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.

This text shares many topics and features with Dr. Lathi's Signal Processing and Linear System, but differs in its sequence of topics, particularly in the placement of the Laplace transform ahead of the Fourier Transform. The two books cover much the same ground but their different organizations mirror the two different approaches in wide use by instructors.

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