Signal Processing and Linear Systems

Chapter B: 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 MATLAB: Elementary Operations B.8 Appendix: Useful Mathematical Formulas

Chapter 1: Signals and Systems 1.1 Size of a Signal 1.2 Some Useful Signal Operations 1.3 Classification of Signals 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 1.9 Internal and External Descriptions of a System 1.10 Internal Description: The State-Space Description 1.11 MATLAB: Working with Functions 1.12 Summary

Chapter 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: The Zero-State Response 2.5 System Stability 2.6 Intuitive Insights into System Behavior 2.7 MATLAB: M-Files 2.8 Appendix: Determining the Impulse Response 2.9 Summary

Chapter 3: Signal Representation by Fourier Series 3.1 Signals as Vectors 3.2 Signal Comparison: Correlation 3.3 Signal Representation by an Orthogonal Signal Set 3.4 Trigonometric Fourier Series 3.5 Existence and Convergence of the Fourier Series 3.6 Exponential Fourier Series 3.7 LTIC System Response to Periodic Inputs 3.8 Numerical Computation of Dn 3.9 MATLAB: Fourier Series Applications 3.10 Summary

Chapter 4: Continuous-Time Signal Analysis: The Fourier Transform 4.1 Aperiodic Signal Representation by the Fourier Integral 4.2 Transforms 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 4.10 MATLAB: Fourier Transform Topics 4.11 Summary

Chapter 5: Sampling 5.1 The Sampling Theorem 5.2 Signal Reconstruction 5.3 Analog-to-Digital (A/D) Conversion 5.4 Dual of Time Sampling: Spectral Sampling 5.5 Numerical Computation of the Fourier Transform: The Discrete Fourier Transform 5.6 The Fast Fourier Transform (FFT) 5.7 MATLAB: The Discrete Fourier Transform 5.8 Summary

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 6.3.4 Inverse Systems 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 Summary

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 7.9 MATLAB: Continuous-Time Filters 7.10 Summary

Chapter 8: Discrete-Time Signals and Systems 8.1 Introduction 8.2 Useful Signal Operations 8.3 Some Useful Discrete-Time Signal Models 8.4 Aliasing and Sampling Rate 8.5 Examples of Discrete-Time Systems 8.6 MATLAB: Representing, Manipulating, and Plotting Discrete-Time Signals 8.7 Summary

Chapter 9: Time-Domain Analysis of Discrete-Time Systems 9.1 Classification of Discrete-Time Systems 9.2 Discrete-Time System Equations 9.3 System Response to Internal Conditions: The Zero-Input Response 9.4 The Unit Impulse Response h[n] 9.5 System Response to External Input: The Zero-State Response 9.6 System Stability 9.7 Intuitive Insights into System Behavior 9.8 MATLAB: Discrete-Time Systems 9.9 Appendix: Impulse Response for a Special Case 9.10 Summary

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 the DTFT 10.4 DTFT Connection with the CTFT 10.5 LTI Discrete-Time System Analysis by 10.6 Signal Processing by the DFT and FFT 10.7 Generalization of the DTFT to the z-Transform 10.8 MATLAB: Working with the DTFS and the DTFT 10.9 Summary

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 Connecting the Laplace and z-Transforms 11.6 Sampled-Data (Hybrid) Systems 11.7 The Bilateral z-Transform 11.8 Summary

Chapter 12: Frequency Response and Digital Filters 12.1 Frequency Response of Discrete-Time Systems 12.2 Frequency Response from Pole-Zero Locations 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 12.9 MATLAB: Designing High-Order Filters 12.10 Summary

Chapter 13: State-Space Analysis 13.1 Mathematical Preliminaries 13.2 Introduction to State Space 13.3 A Systematic Procedure to Determine State Equations 13.4 Solution of State Equations 13.5 Linear Transformation of a State Vector 13.6 Controllability and Observability 13.7 State-Space Analysis of Discrete-Time Systems 13.8 MATLAB: Toolboxes and State-Space Analysis 13.9 Summary