations

7.3.1 Computing An

7.4 Example: State Space Analysis

7.4.1 Computing the Impulse Response h[n]

7.5 Analyzing a Damped Pendulum

7.5.1 Solution

7.5.2 Solving the Di˛erential Equation Numerically

7.5.3 Numerical Solution with Negligible Damping

7.6 Summary

Part II System Analysis Based on Transformation Theory

Chapter 8 The Fourier Transform Applied to LTI Systems

8.1 The Integral Transform

8.2 The Fourier Transform

8.3 Properties of the Fourier Transform

8.3.1 Convolution

8.3.2 Time Shifting Theorem

8.3.3 Linearity of the Fourier Transform

8.3.4 Di˛erentiation in the Time Domain

8.3.5 Integration in the Time Domain

8.3.6 Multiplication in the Time Domain

8.3.7 Convergence of the Fourier Transform

8.3.8 The Frequency Response of a Continuous Time LTI System

8.3.9 Further Theorems Based on the Fourier Transform

8.4 Applications and Insights Based on the Fourier Transform

8.4.1 Interpretation of the Fourier Transform

8.4.2 Fourier Transform of a Pulse (t)

8.4.3 Uncertainty Principle

8.4.4 Transfer Function of a Piece of Conducting Wire

8.5 Example: Fourier Transform of e tu(t).

8.5.1 Fourier Transform of u(t)

8.6 The Transfer Function of the RC Circuit

8.7 Fourier Transform of a Sinusoid and aCosinusoid

8.8 Modulation and a Filter

8.8.1 A Design Example

8.8.2 Frequency Translation and Modulation

8.9 Nyquist-Shannon Sampling Theorem

8.9.1 Examples

8.10 Summary

Chapter 9 The Laplace Transform and LTI Systems

9.1 Introduction

9.2 Definition of the Laplace Transform

9.2.1 Convergence of the Laplace Transform

9.3 Examples of the Laplace Transformation

9.3.1 An Exponential Function

9.3.2 The Dirac Impulse

9.3.3 The Step Function

9.3.4 The Damped Cosinusoid

9.3.5 The Damped Sinusoid

9.3.6 Laplace Transform of e-ajt

9.4 Properties of the Laplace Transform

9.4.1 Convolution

9.4.2 Time Shifting Theorem

9.4.3 Linearity of the Laplace Transform

9.4.4 Di˛erentiation in the Time Domain

9.4.5 Integration in the Time Domain

9.4.6 Final Value Theorem

9.5 The Inverse Laplace Transformation

9.5.1 Proper Rational Function: M &lt

N

9.5.2 Improper Rational Function: M N

9.5.3 Example: Inverse with a Multiple Pole

9.5.4 Example: Inverse without a Multiple Pole

9.5.5 Example: Inverse with Complex Poles

9.6 Table of Laplace Transforms

9.7 Systems and the Laplace Transform

9.8 Example: System Analysis Based on the Laplace Transform

9.9 Linear Di˛erential Equations and Laplace

9.9.1 Capacitor

9.9.2 Inductor

9.10 Example: RC Circuit at Rest

9.11 Example: RC Circuit Not at Rest

9.12 Example: Second Order Circuit Not at Rest

9.13 Forced Response and Transient

9.13.1 An Example with a Harmonic Driving Function

9.14 The Transfer Function H(w)

9.15 Transfer Function with Second Order Real Poles

9.16 Transfer Function for a Second Order System with Complex Poles

9.17 Summary

References.

Chapter 10 The z-Transform and Discrete LTI Systems

10.1 The z-Transform

10.1.1 Region of Convergence

10.2 Examples of the z-Transform

10.2.1 The Kronecker Delta d[n]

10.2.2 The Unit Step u[n]

10.2.3 The Sequence anu[n]

10.3 Table of z-Transforms

10.4 Properties of the z-Transform

10.4.1 Convolution

10.4.2 Time Shifting Theorem

10.4.3 Linearity of the z-transform

10.5 The Inverse z-Transform

10.5.1 Example: Repeated Pole

10.5.2 Example: Making use of Shifting Theorem

10.5.3 Example: Using Linearity and the Shifting Theorem

10.6 System Transfer Function for Discrete Time LTI systems

10.7 System Analysis using the z-Transform

10.7.1 Step Response with a Given Impulse Response

10.8 Example: System Not at Rest

10.9 Example: First Order System

10.9.1 Recursive Formulation

10.9.2 Zero Input Response

10.9.3 The Zero State Response

10.9.4 The System Transfer Function H(z)

10.9.5 Impulse Response h[n]

10.10 Second Order System Not at Rest

10.10.1 Numerical Example

10.11 Discrete Time Simulation

10.12 Summary

Chapter 11 Signal Flow Graph Representation

11.1 Block Diagrams

11.2 Block Diagram Simplification

11.3 The Signal Flow Graph

11.4 Mason's Rule: The Transfer Function

11.5 A First Example: Third Order Low Pass Filter

11.5.1 Making Use of a Graph

11.6 A Second Example: Canonical Feedback System

11.7 A Third Example: Transfer Function of a Block Diagram

11.8 Summary

Chapter 12 Fourier Analysis of Discrete-Time Systems and Signals

12.1 Introduction

12.2 Fourier Transform of a Discrete Signal

12.3 Properties of the Fourier Transform of Discrete Signals

12.4 LTI Systems and Di˛erence Equations

12.5 Example: Discrete Pulse Sequence

12.6 Example: A Periodic Pulse Train.

12.7 The Discrete Fourier Transform

12.8 Inverse Discrete Fourier Transform

12.9 Increasing Frequency Resolution

12.10 Example: Pulse with 1 and N Samples

12.11 Example: Lowpass Filter with the DFT

12.12 The Fast Fourier Transform

12.13 Summary

Part III Stochastic Processes and Linear Systems

Chapter 13 Introduction to Random Processes and Ergodicity

13.1 A Random Process

13.1.1 A Discrete Random Process: A Set of Dice

13.1.2 A Continuous Random Process: A Wind Electricity Farm

13.2 Random Variables and Distributions

13.2.1 First Order Distribution

13.2.2 Second Order Distribution

13.3 Statistical Averages

13.3.1 The Ensemble Mean

13.3.2 The Ensemble Correlation

13.3.3 The Ensemble Cross-Correlation

13.4 Properties of Random Processes

13.4.1 Statistical Independence

13.4.2 Uncorrelated

13.4.3 Orthogonal Processes

13.4.4 A Stationary Random Process

13.5 Time Averages and Ergodicity

13.5.1 Implications for a Stationary Random Process

13.5.2 Ergodic Random Processes

13.6 A First Example

13.6.1 Ensemble or Statistical Averages

13.6.2 Time Averages

13.6.3 Ergodic in the Mean and the Autocorrelation

13.7 A Second Example

13.7.1 Ensemble or Statistical Averages

13.7.2 Time Averages

13.8 A Third Example

13.9 Summary

Chapter 14 Spectral Analysis of Random Processes

14.1 Correlation and Power Spectral Density

14.1.1 Properties of the Autocorrelation for a WSS Process

14.1.2 Power Spectral Density of a WSS Random Process

14.1.3 Cross-Power Spectral Density

14.2 White Noise and a Constant Signal (DC)

14.2.1 White Noise

14.2.2 A Constant Signal

14.3 Linear Systems with a Random Process as Input

14.3.1 Cross-Correlation Between Input and Response

14.3.2 Relationship Between PSD of Input and Response.

14.4 Practical Applications.

Notes:

Includes index.

Description based on print version record.

Includes bibliographical references and index.

ISBN:

1-63081-615-9