Signal Processing And Linear Systems

BACKGROUND B.1 Complex Numbers B.2 Sinusoids B.3 Sketching Signals B.4 Cramer's Rule B.5 Partial Fraction Expansion B.6 Vectors and Matrices B.7 Miscellaneous CHAPTER 1. INTRODUCTION TO SIGNALS AND SYSTEMS 1.1 Size of a Signal 1.2 Classification of Signals 1.3 Some Useful Signal Operations 1.4 Some Useful Signal Models 1.5 Even and Odd Functions 1.6 Systems 1.7 Classification of Systems 1.8 System Model: Input-Output Description CHAPTER 2. TIME-DOMAIN ANALYSIS OF CONTINUOUS-TIME SYSTEMS 2.1 Introduction 2.2 System Response to Internal Conditions: 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 CHAPTER 3. SIGNAL REPRESENTATION BY FOURIER SERIES 3.1 Signals and Vectors 3.2 Signal Comparison: Correlation 3.3 Signal Representation by Orthogonal Signal Set 3.4 Trigonometric Fourier Series 3.5 Exponential Fourier Series 3.6 Numerical Computation of D[n 3.7 LTIC System response to Periodic Inputs 3.8 Appendix CHAPTER 4. CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER TRANSFORM 4.1 Aperiodic Signal Representation by Fourier Integral 4.2 Transform of Some Useful Functions 4.3 Some Properties of the Fourier Transform 4.4 Signal Transmission through LTIC Systems 4.5 Ideal and Practical Filters 4.6 Signal Energy 4.7 Application to Communications: Amplitude Modulation 4.8 Angle Modulation 4.9 Data Truncation: Window Functions CHAPTER 5. SAMPLING 5.1 The Sampling Theorem 5.2 Numerical Computation of Fourier Transform: The Discrete Fourier Transform (DFT) 5.3 The Fast Fourier Transform (FFT) 5.4 Appendix 5.1 CHAPTER 6. CONTINUOUS-TIME SYSTEM ANALYSIS USING THE LAPLACE TRANSFORM 6.1 The Laplace Transform 6.2 Some Properties of the Laplace Transform 6.3 Solution of Differential and Integro-Differential Equations 6.4 Analysis of Electrical Networks: The Transformed Network 6.5 Block Diagrams 6.6 System Realization 6.7 Application to Feedback and Controls 6.8 The Bilateral Laplace Transform 6.9 Appendix 6.1: Second Canonical Realization CHAPTER 7. FREQUENCY RESPONSE AND ANALOG FILTERS 7.1 Frequency Response of an LTIC System 7.2 Bode Plots 7.3 Control System Design Using Frequency Response 7.4 Filter Design by Placement of Poles and Zeros of H(s) 7.5 Butterworth Filters 7.6 Chebyshev Filters 7.7 Frequency Transformations 7.8 Filters to Satisfy Distortionless Transmission Conditions CHAPTER 8. DISCRETE-TIME SIGNALS AND SYSTEMS 8.1 Introduction 8.2 Some Useful Discrete-Time Signal Models 8.3 Sampling Continuous-Time Sinusoids and Aliasing 8.4 Useful Signal Operations 8.5 Examples of Discrete-Time Systems CHAPTER 9. TIME-DOMAIN ANALYSIS OF DISCRETE-TIME SYSTEMS 9.1 Discrete-Time System Equations 9.2 System Response to Internal Conditions: Zero-Input Response 9.3 Unit Impulse Response h[k] 9.4 System Response to External Input: Zero-State Response 9.5 Classical Solution of Linear Difference Equations 9.6 System Stability 9.7 Appendix 9.1: Determining Impulse Response CHAPTER 10. FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS 10.1 Periodic Signal Representation by Discrete-Time Fourier Series 10.2 Aperiodic Signal Representation by Fourier Integral 10.3 Properties of DTFT 10.4 DTFT Connection with the Continuous-Time Fourier Transform 10.5 Discrete-Time Linear System Analysis by DTFT 10.6 Signal Processing Using DFT and FFT 10.7 Generalization of DTFT to the Z-Transform CHAPTER 11. DISCRETE-TIME SYSTEM ANALYSIS USING THE Z-TRANSFORM 11.1 The Z-Transform 11.2 Some Properties of the Z-Transform 11.3 Z-Transform Solution of Linear Difference Equations 11.4 System Realization 11.5 Connection Between the Laplace and the Z-Transform 11.6 Sampled-Data (Hybrid) Systems 11.7 The Bilateral Z-Transform CHAPTER 12. FREQUENCY RESPONSE AND DIGITAL FILTERS 12.1 Frequency Response of Discrete-Time Systems 12.2 Frequency Response From Pole-Zero Location 12.3 Digital Filters 12.4 Filter Design Criteria 12.5 Recursive Filter Design: The Impulse Invariance Method 12.6 Recursive Filter Design: The Bilinear Transformation Method 12.7 Nonrecursive Filters 12.8 Nonrecursive Filter Design CHAPTER 13. STATE-SPACE ANALYSIS 13.1 Introduction 13.2 Systematic Procedure for Determining State Equations 13.3 Solution of State Equations 13.4 Linear Transformation of State Vector 13.5 Controllability and Observability 13.6 State-Space Analysis of Discrete-Time Systems ANSWERS TO SELECTED PROBLEMS SUPPLEMENTARY READING INDEX Each chapter ends with a Summary