Synopses & Reviews
The State-Space Description
MATLAB Session 1: Working with Functions
1.M.1. Inline Functions
1.M.2. Relational Operators and the Unit Step Function
1.M.3. Visualizing Operations on the Independent Variable
1.M.4. Numerical Integration and Estimating Signal Energy
2. Time-Domain Analysis of Continuous-Time Systems
2.1. Introduction
2.2. System Response to Internal Conditions: The Zero-Input Response
2.3. The Unit Impulse Response h(t)
2.4. System Response to External Input: Zero-State Response
2.5. Classical Solution of Differential Equations
2.6. System Stability
2.7. Intuitive Insights into System Behavior
2.8. Appendix 2.1: Determining the Impulse Response
MATLAB Session 2: M-Files
2.M.1. Script M-Files
2.M.2. Function M-Files
2.M.3. For Loops
2.M.4. Graphical Understanding of Convolution
3. Time-Domain Analysis of Discrete-Time Systems
3.1. Introduction
3.2. Useful Signal Operations
3.3. Some Useful Discrete-Time Signal Models
3.4. Examples of Discrete-Time Systems
3.5. Discrete-Time System Equations
3.6. System Response to Internal Conditions: The Zero-Input Response
3.7. The Unit Impulse Response h[n]
3.8. System Response to External Input: The Zero-State Response
3.9. Classical Solution of Linear Difference Equations
3.10. System Stability: The External (BIBO) Stability Criterion
3.11. Intuitive Insights into System Behavior
3.12. Appendix 3.1: Impulse Response for a Special Case When aN = 0
MATLAB Session 3: Discrete-Time Signals and Systems
3.M.1. Discrete-Time Functions and Stem Plots
3.M.2. System Responses Through Filtering
3.M.3. A Custom Filter Function
3.M.4. Discrete-Time Convolution
4. Continuous-Time System Analysis Using the Laplace Transform
4.1. The Laplace Transform
4.2. Some Properties of the Laplace Transform
4.3. Solution of Differential and Integro-Differential Equations
4.4. Analysis of Electrical Networks: The Transformed Network
4.5. Block Diagrams
4.6. System Realization
4.7. Application to Feedback and Controls
4.8. Frequency-Response of an LTIC System
4.9. Bode Plots
4.10. Filter Design by Placement of Poles and Zeros of H(s)
4.11. The Bilateral Laplace Transform
MATLAB Session 4: Continuous-Time Filters
4.M.1. Frequency Response and Polynomial Evaluation
4.M.2. Design and Evaluation of a Simple RC Filter
4.M.3. A Cascaded RC Filter and Polynomial Expansion
4.M.4. Butterworth Filters and the FIND Command
4.M.5. Butterworth Filter Realization Using Cascaded Second.Order Sections
4.M.6. Chebyshev Filters
5. Discrete-Time System Analysis Using the z-Transform
5.1. The z-Transform
5.2. Some Properties of the z-Transform
5.3. z-Transform Solution of Linear Difference equations
5.4. System Realization
5.5. Frequency Response of Discrete-Time Systems
5.6. Frequency Response from Pole-Zero Location
5.7. Digital Processing of Analog Signals
5.8. Connection Between the Laplace and the z-Transform
5.9. The Bilateral z-Transform
MATLAB Session 5: Discrete-Time IIR Filters
5.M.1. Frequency Response and Pole-Zero Plots
5.M.2. Transformation Basics
5.M.3. Transformation by First-Order Backward Difference
5.M.4. Bilinear Transformation
5.M.5. Bilinear Transformation with Prewarping
5.M.6. Example: Butterworth Filter Transformation
5.M.7. Problems Finding Polynomial Roots
5.M.8. Improved Design Using Cascaded Second-Order Sections
6. Continuous-Time Signal Analysis: The Fourier Series
6.1. Periodic Signal Representation by Trigonometric Fourier Series
6.2. Existence and Convergence of the Fourier Series
6.3. Exponential Fourier Series
6.4. LTIC System Response to Periodic Inputs
6.5. Generalized Fourier Series: Signals as Vectors
6.6. Numerical Computation of Dn
MATLAB Session 6: Fourier Series Applications
6.M.1. Periodic Functions and the Gibbs Phenomenon
6.M.2. Optimization and Phase Spectra
7. Continuous-Time Signal Analysis: The Fourier Transform
7.1. Aperiodic Signal Representation by Fourier Integral
7.2. Transforms of Some Useful Functions
7.3. Some Properties of the Fourier Transform
7.4. Signal Transmission Through LTIC Systems
7.5. Ideal and Practical Filters
7.6. Signal Energy
7.7. Application to Communications: Amplitude Modulation
7.8. Data Truncation: Window Functions
MATLAB Session 7: Fourier Transform Topics
7.M.1. The Sinc Function and the Scaling Property
7.M.2. Parseval's Theorem and Essential Bandwidth
7.M.3. Spectral Sampling
7.M.4. Kaiser Window Functions
8. Sampling: The Bridge from Continuous to Discrete
8.1. The Sampling Theorem
8.2. Signal Reconstruction
8.3. Analog-to-Digital (A/D) Conversion
8.4. Dual of Time-Sampling: The Spectral Sampling
8.5. Numerical Computation of the Fourier Transform: The Discrete Fourier Transform (DFT)
8.6. The Fast Fourier Transform (FFT)
MATLAB Session 8: The Discrete Fourier Transform
8.M.1. Computing the Discrete Fourier Transform
8.M.2. Improving the Picture with Zero-Padding
8.M.3. Quantization
9. Fourier Analysis of Discrete-Time Signals
9.1. Discrete-Time Fourier Series (DTFS)
9.2. Aperiodic Signal Representation by Fourier Integral
9.3. Properties of DTFT
9.4. LTI Discrete-Time System Analysis by DTFT
9.5. DTFT Connection with the CTFT
9.6. Generalization of the DTFT and the z-Transform
MATLAB Session 9: Working with the DTFS and the DTFT
9.M.1. Computing the Discrete-Time Fourier Series
9.M.2. Measuring Code Performance
9.M.3. FIR Filter Design by Frequency Sampling
10. State-Space Analysis
10.1. Introduction
10.2. A Systematic Procedure for Determining State Equations
10.3. Solution of State Equations
10.4. Linear Transformation of State Vectors
10.5. Controllability and Observability
10.6. State-Space Analysis of Discrete-Time Systems
MATLAB Session 10: Toolboxes and State-Space Analysis
10.M.1. z-Transform Solutions to Discrete-Time State-Space Systems
10.M.2. Transfer Functions from State-Space Representations
10.M.3. Controllability and Observability of Discrete-Time Systems
10.M.4. Matrix Exponentiation and the Matrix Exponential
Index
Synopsis
B. P. Lathi's trademark strengths as a writer have made this introductory volume a well-established leader in the field of signals and linear systems. His rigorous but clear explanations, engaging writing style, vivid examples, and sensitivity to student needs enliven the subject in a comfortable non-threatening way. Now published by Oxford University Press, Linear Systems and Signals provides a comprehensive treatment of the subject and encourages students to discover information and principles on their own. Lathi uses mathematics to enhance physical and intuitive understanding, instead of merely employing it to prove axiomatic theory. The book is conveniently organized into five parts that allow flexibility in teaching discrete-time and continuous-time systems. An accompanying solutions manual is available on CD-ROM.
Synopsis
Incorporating new problems and examples, the second edition of Linear Systems and Signals features MATLAB® material in each chapter and at the back of the book. It gives clear descriptions of linear systems and uses mathematics not only to prove axiomatic theory, but also to enhance physical and intuitive understanding.
Synopsis
B. P. Lathi's trademark strengths as a writer have made this introductory volume a well-established leader in the field of signals and linear systems. His rigorous but clear explanations, engaging writing style, vivid examples, and sensitivity to student needs enliven the subject in a
comfortable non-threatening way. Now published by Oxford University Press, Linear Systems and Signals provides a comprehensive treatment of the subject and encourages students to discover information and principles on their own. Lathi uses mathematics to enhance physical and intuitive understanding,
instead of merely employing it to prove axiomatic theory. The book is conveniently organized into five parts that allow flexibility in teaching discrete-time and continuous-time systems. An accompanying solutions manual is available on CD-ROM.
About the Author
B. P. Lathi is Professor Emeritus of Electrical Engineering at California State University, Sacramento. He is the author of
Signal Processing and Linear Systems (OUP, 2000) and
Modern Digital and Analog Communications Systems, 3/e (OUP, 1998).
Table of Contents
PART I: INTRODUCTION
B. Background
B.1. Complex Numbers
B.2. Sinusoids
B.3. Sketching Signals
B.4. Some Useful Signal Operations
B.5. Mathematical Description of a Signal from its Sketch
B.6. Even and Odd Functions
B.7. Cramer's Rule
B.8. Partial Fraction Expansion
B.9. Vectors and Matrices
B.10. Miscellaneous
1. Introduction to Systems
1.1. Signals and Systems
1.2. Classification of Systems
1.3. System Model: Input-output Description
1.4. Simultaneous Differential Equations
1.5. Internal and External Description of a System
1.6. State-Space Description of a System
1.7. Summary
PART II: TIME-DOMAIN ANALYSIS OF LTI SYSTEMS
2. Time-Domain Analysis: Continuous-Time Systems
2.1. Introduction
2.2. System Response to Internal Conditions: Zero-Input Response
2.3. Unit Impulse Function
2.4. System Response to External Input: Zero-State Response
2.5. Numerical Convolution
2.6. System Stability
2.7. Intuitive Insights in System Behavior
2.8. Classical Solution of Differential Equations
2.9. Appendix 2.1: Determining the Impulse Response
2.10. Summary
3. Time-Domain Analysis: Discrete-Time Systems
3.1. Discrete-Time Systems
3.2. Discrete-Time Systems Equations
3.3. System Response to Internal Conditions: Zero-Input Response
3.4. Unit Impulse Response
3.5. System Response to External Input: Zero-State Response
3.6. System Stability
3.7. Intuitive Insights in System Behavior
3.8. Classical Solution of Linear Difference Equations
3.9. Appendix 3.1: Determining Impulse Response
3.10. Summary
PART III: FREQUENCY-DOMAIN (TRANSFORM) ANALYSIS OF LTI SYSTEMS
4. Continuous-Time Systems: Laplace Transform Analysis
4.1. The Laplace Transform
4.2. Some Properties of the Laplace Transform
4.3. Transform Solution of Differential and Integro-Differential Equations
4.4. Analysis of Electrical Networks: Transformed Network Method
4.5. Block Diagrams
4.6. System Realization
4.7. Frequency-Response of an LTIC System
4.8. Bilateral Laplace Transform
4.9. Appendix 4.1: Second Canonical Realization
4.10. Summary
5. Discrete-Time Systems: Z-Transform Analysis
5.1. The Z-Transform
5.2. Some Properties of the Z-Transform
5.3. Z-Transform Solution of Difference Equations
5.4. System Realization
5.5. Frequency Response of Discrete-Time Systems
5.6. Connection between the Z-Transform and Laplace Transform
5.7. Bilateral Z-Transform
5.8. Summary
PART IV: SIGNAL ANALYSIS
6. Continuous-Time Signal Analysis: The Fourier Series
6.1. Representation of Periodic Signals by Trigonometric Fourier Series
6.2. Exponential
6.3. Alternate View of Fourier Representation: Signal-Vector Analogy
6.4. Summary
7. Continuous-Time Signal Analysis: The Fourier Transform
7.1. Nonperiodic Signal Representation by Fourier Integral
7.2. Physical Appreciation of the Fourier Transform
7.3. Transform of Some Useful Functions
7.4. Some Properties of the Fourier Transform
7.5. LTI System Analysis by Fourier Transform
7.6. Signal Distortion During Transmission
7.7. Ideal and Practical Filters
7.8. Thinking in Time-Domain and Frequency-Domain: Two-Dimensional View of Signals and Systems
7.9. Signal Energy
7.10. Data Truncation: Window Functions
7.11. Summary
8. Sampling
8.1. The Sampling Theorem
8.2. Dual of the Sampling Theorem: Spectral Sampling
8.3. Numerical Computation of Fourier Transform: The Discrete Fourier Transform (DFT)
8.4. Summary
9. Analysis of Discrete-Time Signals
9.1. Discrete-Time Periodic Signals
9.2. Nonperiodic Signals: The Discrete-Time Fourier Transform (DTFT)
9.3. Properties of DTFT
9.4. LTID System Analysis by STFT
9.5. Relationships Among Various Transforms
9.6. Derivation of the Z-Transform Pair
9.7. Summary
PART V: STATE-SPACE ANALYSIS
10. State-Space Analysis
10.1. Introduction
10.2. Systematic Procedure for Determining State Equations
10.3. Solution of State Equations
10.4. Linear Transformation of State Vector
10.5. Controllability and Observability
10.6. State-Space Analysis of Discrete-Time Systems
10.7. Summary
Supplementary Reading
Index