Efnisyfirlit

• Cover Page
• THE OXFORD SERIES IN ELECTRICAL AND COMPUTER ENGINEERING
• Title page
• Copyright page
• Contents
• Preface
  • Notable Features
  • Organisation
  • Suggestions for Using This Book
  • MATLAB
  • Credits and Acknowledgements
• CHAPTER 1 Background
  • 1.1 Complex Numbers
    • 1.1-1 A Historical Note
      • Origins of Complex Numbers
    • 1.1-2 Algebra of Complex Numbers
      • Conjugate of a Complex Number
      • Understanding Some Useful Identities
      • A Warning About Computing Angles with Calculators
      • Arithmetical Operations, Powers, and Roots of Complex Numbers
      • Logarithms 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
      • Distinct Factors of Q(x)
      • Complex Factors of Q(x)
      • Quadratic Factors
      • Shortcuts
    • 1.4-3 Repeated Factors of Q(x)
    • 1.4-4 A Combination of Heaviside “Cover-Up” and Clearing Fractions
      • A Combination of Heaviside “Cover-Up” and Shortcuts
    • 1.4-5 Improper F(x) with m=n
    • 1.4-6 Modified Partial Fractions
  • 1.5 Vectors and Matrices
    • 1.5-1 Some Definitions and Properties
    • 1.5-2 Matrix Algebra
      • Addition of Matrices
      • Multiplication of a Matrix by a Scalar
      • Matrix Multiplication
      • Multiplication of a Matrix by a Vector
      • Matrix Inversion
  • 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’Hôpital’s Rule
    • 1.7-10 Solution of Quadratic and Cubic Equations
  • REFERENCES
  • PROBLEMS
• CHAPTER 2 Signals and Systems
  • 2.1 Size of a Signal
    • 2.1-1 Signal Energy
    • 2.1-2 Signal Power
      • Comments.
      • Units of Energy and Power.
      • Comment.
  • 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
      • Comment.
    • 2.3-4 Energy and Power Signals
      • Comments.
    • 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 δ(t)
      • Multiplication of a Function by an Impulse
      • Sampling Property of the Unit Impulse Function
      • Unit Impulse as a Generalised Function
    • 2.4-3 The Exponential Function estst
  • 2.5 Even and Odd Functions
    • 2.5-1 Some Properties of Even and Odd Functions
      • Area
    • 2.5-2 Even and Odd Components of a Signal
      • A Modification for Complex Signals
  • 2.6 Systems and System Classification
    • 2.6-1 Classification of Systems
    • 2.6-2 Linear and Nonlinear Systems
      • The Concept of Linearity
      • Response of a Linear System
      • More Comments on Linear Systems
    • 2.6-3 Time-Invariant and Time-Varying Systems
    • 2.6-4 Instantaneous and Dynamic Systems
    • 2.6-5 Causal and Noncausal Systems
      • Why Study 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
      • Translational Systems
      • Rotational 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 Function
    • 2.9-3 Visualising Operations on the Independent Variable
    • 2.9-4 Numerical Integration and Estimating Signal Energy
  • 2.10 Summary
  • REFERENCES
  • PROBLEMS
• CHAPTER 3 Time-Domain Analysis of Continuous-Time Systems
  • 3.1 Introduction
  • 3.2 System Response to Internal Conditions: The Zero-Input Response
    • Practical Initial Conditions and the Meaning of 0− and 0+
      • Independence of the Zero-Input and Zero-State Responses
      • Role of Auxiliary Conditions in Solution of Differential Equations
    • 3.2-1 Some Insights into the Zero-Input Behaviour of a System
      • The Resonance Phenomenon
  • 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
      • The Commutative Property
      • The Distributive Property
      • The Associative Property
      • The Shift Property
        • Proof.
      • Convolution with an Impulse
      • The Width Property
      • Zero-State Response and Causality
      • The Convolution Table
      • Response to Complex Inputs
      • Multiple Inputs
    • 3.4-2 Graphical Understanding of Convolution Operation
      • Summary of the Graphical Procedure
      • The Width of Convolved Functions
      • The Phantom of the Signals and Systems Opera
      • Why Convolution? An Intuitive Explanation of System Response
    • 3.4-3 Interconnected Systems
      • Inverse Systems
    • 3.4-4 A Very Special Function for LTIC Systems: The Everlasting Exponential est
      • A Fundamental Property of LTI Systems
    • 3.4-5 Total Response
      • Natural and Forced 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
      • Implications of 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
      • Importance of 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
• CHAPTER 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
      • Shifting
      • Time Reversal
      • Sampling Rate Alteration: Downsampling, Upsampling, and Interpolation
  • 4.2 Some Useful Discrete-Time Signal Models
    • 4.2-1 Discrete-Time Impulse Function δ[n]
    • 4.2-2 Discrete-Time Unit Step Function u[n]
    • 4.2-3 Discrete-Time Exponential γn
    • 4.2-4 Discrete-Time Sinusoid cos(Ωn+θ)
      • Sampled Continuous-Time Sinusoid Yields a Discrete-Time Sinusoid
    • 4.2-5 Discrete-Time Complex Exponential ejΩn
  • 4.3 Examples of Discrete-Time Systems
    • 4.3-1 Classification of Discrete-Time Systems
      • Linearity and Time Invariance
      • Causal and Noncausal Systems
      • Invertible and Noninvertible Systems
      • Stable and Unstable Systems
      • Memoryless Systems and Systems with Memory
  • 4.4 Discrete-Time System Equations
    • 4.4-1 Recursive (Iterative) Solution of Difference Equation
      • Operator Notation
      • Response of Linear Discrete-Time Systems
  • 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
      • An Alternative Form of Graphical Procedure: The Sliding-Tape Method
    • 4.7-2 Interconnected Systems
      • Inverse Systems
      • System Response to ∑k=−∞nx[k]
      • A Very Special Function for LTID Systems: The Everlasting Exponential zn
    • 4.7-3 Total Response
      • Natural and Forced 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
• CHAPTER 5 Continuous-Time System Analysis Using the Laplace Transform
  • 5.1 The Laplace Transform
    • 5.1-1 Finding the Inverse Transform
      • A Historical Note: Marquis Pierre-Simon de Laplace (1749–1827)
      • Oliver Heaviside (1850–1925)
  • 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
      • Initial and Final Values
        • Comment.
        • Comment.
  • 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
      • Intuitive Interpretation of the Laplace Transform
    • 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
      • Realisation of Complex Conjugate Poles
      • Realisation of Repeated Poles
    • 5.5-4 Transposed Realisation
    • 5.5-5 Using Operational Amplifiers for System Realisation
      • Operational Amplifier Circuits
      • The Scalar Multiplier
      • The Integrator
      • The Adder
    • 5.5-6 Application to Feedback and Controls
    • 5.5-7 Analysis of a Simple Control System
      • Step Input
      • Ramp Input
      • Design Specifications
  • 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
      • Log Magnitude
      • Phase
    • 5.7-3 First-Order Pole (or Zero)
      • The Log Magnitude
      • Phase
    • 5.7-4 Second-Order Pole (or Zero)
      • The Log Magnitude
      • Phase
        • Comment.
      • Poles and Zeros in the Right Half-Plane
    • 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)
      • Gain Enhancement by a Pole
      • Gain Suppression by a Zero
    • 5.8-2 Lowpass Filters
      • Wall of Poles
    • 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
      • Linearity
      • Time Shift
      • Frequency Shift
      • Time Differentiation
      • Time Integration
      • Time Scaling
      • Time Convolution
      • Frequency Convolution
      • Time Reversal
    • 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
      • Design and Evaluation of a Simple RC Filter
      • A Cascaded RC Filter and Polynomial Expansion
    • 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
• CHAPTER 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
      • Relationship Between h[n] and H[z]
  • 6.2 Some Properties of the z-Transform
    • 6.2-1 Time-Shifting Properties
      • Right Shift (Delay)
        • Proof.
      • Left Shift (Advance)
        • Proof.
    • 6.2-2 z-Domain Scaling Property (Multiplication by γn)
    • 6.2-3 z-Domain Differentiation Property (Multiplication by n)
    • 6.2-4 Time-Reversal Property
    • 6.2-5 Convolution Property
      • LTID System Response
      • Initial and Final Values
  • 6.3 z-Transform Solution of Linear Difference Equations
    • 6.3-1 Zero-State Response of LTID Systems: The Transfer Function
      • Alternate Interpretation of the z-Transform
    • 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
      • Non-uniqueness of Discrete-Time Sinusoid Waveforms
      • All Discrete-Time Signals Are Inherently Bandlimited
      • A Man Named Robert
      • Further Reduction in the Frequency Range
    • 6.5-2 Aliasing and Sampling Rate
      • Anti-aliasing Filter
    • 6.5-3 Frequency Response from Pole-Zero Locations
      • Controlling Gain by Placement of Poles and Zeros
      • Lowpass Filters
      • Highpass Filters
  • 6.6 Digital Processing of Analogue Signals
  • 6.7 The Bilateral z-Transform
    • 6.7-1 Properties of the Bilateral z-Transform
      • Linearity
      • Shift
      • Convolution
      • Multiplication by γn
      • Multiplication by n
      • Time Reversal
      • Complex Conjugation
    • 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
• CHAPTER 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
      • A Historical Note: Baron Jean-Baptiste-Joseph Fourier (1768–1830)
  • 7.2 Existence and Convergence of the Fourier Series
    • 7.2-1 Convergence of a Series
      • Dirichlet Conditions
    • 7.2-2 The Role of Amplitude and Phase Spectra in Waveshaping
      • Asymptotic Rate of Amplitude Spectrum Decay
      • Phase Spectrum: The Woman Behind a Successful Man
      • Fourier Synthesis of Discontinuous Functions: The Gibbs Phenomenon
      • A Historical Note on the Gibbs Phenomenon
  • 7.3 Exponential Fourier Series
    • 7.3-1 Exponential Fourier Spectra
      • What is a Negative Frequency?
      • Bandwidth of a Signal
      • Effect of Symmetry in Exponential Fourier Series
    • 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
      • Energy of the Sum of Orthogonal Signals
    • 7.5-4 Signal Representation by an Orthogonal Signal Set
      • Orthogonal Vector Space
      • Orthogonal Signal Space
        • Finality Property.
      • Energy of the Error Signal
      • Generalisation to Complex Signals
      • Some Examples of Generalised Fourier Series
      • Legendre Fourier Series
      • Trigonometric Fourier Series
      • Exponential Fourier Series
      • Why Use the Exponential 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
• CHAPTER 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
      • A Marvelous Balancing Act
  • 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
      • Distortionless Transmission
      • Measure of Time-Delay Variation with Frequency
      • The Nature of Distortion in Audio and Video Signals
    • 8.4-2 Bandpass Systems and Group Delay
    • 8.4-3 Ideal and Practical Filters
      • Thinking in the Time and Frequency Domains: A Two-Dimensional View of Signals and Systems
  • 8.5 Signal Energy
  • 8.6 Application to Communications: Amplitude Modulation
    • 8.6-1 Double-Sideband, Suppressed-Carrier (DSB-SC) Modulation
      • Demodulation of DSB-SC Signals
    • 8.6-2 Amplitude Modulation (AM)
      • Demodulation of AM: The Envelope Detector
    • 8.6-3 Single-Sideband Modulation (SSB)
      • Generation of SSB Signals
    • 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
• CHAPTER 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
      • The Treachery of Aliasing
      • Defectors Eliminated: The Anti-aliasing Filter
      • Sampling Forces Nonbandlimited Signals to Appear Bandlimited
      • Verification of Aliasing in Sinusoids
      • General Condition for Aliasing in Sinusoids
    • 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
      • Linearity
      • Conjugate Symmetry
      • Time Shifting
        • Proof.
      • Frequency Shifting
        • Proof.
      • Circular Convolution
    • 9.5-2 Some Applications of the DFT
      • Linear Convolution
      • Filtering
    • 9.5-3 The Fast Fourier Transform (FFT)
      • How Does the FFT Reduce the Number of Computations?
      • The Decimation-in-Time Algorithm
  • 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
• CHAPTER 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]
      • Periodic Extension of Fourier Spectrum
  • 10.2 Aperiodic Signal Representation by Fourier Integral
    • 10.2-1 Nature of Fourier Spectra
      • Fourier Spectra Are Continuous Functions of Ω
      • Fourier Spectra Are Periodic Functions of Ω with Period 2π
      • Conjugate Symmetry of X(Ω)
      • Physical Appreciation of the Discrete-Time Fourier Transform
      • Existence of the DTFT
    • 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
      • Measure of Delay Variation
      • Distortionless Transmission over Bandpass Systems
    • 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
      • Computation of Discrete-Time Fourier Series (DTFS)
    • 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
• CHAPTER 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
      • Functions of a Matrix
    • 11.1-3 Computation of an Exponential and a Power of a Matrix
      • Computation of Ak
  • 11.2 Introduction to State Space
  • 11.3 A Systematic Procedure to Determine State Equations
    • 11.3-1 Electrical Circuits
      • An Alternative Procedure
    • 11.3-2 State Equations from a Transfer Function
      • A General Case
  • 11.4 Solution of State Equations
    • 11.4-1 Laplace Transform Solution of State Equations
      • The Output
      • Characteristic Roots (Eigenvalues) of a Matrix
    • 11.4-2 Time-Domain Solution of State Equations
      • Determining eAt
      • The Output
  • 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
      • Linear Transformation, Controllability, and Observability
  • 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
• List of Illustrations
• List of Tables
• Images
  • CHAPTER 1 Background
  • CHAPTER 2 Signals and Systems
  • CHAPTER 3 Time-Domain Analysis of Continuous-Time Systems
  • CHAPTER 4 Time-Domain Analysis of Discrete-Time Systems
  • CHAPTER 5 Continuous-Time System Analysis Using the Laplace Transform
  • CHAPTER 6 Discrete-Time System Analysis Using the z-Transform
  • CHAPTER 7 Continuous-Time Signal Analysis: The Fourier Series
  • CHAPTER 8 Continuous-Time Signal Analysis: The Fourier Transform
  • CHAPTER 9 Sampling: The Bridge from Continuous to Discrete
  • CHAPTER 10 Fourier Analysis of Discrete-Time Signals
  • CHAPTER 11 State-Space Analysis

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  Þú lagar síðuna að þínum þörfum. Stækkaðu eða minnkaðu myndir og texta með multi-level zoom til að sjá síðuna eins og þér hentar best í þínu námi.
  
  
  
  Fleiri góðir kostir
  - Þú getur prentað síður úr bókinni (innan þeirra marka sem útgefandinn setur)
  - Möguleiki á tengingu við annað stafrænt og gagnvirkt efni, svo sem myndbönd eða spurningar úr efninu
  - Auðvelt að afrita og líma efni/texta fyrir t.d. heimaverkefni eða ritgerðir
  - Styður tækni sem hjálpar nemendum með sjón- eða heyrnarskerðingu