Table of contents for Fundamentals of signals and systems / M.J. Roberts.

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Fundamentals of Signals and Systems
Chapter 1 - Introduction
	1.1	Signals and Systems Defined	1-1
	1.2	Types of Signals	1-2
			Continuous-Time, Continuous-Value, Discrete-Time, Discrete-
Value, Random
	1.3	Examples of Systems	1-8
			A Mechanical System
				Differential Equations
			A Fluid System
			A Discrete-Time System
				Difference Equations
			Feedback Systems
				Stability
	1.4	A Familiar Signal and System Example	1-16
			Power Spectrum, Signal-to-Noise Ratio
	1.5	Use of MATLAB	1-21
Chapter 2 - Mathematical Description of Continuous-Time Signals
	2.1	Introduction and Goals	2-1
	2.2	Functions and Functional Notation	2-2
			Domain, Range
	2.3	Signal Functions	2-2
			Continuous-Time Functions
			Complex Exponentials and Sinusoids
				Cyclic and Radian Frequency
			Functions with Discontinuities
			Singularity Functions and Related Functions
				The Unit Step Function
				The Signum Function
				The Unit Ramp Function
				The Unit Impulse
					Generalized Derivatives, Equivalence, Sampling and 
Scaling 
 Properties
				The Periodic Impulse or Impulse Train
				A Coordinated Notation for Singularity Functions
				The Unit Rectangle Function
				The Unit Triangle Function
				The Unit Sinc Function
				The Dirichlet Function
				MATLAB m-Files for Some Singularity Functions and
 Related Functions
	2.4	Functions and Combinations of Functions	2-24
			Functional Notation - Conventions and Conversions
			Combinations of Functions
	2.5	Scaling and Shifting	2-26
			Amplitude Scaling
			Time Shifting
			Time Scaling
			Simultaneous Scaling and Shifting
				Significance of Sequence
	2.6	Differentiation and Integration	2-39
			Antiderivative, Indefinite Integral, Definite Integral, 
Cumulative Integral
	2.7	Even and Odd Functions	2-42
			Sums, Products, Differences, Quotients, Derivatives, Integrals
	2.8	Periodic Functions		2-46
			Least Common Multiple, Greatest Common Divisor
	2.9	Signal Energy and Power	2-50
			Energy Signals, Power Signals
	2.10	Summary of Important Points	2-55
		Exercises				2-56
Chapter 3 - Mathematical Description of Discrete-Time Signals
	3.1	Introduction and Goals	3-1
 3.2	Signal Functions	3-2
 		Sampling and Discrete Time
 			Uniform Sampling, Sequential-State Machines
 		Exponentials and Sinusoids
 			Periods, Normalized Frequency
 		Singularity Functions
				The Unit Impulse or Kronecker Delta Function
 			The Unit Sequence 
				The Signum Function
				The Rectangle Function
				The Unit Ramp Function
				The Periodic Impulse or Impulse Train
	3.3	Scaling and Shifting	2-68
			Amplitude Scaling
			Time Shifting
			Time Scaling
				Compression, Expansion, Decimation, Interpolation
	3.4	Differencing and Accumulation	3-22
			Approximation of Derivatives, Forward, Backward and Central 
Differences
	3.5	Even and Odd Functions	3-26
			Sums, Products, Differences and Quotients
			Accumulation
	3.6	Periodic Functions	3-30
	3.7	Signal Energy and Power	3-31
	3.8	Summary of Important Points	3-34
		Exercises	3-36
Chapter 4 - Properties of Continuous-Time Systems
	4.1	Introduction and Goals	4-1
	4.2	Block Diagrams and System Terminology 	4-2
			Components, Amplifiers, Summing Junctions, Integrators
	4.3	System Modeling	4-7
			Differential Equations, Model Complexity, Feedback and 
Stability
	4.4	System Properties	4-14
			Introductory Example
				Zero-Input Response, Zero-State Response
			Homogeneity
			Time Invariance
			Additivity
			Linearity and Superposition
				Linear, Time-Invariant Systems, Non-Linearity and 
Linearization
			Stability
				Bounded-Input-Bounded-Output
			Incremental Linearity
			Causality
			Memory
				Static and Dynamic Systems
			Static Non-Linearity
			Invertibility
				Inverse System
	4.5	Eigenfunctions of LTI Systems	4-38
			Natural Radian Frequency, Damping Factor, Critical Radian 
Frequency, 
 Damping Ratio, Complex Exponential Excitation
	4.6	Summary of Important Points	4-41
		Exercises	4-42
Chapter 5 - Properties of Discrete-Time Systems
	5.1	Introduction and Goals	5-1
	5.2	Block Diagrams and System Terminology 	5-1
			Delay
	5.3	System Modeling	5-2
			Approximation of Differential Equations with Difference 
Equations, Feedback, 
 Oscillation, Stability
	5.4	System Properties	5-10
			Stability Criterion
	5.5	Eigenfunctions of LTI Systems	5-14
			Complex Exponential Excitation
	5.6	Summary of Important Points	5-14
		Exercises	5-15
Chapter 6 - Time-Domain Analysis of Continuous-Time Systems
	6.1	Introduction and Goals	6-1
 6.2	The Convolution Integral	6-1
 		Impulse Response
 			Calculation from Differential Equations
 		Convolution
 			Derivation from Rectangular-Pulse Approximation
 		Convolution Properties
Convolution with an Impulse, Graphical Convolution Methods, Time 
Shifting, Commutativity, Associativity, Distributivity, Differentiation, 
Area, Scaling, Convergence of Convolution Integral
 		System Interconnections
 			Cascade, Parallel
 		Stability and Impulse Response
 		Responses of Systems to Standard Signals
 			Unit-Step Response, Complex Exponential Response, 
Transfer 
 Function, Frequency Response
	6.3	Block-Diagram Realization of Differential Equations		6-31
			Preference for Integrators over Differentiators, Direct Forms 
1 and 2
	6.4	Summary of Important Points	6-37
		Exercises	6-39
Chapter 7 - Time-Domain Analysis of Discrete-Time Systems
	7.1	Introduction and Goals	7-1
 7.2	The Convolution Sum		7-1
 		Impulse Response
 			Calculation from Difference Equations
 		Convolution
 			Development, Graphical Method, Array Method
 		Convolution Properties
Convolution with an Impulse, Time Shifting, Commutativity, 
Associativity, Distributivity, Differencing, Sum, Convergence of 
Convolution Sum
 		Numerical Convolution
 			Approximating the Convolution Integral
 		System Interconnections
 			Cascade, Parallel
 		Stability and Impulse Response
 		Responses to Standard Signals
 			Unit-Sequence Response, Complex Exponential Response, 
Transfer 
 Function, Frequency Response
	7.3	Block-Diagram Realization of Difference Equations		7-31
			Direct Forms 1 and 2
	7.4	Summary of Important Points	7-35
		Exercises	7-36
Chapter 8 - The Continuous-Time Fourier Series
	8.1	Introduction and Goals	8-1
	8.2	Periodic Excitation and Response of LTI Systems	8-2
			Inadequacy of Convolution	
	8.3	Basic Concepts and Development of the Fourier Series	8-5
			Linearity and Complex-Exponential Excitation
				Illustrative Example, Trigonometric and Complex Forms
			Derivation of the Fourier Series
				Inner Products and Orthogonality,
			Limitations on Functions Representable by a Fourier Series
				The Dirichlet Conditions
			The Trigonometric Fourier Series
				Relation to Complex Form
			Cyclic-Frequency and Radian-Frequency Forms
			Periodicity of Fourier Series Representations
	8.4	Calculation of the Fourier Series		8-19
			Sinusoidal Signals
			Non-sinusoidal Signals
			The Fourier Series of Periodic Signals over an Integer Number 
of 
 Fundamental Periods
			Minimum Mean-Squared Error of Fourier-Series Partial Sums
			The Fourier Transform of Even and Odd Periodic Signals
	8.5	Numerical Computation of the Fourier Series		8-32
			The Discrete Fourier Transform (DFT)
	8.6	Convergence of the Fourier Series	8-38
			Continuous Signals
			Signals with Discontinuities and The Gibbs Phenomenon
	8.7	 Properties of the Fourier Series	8-42
			Linearity
			Time Shifting
			Frequency Shifting
			Time Reversal
			Time Scaling
			Change of Period
			Time Differentiation
			Time Integration
				Effect of Average Value
			Multiplication-Convolution Duality
				Periodic Convolution Integral
			Conjugation
			Parseval?s Theorem
	8.8	Use of Tables and Properties		8-60
	8.9	Bandlimited Signals		8-63
	8.10	Responses of LTI Systems with Periodic Excitation		8-68
			Harmonic Response
	8.11	Summary of Important Points	8-70
		Exercises	8-71
Chapter 9 - The Discrete-Time Fourier Series
	9.1	Introduction and Goals	9-1
	9.2	Periodic Excitation and Response of LTI Systems	9-1
			Inadequacy of Convolution	
	9.3	Basic Concepts and Development of the Fourier Series	9-3
			Linearity and Complex-Exponential Excitation
				Illustrative Example, Trigonometric and Complex Forms
			Derivation of the Fourier Series
				Completeness of a Finite Sum, Vector and Matrix Methods, 
Orthogonality, Projections, Summation Forms, Relation to the Discrete 
Fourier Transform (DFT), Complex and Trigonometric Forms
			Representing Periodic Functions with the DTFS
				Conservation of Information
	9.4	Properties of the Fourier Series	9-30
			Linearity, Time Shifting, Frequency Shifting, Conjugation and 
Time 
 Reversal
			Time Scaling
				Restrictions Stemming from Discrete Time
			Change of Period
			Multiplication-Convolution Duality
				Periodic Convolution Sum
			First Backward Difference
			Accumulation
			Even and Odd Signals
			Parseval?s Theorem
	9.5	Convergence of the Fourier Series	9-49
	9.6	Responses of LTI Systems with Periodic Excitation		9-52
			Harmonic Response
	9.7	Summary of Important Points		9-57
		Exercises	9-58
Chapter 10 - The Continuous-Time Fourier Transform
	10.1	Introduction and Goals	10-1
	10.2	Aperiodic Excitation and Response of LTI Systems		10-1
			Inadequacy of the Fourier Series
	10.3	Basic Concepts and Development of the Fourier Transform	10-3
			The Transition from the Fourier Series to the Fourier 
Transform
				Normalization and Notation Changes
			Definition of the Fourier Transform
				Cyclic and Radian Frequency Forms, Time and Frequency 
Domains, 
 Physical Interpretation
	10.4	Convergence and the Generalized Fourier Transform	10-14
			Convergence Factor, Negative Frequency,
	10.5	Numerical Computation of the Fourier Transform		10-21
	10.6	Properties of the Fourier Transform	10-25
			Linearity
			Time Shifting and Frequency Shifting
			Time Scaling and Frequency Scaling
				The Uncertainty Principle
			Transform of a Conjugate
				Even Magnitude and Odd Phase
			Multiplication-Convolution Duality
				System Interconnection, Frequency Response
			Time Differentiation
			Transforms of Periodic Signals
			Parseval?s Theorem
			Integral Definition of an Impulse
			Duality
			Total-Area Integral Using Fourier Transforms
			Time Integration
	10.7	Summary of Important Points	10-48
		Exercises 10-50
Chapter 11 - The Discrete-Time Fourier Transform
	11.1	Introduction and Goals	11-1
	11.2	Basic Concepts and Development of the Fourier Transform	11-1
			Graphical Illustration
			Analytical Derivation
			Definition of the Fourier Transform
				Cyclic and Radian Frequency Forms, Four Fourier Methods 
 Comparison Summary
	11.3	Convergence of the Fourier Transform	11-6
	11.4	Numerical Computation of the Fourier Transform	11-6
	11.5	Properties of the Fourier Transform	11-7
			Linearity
			Time Shifting and Frequency Shifting
			Time Scaling and Frequency Scaling
				Limitations Due to Discrete Time
			Transform of a Conjugate
			Differencing and Accumulation
			Time Reversal
			Multiplication-Convolution Duality
				System Interconnection, Frequency Response
 Accumulation Definition of a Periodic Impulse Function
			Parseval?s Theorem
	11.6	Relations Among Fourier Methods	11-24
			Discrete-Periodic Duality
			CTFT and CTFS
				Information Equivalence, Periodic Extension
			CTFT and DTFT
				Sampling and Impulse Sampling
			DTFT and DTFS
				Information Equivalence, Periodic Extension
			Method Comparison Examples
	11.7	Summary of Important Points		11-45
	Exercises	11-46
Chapter 12 - Continuous-Time Fourier Transform Analysis of Signals 
 and Systems
	12.1	Introduction and Goals	12-1
	12.2	Frequency Response		12-1
			Cascade and Parallel Connections, Power Spectrum, Audio 
Amplifiers and 
 Filters, Graphic Equalizer
	12.3	Ideal Filters	12-9
			Distortion
				Distortionless System
			Filter Classifications
				Lowpass, Highpass, Bandpass, Bandstop
			Ideal Filter Frequency Responses
				Distortionless in Passband
			Bandwidth
			Impulse Responses and Causality
				Impulse and Frequency Responses of Causal Filters 
			The Power Spectrum
			Noise Removal
	12.4	Practical Passive Filters	12-18
			The RC Lowpass Filter
				Impedance and Voltage Division
			The RLC Bandpass Filter
				Resonance
			Examples of Filters
				Automobile Suspension
 12.5	Log-Magnitude Frequency-Response Graphs and Bode Diagrams	12-27
			Component Diagrams
				Poles and Zeros
				One-Real-Pole System
					Asymptotes, Octaves, Decades
				One-Real-Zero-System
				Integrators and Differentiators
				Frequency-Independent Gain
			Complex Pole and Zero Pairs
				Natural Radian Frequency, Damping Ratio
	12.6	Practical Active Filters	12-44
			Operational Amplifiers
				Inverting and Non-Inverting Amplifiers, Integrator, 
Lowpass Filter
	12.7	Communication Systems	12-56
			Modulation
				Problems of Communicating at a Distance, Frequency 
Multiplexing
 Double-Sideband Suppressed-Carrier Modulation			
		Sidebands, Demodulation, Synchronous Demodulation, Local 
 Oscillator
			Double-Sideband Transmitted-Carrier Modulation
				Envelope Detector, Asynchronous Demodulation, 
Overmodulation
			Single-Sideband Modulation and Demodulation
			Pulse Amplitude Modulation
	12.8	Impulse Sampling	12-70
			Aliases, The Sampling Theorem, Intrerpolation
	12.9	Summary of Important Points	12-76
		Exercises	12-78
Chapter 13 - Discrete-Time Fourier Transform Analysis of Signals and 
 Systems
	13.1	Introduction and Goals	13-1
 13.2	Ideal Filters	13-1
			Distortion
				Distortionless System
			Filter Classifications
				Lowpass, Highpass, Bandpass, Bandstop
			Ideal Filter Frequency Responses
				Distortionless in Passband
			Impulse Responses and Causality
				Impulse and Frequency Responses of Causal Filters 
 Filtering Images
 	Pixels, Discrete Space, Causality,
	13.3	Practical Filters	13-12
			Lowpass, Highpass, Bandpass, Bandstop, Responses to Standard 
Signals, 
 Moving Average Filters, Advantages over Continuous-Time Filters
	13.4	Summary of Important Points		13-25
	Exercises	13-26
Chapter 14 - Sampling and the Discrete Fourier Transform
	14.1	Introduction and Goals	14-1
	14.2	Representing a Continuous-Time Signal by Samples		14-2
			Qualitative Concepts
			The Sampling Theorem
				Aliases, Nyquist Rate, Oversampling, Undersampling
			Aliasing
				Anti-Aliasing Filter
			Timelimited and Bandlimited Signals
			Interpolation
				Sinc Function, Zero-Order Hold, First-Order Hold
			Sampling a Sinusoid
	14.3	Bandlimited Periodic Signals		14-22
			Described by a Finite Set of Numbers
	14.4	The Discrete Fourier Transform and its Relation to Other Fourier 
 Methods			14-27
 	Sampling, Windowing, Frequency-Domain Sampling, Periodic Repetition
 	Approximating the CTFT with the DFT
 	Computing the CTFS with the DFT
 	Computing the DTFS with the DFT
 	Approximating the DTFT with the DFT
 	Approximating Continuous-Time Convolution with the DFT
 	Approximating Discrete-Time Convolution with the DFT
 	Approximating Continuous-Time Periodic Convolution with the 
 DFT
 	Computing Discrete-Time Periodic Convolution with the DFT
	14.5	The Fast Fourier Transform		14-36
			Number of Complex Multiplications and Additions, Importance of 
an Integer 
 Power of 2 as Number of Points
	14.6	Summary of Important Points	14-38
		Exercises	14-40
Chapter 15 - The Laplace Transform
	15.1	Introduction and Goals	15-1
	15.2	Development of the Laplace Transform	15-2
			Derivation and Definition
				Generalization of Fourier Transform, Natural Result of 
Complex-
 Exponential Excitation
			Region of Convergence
				Relation to Causality
			The Unilateral Laplace Transform
	15.3	Properties of the Laplace Transform		15-16
			Linearity
			Time Shifting
			Complex-Frequency Shifting
			Time Scaling
			Frequency Scaling
			First Time Derivative
			Nth Time Derivative
			Complex-Frequency Differentiation
			Multiplication-Convolution Duality
			Integration
			Initial Value Theorem
			Final Value Theorem
				Conditions for Validity
	15.4	The Inverse Laplace Transform Using Partial-Fraction Expansion
	15-25
			Proper Rational Functions of s, Handling Repeated Poles
	15.5	Laplace Transform - Fourier Transform Equivalence	15-38
	15.6	Solution of Differential Equations with Initial Conditions	15-39
	15.7	Transfer Functions from Circuit and System Diagrams	15-41		
	15.8	System Stability	15-47
			Pole Locations, Marginal Stability
	15.9	Parallel, Cascade and Feedback Connections		15-50
			Loop Transfer Function, Beneficial Effects
	15.10	System Responses to Standard Signals	15-56
			Unit Step Response
				Stable and Unstable First and Second Order Systems, 
Damping, 
 Resonance
			Response to a Sinusoid Applied at a Finite Time
				Steady-State or Forced Response
	15.11	Pole-Zero Diagrams and Graphical Calculation of Frequency Response
	
		15-66
			Vector Interpretation, Influences of Poles and Zeros, Lowpass, 
Bandpass, 
 Highpass Examples
	15.12	Standard Realizations of Systems	15-77
			Canonical Direct-Form 2, Cascade, Parallel
	15.13	Summary of Important Points		15-82
	Exercises	15-84
Chapter 16 - The z Transform
	16.1	Introduction and Goals	16-1
	16.2	Development of the z Transform	16-1
			Definition and Derivation
				Generalization of Discrete-Time Fourier Transform, 
Natural Result of 
 Complex-Exponential Excitation
			Region of Convergence
			The Unilateral z Transform
	16.3	Properties of the z Transform		16-8
			Linearity
			Time Shifting
				Delay and Advance, Relation to Block Diagrams
			Change of Scale
				Relation to Frequency Shifting
			Initial Value Theorem
			z-Domain Differentiation
			Convolution in Discrete Time
			Differencing
			Accumulation
			Final Value Theorem
				Conditions for Validity
	16.4	The Inverse z Transform	16-17
			Synthetic Division, Partial-Fraction Expansion
	16.5	Solution of Difference Equations with Initial Conditions	16-23
16.6	The Relationships Among the z Transform, the Discrete-Time Fourier 
Transform and the Laplace Transform	16-25
		s-Plane-to-z-Plane Mapping, Relation to Aliasing
	16.7	Transfer Functions	16-29
	16.8	System Stability	16-31
			Pole Locations, Marginal Stability
	16.9	Parallel, Cascade and Feedback Connections		16-32
			Loop Transfer Function
	16.10	System Responses to Standard Signals	16-33
			Unit Sequence Response
				First and Second Order Systems
			Response to a Sinusoid Applied at a Finite Time
				Steady-State or Forced Response
	16.11	Pole-Zero Diagrams and the Graphical Calculation of Frequency 
Response	
		16-41
 Vector Interpretation, Influences of Poles and Zeros
	16.12	Simulating Continuous-Time Systems with Discrete-Time Systems
	16-47
			Discretization, Impulse-Invariant Design
	16.13	Sampled-Data Systems	16-49
			Analog-to-Digital and Digital-to-Analog Converters, Zero-Order 
Hold, 
 Sampling-Rate Effects
	16.14	Standard Realizations of Systems	16-57
			Canonical Direct-Form 2, Cascade, Parallel
	16.15	Summary of Important Points		16-60
	Exercises	16-62
Appendix A - Useful Mathematical Relations
Appendix B - The Continuous-Time Fourier Series Pairs
Appendix C - Discrete-Time Fourier Series Pairs
Appendix D - Continuous-Time Fourier Transform Pairs
Appendix E - Discrete-Time Fourier Transform Pairs
Appendix F - Laplace Transform Pairs
Appendix G - z Transform Pairs
Web Appendix A - Introduction to MATLAB
Web Appendix B - Method for Finding Least Common Multiples
Web Appendix C - Example of Linearizing and Small Signal Analysis
Web Appendix D - Derivations of Convolution Properties
Web Appendix E - An Exploration of Impulse Properties using 
 Convolution
Web Appendix F - Derivations of the Properties of the Continuous-
 Time Fourier Series
Web Appendix G - Derivations of the Properties of the Discrete-
 Time Fourier Series
Web Appendix H - Derivations of the Properties of the Continuous-
 Time Fourier Transform
Web Appendix I - Derivations of the Properties of the Discrete-
 Time Fourier Transform
Web Appendix J - Frequency Response of an Ideal Lowpass Filter
Web Appendix K - Sampling Methods
Web Appendix L - The DFT in Relation to the Other Fourier Methods 
 - With Examples
Web Appendix M - The Fast Fourier Transform
Web Appendix N - Derivations of the Properties of the Laplace 
 Transform
Web Appendix O - Derivations of the Properties of the z Transform
Web Appendix P - Complex Numbers and Complex Functions
Web Appendix Q - Differential and Difference Equations
Web Appendix R - Vectors and Matrices

Library of Congress Subject Headings for this publication:

Signal processing -- Textbooks.
System analysis -- Textbooks.