ContentsPreface 1 Introduction 1.1 Modeling 1.2 Continuous-Time Physical Systems Electric Circuits, Operational Amplifier Circuits, Simple Pendulum, DC Power Supplies, Analogous Systems, 1.3 Samplers and Discrete-Time Physical Systems Analog-to-Digital Converter, Numerical Integration, Picture in a Picture, Compact Disks, Sampling in Telephone Systems, Data-Acquisition System, 1.4 Matlab and Simulink 2 Continuous-Time Signals and Systems 2.1 Transformations of Continuous-Time Signals Time Transformations, Amplitude Transformations, 2.2 Signal Characteristics Even and Odd Signals, Periodic Signals, 2.3 Common Signals in Engineering 2.4 Singularity Functions Unit Step Function, Unit Impulse Function, 2.5 Mathematical Functions for Signals 2.6 Continuous-Time Systems Interconnecting Systems, Feedback System, 2.7 Properties of Continuous-Time Systems Stability Linearity Summary Problems 3 Continuous-Time Linear Time-Invariant Systems 3.1 Impulse Representation of Continuous-Time Signals 3.2 Convolution for Continuous-Time LTI Systems 3.3 Properties of Convolution 3.4 Properties of Continuous-Time LTI Systems Memoryless Systems, Invertibility, Causality, Stability, Unit Step Response, 3.5 Differential-Equation Models Solution of Differential Equations, General Case, Relation to Physical Systems, 3.6 Terms in the Natural Response Stability, 3.7 System Response for Complex-Exponential Inputs Linearity, Complex Inputs for LTI Systems, Impulse Response, 3.8 Block Diagrams Direct Form I, Direct Form II, nth-Order Realizations, Practical Considerations, Summary Problems 4 Fourier Series 4.1 Approximating Periodic Functions Periodic Functions, Approximating Periodic Functions, 4.2 Fourier Series Fourier Series,Fourier Coefficients, 4.3 Fourier Series and Frequency Spectra Frequency Spectra, 4.4 Properties of Fourier Series 4.5 System Analysis 4.6 Fourier Series Transformations Amplitude Transformations, Time Transformations, Summary Problems 5 The Fourier Transform 5.1 Definition of the Fourier Transform 5.2 Properties of the Fourier Transform Linearity, Time Scaling, Time Shifting, Time Transformation, Duality, Convolution, Frequency Shifting, Time Differentiation, Time Integration, Frequency Differentiation, Summary, 5.3 Fourier Transforms of Time Functions DC Level, Unit Step Function, Switched Cosine, Pulsed Cosine, Exponential Pulse, Fourier Transforms of Periodic Functions, Summary, 5.4 Sampling Continuous-Time Signals Impulse Sampling, Shannon's Sampling Theorem, Practical Sampling, 5.5 Application of the Fourier Transform Frequency Response of Linear Systems, Frequency Spectra of Signals, Summary, 5.6 Energy and Power Density Spectra Energy Density Spectrum, Power Density Spectrum, Power and Energy Transmission, Summary, Summary Problems 6 Applications of the Fourier Transform 6.1 Ideal Filters 6.2 Real Filters RC Low-Pass Filter, Butterworth Filter, Chebyschev and Elliptic Filters, Bandpass Filters, Summary, 6.3 Bandwidth Relationships 6.4 Reconstruction of signals from sample data Interpolating Function, Digital-to-analog Conversion, 6.5 Sinusoidal Amplitude Modulation Frequency-Division Multiplexing, 6.6 Pulse-Amplitude Modulation Time-Division Multiplexing, Flat-Top PAM, Summary Problems 7 The Laplace Transform 7.1 Definitions of Laplace Transforms 7.2 Examples 7.3 Laplace Transforms of Functions 7.4 Laplace Transform Properties Real Shifting, Differentiation, Integration, 7.5 Additional Properties Multiplication by t, Initial Value, Final Value, Time Transformation, 7.6 Response of LTI Systems Initial Conditions, Transfer Functions, Convolution, Transforms with Complex Poles, Functions with Repeated Poles, 7.7 LTI Systems Characteristics Causality, Stability, Invertibility, Frequency Response, 7.8 Bilateral Laplace Transform Region of Convergence, Bilateral Transform from Unilateral Tables, Inverse Bilateral Laplace Transform, 7.9 Relationship of the Laplace Transform to the Fourier Transform Summary Problems 8 State Variables for Continuous-Time Systems 8.1 State-Variable Modeling 8.2 Simulation Diagrams 8.3 Solution of State Equations Laplace-Transform Solution, Convolution Solution, Infinite Series Solution, 8.4 Properties of the State Transition Matrix 8.5 Transfer Functions Stability, 8.6 Similarity Transformations Transformations, Properties, Summary Problems 9 Discrete-Time Signals and Systems 9.1 Discrete-Time Signals and Systems Unit Step and Unit Impulse Functions, Equivalent Operations, 9.2 Transformations of Discrete-Time Signals Time Transformations, Amplitude Transformations, 9.3 Characteristics of Discrete-Time Signals Even and Odd Signals, Signals Periodic in n, Signals Periodic in W 9.4 Common Discrete-Time Signals 9.5 Discrete-Time Systems Interconnecting Systems, 9.6 Properties of Discrete-Time Systems Systems with Memory, Invertibility, Inverse of a System, Causality, Stability, Time Invariance, Linearity, Summary Problems 10 Discrete-Time Linear Time-Invariant Systems 10.1 Impulse Representation of Discrete-Time Signals 10.2 Convolution for Discrete-Time Systems Properties of Convolution, 10.3 Properties of Discrete-Time LTI Systems Memory, Invertibility, Causality, Stability, Unit Step Response, 10.4 Difference-Equation Models Difference-Equation Models, Classical Method, Solution by Iteration, 10.5 Terms in the Natural Response Stability, 10.6 Block Diagrams Two Standard Forms, 10.7 System Response for Complex-Exponential Inputs Linearity, Complex Inputs for LTI Systems, Stability, Sampled Signals, Impulse Response, Summary Problems 11 The z-Transform 11.1 Definitions of z-Transforms 11.2 Examples Two z-Transforms, Digital-Filter Example, 11.3 z-Transforms of Functions Sinusoids, 11.4 z-Transform Properties Real Shifting, Initial and Final Values, 11.5 Additional Properties Time Scaling, Convolution in Time, 11.6 LTI System Applications Transfer Functions, Inverse z-Transform, Complex Poles, Causality, Stability, Invertibility, 11.7 Bilateral z-Transform Bilateral Transforms, Regions of Convergence, Inverse Bilateral Transforms, Summary Problems 12 Fourier Transforms of Discrete-Time Signals 12.1 Discrete-Time Fourier Transform z-Transform, 12.2 Properties of the Discrete-Time Fourier Transform Periodicity, Linearity, Time Shift, Frequency Shift, Symmetry, Time Reversal, Convolution in Time, Convolution in Frequency, Multiplication by n, Parseval's Theorem, 12.3 Discrete-Time Fourier Transform of Periodic Sequences 12.4 Discrete Fourier Transform Shorthand Notation for the DFT, Frequency Resolution of the DFT, Validity of the DFT, Summary, 12.5 Fast Fourier Transform Decomposition-in-Time Fast Fourier Transform Algorithm, Decomposition-in-Frequency Fast Fourier Transform, Summary, 12.6 Applications of the Discrete Fourier Transform Calculation of Fourier Transforms, Convolution, Filtering, Correlation, Energy Spectral Density Estimation, Summary, 12.7 The Discrete Cosine Transform, Summary Problems 13 State Variables for Discrete-Time Systems 13.1 State-Variable Modeling 13.2 Simulation Diagrams 13.3 Solution of State Equations Recursive Solution, z-Transform Solution, 13.4 Properties of the State Transition Matrix 13.5 Transfer Functions Stability, 13.6 Similarity Transformations Properties, Summary Problems Appendices A. Integrals and Trigonometric Identities Integrals, Trigonometric Identities, B. Leibnitz's and L'Hopital's Rules Leibnitz's Rule, L'Hopital's Rule, C. Summation Formulas for Geometric Series D. Complex Numbers and Euler's Relation Complex-Number Arithmetic, Euler's Relation, Conversion Between Forms, E. Solution of Differential Equations Complementary Function, Particular Solution, General Solution, Repeated Roots, F. Partial-Fraction Expansions G. Review of Matrices Algebra of Matrices, Other Relationships H. Answers to Selected Problems I. Signals and Systems References Index