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.
This introductory level book gives comprehensive treatment to signals and linear systems. In it, the physical appreciation of concepts is emphasized rather than the mere mathematical manipulation of symbols. Mathematics is used to enhance physical and intuitive understanding, instead of to prove axiomatic theory. This conveniently organized book is divided into five parts and allows for the flexible teaching of discrete-time and continuous-time systems. Wherever possible, theoretical results are interpreted heuristically and are supported by carefully chosen examples and analogies.
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