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