图书简介

1 BACKGROUND; 1.1 Complex Numbers; 1.1-1 A Historical Note; 1.1-2 Algebra of Complex Numbers; 1.2 Sinusoids and Exponentials; 1.2-1 Addition of Sinusoids; 1.2-2 Sinusoids in Terms of Exponentials; 1.2-3 Monotonic Exponentials; 1.2-4 The Exponentially Varying Sinusoid; 1.3 Cramer’s Rule; 1.4 Partial Fraction Expansion; 1.4-1 Method of Clearing Fractions; 1.4-2 The Heaviside Cover-Up Method; 1.4-3 Repeated Factors of Q(x); 1.4-4 A Combination of Heaviside Cover-Up and Clearing Fractions; 1.4-6 Modified Partial Fractions; 1.5 Vectors and Matrices; 1.5-1 Some Definitions and Properties; 1.5-2 Matrix Algebra; 1.6 MATLAB: Elementary Operations; 1.6-1 MATLAB Overview; 1.6-2 Calculator Operations; 1.6-3 Vector Operations; 1.6-4 Simple Plotting; 1.6-5 Element-by-Element Operations; 1.6-6 Matrix Operations; 1.6-7 Partial Fraction Expansions; 1.7 Appendix: Useful Mathematical Formulas; 1.7-1 Some Useful Constants; 1.7-2 Complex Numbers; 1.7-3 Sums; 1.7-4 Taylor and Maclaurin Series; 1.7-5 Power Series; 1.7-6 Trigonometric Identities; 1.7-7 Common Derivative Formulas; 1.7-8 Indefinite Integrals; 1.7-9 L’Hopital’s Rule; 1.7-10 Solution of Quadratic and Cubic Equations; References; Problems ; 2 SIGNALS AND SYSTEMS; 2.1 Size of a Signals; 2.1-1 Signal Energy; 2.1-2 Signal Power; 2.2 Some Useful Signal Operations; 2.2-1 Time Shifting; 2.2-2 Time Scaling; 2.2-3 Time Reversal; 2.2-4 Combined Operations; 2.3 Classification of Signals; 2.3-1 Continuous-Time and Discrete-Time Signals; 2.3-2 Analogue and Digital Signals; 2.3-3 Periodic and Aperiodic Signals; 2.3-4 Energy and Power Signals; 2.3-5 Deterministic and Random Signals; 2.4 Some Useful Signal Models; 2.4-1 The Unit Step Function u(t); 2.4-2 The Unit Impulse Function ?(t); 2.4-3 The Exponential Function est; 2.5 Even and Odd Functions; 2.5-1 Some Properties of Even and Odd Functions; 2.5-2 Even and Odd Components of a Signal; 2.6 Systems and System Classification; 2.6-1 Classification of Systems; 2.6-2 Linear and Nonlinear Systems; 2.6-3 Time-Invariant and Time-Varying Systems; 2.6-4 Instantaneous and Dynamic Systems; 2.6-5 Causal and Noncausal Systems; 2.6-6 Continuous-Time and Discrete-Time Systems; 2.6-7 Analogue and Digital Systems; 2.6-8 Invertible and Noninvertible Systems; 2.6-9 Stable and Unstable Systems; 2.7 System Model: Input-Output Description; 2.7-1 Electrical Systems; 2.7-2 Mechanical Systems; 2.7-3 Electromechanical Systems; 2.8 Internal and External Descriptions of a System; 2.8-1 Internal Description: The State-Space Description; 2.9 MATLAB: Working with Functions; 2.9-1 Anonymous Functions; 2.9-2 Relational Operators and the Unit Step Functions; 2.9-3 Visualising Operations on the Independent Variable; 2.9-4 Numerical Integration and Estimating Signal Energy; 2.10 Summary; References; Problems ; 3 TIME-DOMAIN ANALYSIS OF CONTINUOUS-TIME SYSTEMS; 3.1 Introduction; 3.2 System Response to Internal Conditions: The Zero-Input Response; 3.2-1 Some Insights into the Zero-Input Behaviour of a System; 3.3 The Unit Impulse Response h(t); 3.4 System Response to External Input: The Zero-State Response; 3.4-1 The Convolution Integral; 3.4-2 Graphical Understanding of Convolution Operation; 3.4-3 Interconnected Systems; 3.4-4 A Very Special Function for LTIC Systems:; The Everlasting Exponential est; 3.4-5 Total Response; 3.5 System Stability; 3.5-1 External (BIBO) Stability; 3.5-2 Internal (Asymptotic) Stability; 3.5-3 Relationship Between BIBO and Asymptotic Stability; 3.6 Intuitive Insights into System Behaviour; 3.6-1 Dependence of System Behaviour on Characteristic Modes; 3.6-2 Response Time of a System: The System Time Constant; 3.6-3 Time Constant and Rise Time of a System; 3.6-4 Time Constant and Filtering; 3.6-5 Time Constant and Pulse Dispersion (Spreading); 3.6-6 Time Constant and Rate of Information Transmission; 3.6-7 The Resonance Phenomenon; 3.7 MATLAB: M-Files; 3.7-1 Script M-Files; 3.7-2 Function M-Files; 3.7-3 For-Loops; 3.7-4 Graphical Understanding of Convolution; 3.8 Appendix: Determining the Impulse Response; 3.9 Summary; References; Problems ; 4 TIME-DOMAIN ANALYSIS OF DISCRETE-TIME SYSTEMS; 4.1 Introduction; 4.1-1 Size of a Discrete-Time Signal; 4.1-2 Useful Signal Operations; 4.2 Some Useful Discrete-Time Signal Models; 4.2-1 Discrete-Time Impulse Function ?[n]; 4.2-2 Discrete-Time Unit Step Function u[n]; 4.2-3 Discrete-Time Exponential ? n; 4.2-4 Discrete-Time Sinusoid cos(\’04n ?); 4.2-5 Discrete-Time Complex Exponential ej\’04n; 4.3 Examples of Discrete-Time Systems; 4.3-1 Classification of Discrete-Time Systems; 4.4 Discrete-Time System Equations; 4.4-1 Recursive (Iterative) Solution of Difference Equation; 4.5 System Response to Internal Conditions: The Zero-Input Response; 4.6 The Unit Impulse Response h[n]; 4.6-1 The Closed-Form Solution of h[n]; 4.7 System Response to External Input: The Zero-State Response; 4.7-1 Graphical Procedure for the Convolution Sum; 4.7-2 Interconnected Systems; 4.7-3 Total Response; 4.8 System Stability and Behaviour; 4.8-1 External (BIBO) Stability; 4.8-2 Internal (Asymptotic) Stability; 4.8-3 Relationship Between BIBO and Asymptotic Stability; 4.8-4 Intuitive Insights into System Behaviour; 4.9 MATLAB: Discrete-Time Signals and Systems; 4.9-1 Discrete-Time Functions and Stem Plots; 4.9-2 System Responses Through Filtering; 4.9-3 A Custom Filter Function; 4.9-4 Discrete-Time Convolution; 4.10 Appendix: Impulse Response for a Special Case; 4.11 Summary; Problems ; 5 CONTINUOUS-TIME SYSTEM ANALYSIS USING THE; LAPLACE TRANSFORM; 5.1 The Laplace Transform; 5.2 Some Properties of the Laplace Transform; 5.2-1 Time Shifting; 5.2-2 Frequency Shifting; 5.2-3 The Time-Differentiation Property; 5.2-4 The Time-Integration Property; 5.2-5 The Scaling Property; 5.2-6 Time Convolution and Frequency Convolution; 5.3 Solution of Differential and Integro-Differential Equations; 5.3-1 Comments on Initial Conditions at 0? and at 0 ; 5.3-2 Zero-State Response; 5.3-3 Stability; 5.3-4 Inverse Systems; 5.4 Analysis of Electrical Networks: The Transformed Network; 5.4-1 Analysis of Active Circuits; 5.5 Block Diagrams and System Realisations; 5.5-1 Direct Form I Realisation; 5.5-2 Direct Form II Realisation; 5.5-3 Cascade and Parallel Realisations; 5.5-4 Transposed Realisation; 5.5-5 Using Operational Amplifiers for System Realisation; 5.5-6 Application to Feedback and Controls; 5.5-7 Analysis of a Simple Control System; 5.6 Frequency Response of an LTIC System; 5.6-1 Steady-State Response to Causal Sinusoidal Inputs; 5.7 Bode Plots; 5.7-1 Constant Ka1a2/b1b3; 5.7-2 Pole (or Zero) at the Origin; 5.7-3 First-Order Pole (or Zero); 5.7-4 Second-Order Pole (or Zero); 5.7-5 The Transfer Function from the Frequency Response; 5.8 Filter Design by Placement of Poles and Zeros of H(s); 5.8-1 Dependence of Frequency Response on Poles and Zeros of H(s); 5.8-2 Lowpass Filters; 5.8-3 Bandpass Filters; 5.8-4 Notch (Bandstop) Filters; 5.8-5 Practical Filters and Their Specifications; 5.9 The Bilateral Laplace Transform; 5.9-1 Properties of the Bilateral Laplace Transform; 5.9-2 Using the Bilateral Transform for Linear System Analysis; 5.10 MATLAB: Continuous-Time Filters; 5.10-1 Frequency Response and Polynomial Evaluation; 5.10-2 Butterworth Filters and the Find Command; 5.10-3 Using Cascaded Second-Order Sections for Butterworth Filter Realisation; 5.10-4 Chebyshev Filters; 5.11 Summary; References; Problems ; 6 DISCRETE-TIME SYSTEM ANALYSIS USING THE Z-TRANSFORM; 6.1 The z-Transform; 6.1-1 Inverse Transform by Partial Fraction Expansion and Tables; 6.1-2 Inverse z-Transform by Power Series Expansion; 6.2 Some Properties of the z-Transform; 6.2-1 Time-Shifting Properties; 6.2-2 z-Domain Scaling Property (Multiplication by ? n); 6.2-3 z-Domain Differentiation Property (Multiplication by n); 6.2-4 Time-Reversal Property; 6.2-5 Convolution Property; 6.3 z-Transform Solution of Linear Difference Equations; 6.3-1 Zero-State Response of LTID Systems: The Transfer Function; 6.3-2 Stability; 6.3-3 Inverse Systems; 6.4 System Realisation; 6.5 Frequency Response of Discrete-Time Systems; 6.5-1 The Periodic Nature of Frequency Response; 6.5-2 Aliasing and Sampling Rate; 6.5-3 Frequency Response from Pole-Zero Locations; 6.6 Digital Processing of Analogue Signals; 6.7 The Bilateral z-Transform; 6.7-1 Properties of the Bilateral z-Transform; 6.7-2 Using the Bilateral z-Transform for Analysis of LTID Systems; 6.7-3 Connecting the Laplace and z-Transforms; 6.8 MATLAB: Discrete-Time IIR Filters; 6.8-1 Frequency Response and Pole-Zero Plots; 6.8-2 Transformation Basics; 6.8-3 Transformation by First-Order Backward Difference; 6.8-4 Bilinear Transformation; 6.8-5 Bilinear Transformation with Prewarping; 6.8-6 Example: Butterworth Filter Transformation; 6.8-7 Problems Finding Polynomial Roots; 6.8-8 Using Cascaded Second-Order Sections to Improve Design; 6.9 Summary; References; Problems ; 7 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER SERIES; 7.1 Periodic Signal Representation by Trigonometric Fourier Series; 7.1-1 The Fourier Spectrum; 7.1-2 The Effect of Symmetry; 7.1-3 Determining the Fundamental Frequency and Period; 7.2 Existence and Convergence of the Fourier Series; 7.2-1 Convergence of a Series; 7.2-2 The Role of Amplitude and Phase Spectra in Waveshaping; 7.3 Exponential Fourier Series; 7.3-1 Exponential Fourier Spectra; 7.3-2 Parseval’s Theorem; 7.3-3 Properties of the Fourier Series; 7.4 LTIC System Response to Periodic Inputs; 7.5 Generalised Fourier Series: Signals as Vectors; 7.5-1 Component of a Vector; 7.5-2 Signal Comparison and Component of a Signal; 7.5-3 Extension to Complex Signals; 7.5-4 Signal Representation by an Orthogonal Signal Set; 7.6 MATLAB: Fourier Series Applications; 7.6-1 Numerical Computation of Dn; 7.6-2 Periodic Functions and the Gibbs Phenomenon; 7.6-3 Optimisation and Phase Spectra; 7.7 Summary; References; Problems ; 8 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER TRANSFORM; 8.1 Aperiodic Signal Representation by the Fourier Integral; 8.1-1 Physical Appreciation of the Fourier Transform; 8.2 Transforms of Some Useful Functions; 8.2-1 Connection Between the Fourier and Laplace Transforms; 8.3 Some Properties of the Fourier Transform; 8.4 Signal Transmission Through LTIC Systems; 8.4-1 Signal Distortion During Transmission; 8.4-2 Bandpass Systems and Group Delay; 8.4-3 Ideal and Practical Filters; 8.5 Signal Energy; 8.6 Application to Communications: Amplitude Modulation; 8.6-1 Double-Sideband, Suppressed-Carrier (DSB-SC) Modulation; 8.6-2 Amplitude Modulation (AM); 8.6-3 Single-Sideband Modulation (SSB); 8.6-4 Frequency-Division Multiplexing; 8.7 Data Truncation: Window Functions; 8.7-1 Using Windows in Filter Design; 8.8 MATLAB: Fourier Transform Topics; 8.8-1 The Sinc Function and the Scaling Property; 8.8-2 Parseval’s Theorem and Essential Bandwidth; 8.8-3 Spectral Sampling; 8.8-4 Kaiser Window Functions; 8.9 Summary; References; Problems ; 9 SAMPLING: THE BRIDGE FROM CONTINUOUS TO DISCRETE; 9.1 The Sampling Theorem; 9.1-1 Practical Sampling; 9.2 Signal Reconstruction; 9.2-1 Practical Difficulties in Signal Reconstruction; 9.2-2 Some Applications of the Sampling Theorem; 9.3 Analogue-to-Digital (A/D) Conversion; 9.4 Dual of Time Sampling: Spectral Sampling; 9.5 Numerical Computation of the Fourier Transform: The Discrete; Fourier Transform; 9.5-1 Some Properties of the DFT; 9.5-2 Some Applications of the DFT; 9.5-3 The Fast Fourier Transform (FFT); 9.6 MATLAB: The Discrete Fourier Transform; 9.6-1 Computing the Discrete Fourier Transform; 9.6-2 Improving the Picture with Zero Padding; 9.6-3 Quantisation; 9.7 Summary; References; Problems ; 10 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS; 10.1 Discrete-Time Fourier Series (DTFS); 10.1-1 Periodic Signal Representation by Discrete-Time Fourier Series; 10.1-2 Fourier Spectra of a Periodic Signal x[n]; 10.2 Aperiodic Signal Representation by Fourier Integral; 10.2-1 Nature of Fourier Spectra; 10.2-2 Connection Between the DTFT and the z-Transform; 10.3 Properties of the DTFT; 10.4 LTI Discrete-Time System Analysis by DTFT; 10.4-1 Distortionless Transmission; 10.4-2 Ideal and Practical Filters; 10.5 DTFT Connection with the CTFT; 10.5-1 Use of DFT and FFT for Numerical Computation of the DTFT; 10.5-2 Generalisation of the DTFT to the z-Transform; 10.6 MATLAB: Working with the DTFS and the DTFT; 10.6-1 Computing the Discrete-Time Fourier Series; 10.6-2 Measuring Code Performance; 10.6-3 FIR Filter Design by Frequency Sampling; 10.7 Summary; Reference; Problems; 11 STATE-SPACE ANALYSIS; 11.1 Mathematical Preliminaries; 11.1-1 Derivatives and Integrals of a Matrix; 11.1-2 The Characteristic Equation of a Matrix: The Cayley-Hamilton Theorem; 11.1-3 Computation of an Exponential and a Power of a Matrix; 11.2 Introduction to State Space; 11.3 A Systematic Procedure to Determine State Equations; 11.3-1 Electrical Circuits; 11.3-2 State Equations from a Transfer Function; 11.4 Solution of State Equations; 11.4-1 Laplace Transform Solution of State Equations; 11.4-2 Time-Domain Solution of State Equations; 11.5 Linear Transformation of a State Vector; 11.5-1 Diagonalisation of Matrix A; 11.6 Controllability and Observability; 11.6-1 Inadequacy of the Transfer Function Description of a System; 11.7 State-Space Analysis of Discrete-Time Systems; 11.7-1 Solution in State Space; 11.7-2 The z-Transform Solution; 11.8 MATLAB: Toolboxes and State-Space Analysis; 11.8-1 z-Transform Solutions to Discrete-Time, State-Space Systems; 11.8-2 Transfer Functions from State-Space Representations; 11.8-3 Controllability and Observability of Discrete-Time Systems; 11.8-4 Matrix Exponentiation and the Matrix Exponential; 11.9 Summary; References; Problems ; Index $ THR $ Electrical engineering

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