Linear Systems and Signals

Höfundar: BP Lathi; Roger Green (Útgáfa: 3)
Linear Systems and Signals

Kaup valmöguleikar

Linear Systems and Signals, Third Edition, is a textbook for the required junior-year signals and systems course in the typical Electrical Engineering department curriculum. The book's success lies in its thorough, inclusive presentation of key concepts supported by a unique, bottom-up explanation of the theories and reasoning behind the material. The heuristic approach is a trademark of Dr. Lathi's books and a vital reason why instructors who adopt the text stick with it.

Nánar um bókina

Útgefandi
Oxford University Press Academic US
ISBN
9780197660683
Print ISBN
9780190200190
Format
ePub
Útgáfa
3
Höfundar
BP Lathi; Roger Green
Tungumál
English
Útgefið
2022-10-12
Prent takmörkun á líftíma
100

Kaflar

  • 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