| |
| |
| |
| Introduction | |
| |
| |
| |
| Basic Definitions | |
| |
| |
| |
| Classification of Signals and Systems | |
| |
| |
| |
| Frequency spectrum in Signal and System Analysis | |
| |
| |
| |
| Scope of the Text Summary Further Reading Problems | |
| |
| |
| |
| Mathematical Modeling and Properties of Basic Signals and Systems Introduction | |
| |
| |
| |
| Mathematical Modeling of Systems and Signals | |
| |
| |
| |
| Basic Signal Operations and Properties | |
| |
| |
| |
| Basic CT Signals | |
| |
| |
| |
| Basic DT Signals | |
| |
| |
| |
| Basic System Properties | |
| |
| |
| |
| Frequency Response and CT Filters | |
| |
| |
| |
| Discretization of CT Signal and System Models | |
| |
| |
| |
| Linearization of Nonlinear Systems Summary Key Equations Further Reading Problems | |
| |
| |
| |
| Continuous-Time System Analysis in Time Domain Introduction | |
| |
| |
| |
| Impulse-Response Characterization and the Convolution Integral for CT LTI Systems | |
| |
| |
| |
| Step and Other Causal Signal Responses of CT LTI Systems | |
| |
| |
| |
| Properties of Convolution | |
| |
| |
| |
| LTI System Properties from Impulse Response | |
| |
| |
| |
| Obtaining the Impulse Response of CT LTI Systems | |
| |
| |
| |
| System Analysis from a Linear Differential-Equation Model | |
| |
| |
| |
| CT System Response to Complex and Real Sinusoids and the system Function | |
| |
| |
| |
| Block Diagram Representation for System Simulation Summary Key Equations Problems | |
| |
| |
| |
| Discrete-Time System Analysis in the Time Domain - The Convolution Summation and Classical Analysis Introduction | |
| |
| |
| |
| Impulse Response Characterization and the Convolution Summation | |
| |
| |
| |
| Step and Other Causal Signal Response of DT LTI Systems | |
| |
| |
| |
| Properties of the Convolution Summation | |
| |
| |
| |
| Obtaining the Impulse Response of DT LTI Systems | |
| |
| |
| |
| LTI System Properties from Impulse Response | |
| |
| |
| |
| System Analysis from the Difference-Equation Model | |
| |
| |
| |
| Forced Response to Complex and Real Sinusoids and the System Function | |
| |
| |
| |
| Block Diagram Representation for System Simulation Summary Key Equations Further Reading Problems | |
| |
| |
| |
| Frequency Domain Analysis of CT Signals and Systems - The Fourier Series and the Fourier Transform Analysis Introduction | |
| |
| |
| |
| Representation of Signals using Basic Functions | |
| |
| |
| |
| Representation of Periodic Functions - The Exponential Fourier Series | |
| |
| |
| |
| Existence of Fourier Series | |
| |
| |
| |
| Other Forms of Fourier Series | |
| |
| |
| |
| Frequency Spectrum of Periodic Signals | |
| |
| |
| |
| Fourier Series Properties | |
| |
| |
| |
| Fourier Series Representation of an Ideal Impulse Train | |
| |
| |
| |
| System Analysis for Nonsinusoidal Periodic Inputs | |
| |
| |
| |
| Frequency Spectrum of Aperiodic Signals - The Fourier Transform | |
| |
| |
| |
| Existence of Fourier Transform | |
| |
| |
| |
| Fourier Transform of Basic Signals | |
| |
| |
| |
| Fourier Transform Properties | |
| |
| |
| |
| LTI System Analysis in the Frequency Domain | |
| |
| |
| |
| Ideal and Practical Filters Summary Key Equations Further Reading Problems | |
| |
| |
| |
| System Analysis Using the Laplace Transform Introduction | |
| |
| |
| |
| The Bilateral and Unilateral Laplace Transforms | |
| |
| |
| |
| Laplace Transforms of Basic Signals | |
| |
| |
| |
| Laplace Transform Properties | |
| |
| |
| |
| Relationship between Fourier and Laplace Transforms | |
| |
| |
| |
| The Inverse Laplace Transform | |
| |
| |
| |
| Applications of the Laplace Transform in Solving Differential Equations | |
| |
| |
| |
| LTI System Transfer Functions | |
| |
| |
| |
| System Response and Stability from Transfer Functions | |
| |
| |
| |
| Step Response of Stable Systems | |
| |
| |
| |
| Sinusoidal Response of Stable Systems and the Frequency Response | |
| |
| |
| |
| Bode Plots | |
| |
| |
| |
| System Simulation Summary Key Equations Further Reading Problems | |
| |
| |
| |
| The z Transform and Discrete-Time System Analysis Introduction | |
| |
| |
| |
| The z-Transform | |
| |
| |
| |
| Convergence of the z-Transform | |
| |
| |
| |
| Basic z-Transforms | |
| |
| |
| |
| Properties of the z-Transform | |
| |
| |
| |
| Right and Left Shifted Signals | |
| |
| |
| |
| Multiplication by an Exponential Signal | |
| |
| |
| |
| Differentiation in the z-Domain | |
| |
| |
| |
| Accumulation | |
| |
| |
| |
| Convolution of Signals | |
| |
| |
| |
| Initial Value | |
| |
| |
| |
| Time Reversal | |
| |
| |
| |
| The Inverse z-Transform | |
| |
| |
| |
| Pole-Zero Plots and Inverse of Rational Functions of z | |
| |
| |
| |
| Inverse z-Transform from a Power Series Expansion | |
| |
| |
| |
| Solving Difference Equations using z-Transforms | |
| |
| |
| |
| DT LTI System Characterization | |
| |
| |
| |
| DT LTI System Transfer Functions from Impulse-Response Characterization | |
| |
| |
| |
| Transfer Functions from Difference-Equation Models | |
| |
| |
| |
| System Properties and Modes from H(z) | |
| |
| |
| |
| Frequency Response of DT Systems | |
| |
| |
| |
| Representation of Discrete-Time Systems for Implementation | |
| |
| |
| |
| The z-Transform of Sampled Signals - Relationship to the Laplace Transform Summary Key Equations Further Reading Problems | |
| |
| |
| |
| Frequency Domain Analysis of DT Signals and Systems - The DTFT and DFT Analysis Introduction | |
| |
| |
| |
| Spectrum of Sampled Signals and the Sampling Theorem | |
| |
| |
| |
| Aliasing | |
| |
| |
| |
| Signal Reconstruction | |
| |
| |
| |
| The Discrete-Time Fourier Transform | |
| |
| |
| |
| Properties of the Discrete-Time Fourier Transform | |
| |
| |
| |
| Frequency Domain Analysis of DT Systems | |
| |
| |
| |
| Discrete Fourier Transform and its Properties | |
| |
| |
| |
| Applications of the DFT in Signal and System Analysis Summary Key Equations Further Reading Problems | |
| |
| |
| |
| State Variable Analysis of Continuous and Discrete-Time Systems Introduction | |
| |
| |
| |
| State Variable Representation of CT Systems | |
| |
| |
| |
| Construction of State-Variable Models from System Configurations | |
| |
| |
| |
| Conversion of Differential-Equation Models to State-Variable Models | |
| |
| |
| |
| Obtaining State-Variable Models from Block Diagrams and Transfer Functions | |
| |
| |
| |
| System Analysis in Time and s-Domains Using State-Variable Models | |
| |
| |
| |
| MATLAB Applications | |
| |
| |
| |
| State Variable Representation and Analysis of DT Systems | |
| |
| |
| |
| Obtaining STate-Variable Models from Block Diagrams | |
| |
| |
| |
| Conversion of Transfer-Function and Difference-Equation Models to State-Variable Models | |
| |
| |
| |
| System Analysis in Time and z-Domains Using State Variable Models | |
| |
| |
| |
| MATLAB Applications Summary Key Equations Further Reading Problems | |
| |
| |
| Appendix | |
| |
| |
| |
| Complex Numbers | |
| |
| |
| |
| Some Useful Mathematical Operations | |
| |
| |
| |
| Basic Matrix Operations | |
| |
| |
| |
| Mathematical Tables | |
| |
| |
| Index | |