Signals and systems : analysis using transform methods and MATLAB

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Title
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Contents
Preface
Chapter 1 Introduction
	1.1 Signals and Systems Defined
	1.2 Types of Signals
	1.3 Examples of Systems
		A Mechanical System
		A Fluid System
		A Discrete-Time System
		Feedback Systems
	1.4 A Familiar Signal and System Example
	1.5 Use of MATLAB®
Chapter 2 Mathematical Description of Continuous-Time Signals
	2.1 Introduction and Goals
	2.2 Functional Notation
	2.3 Continuous-Time Signal Functions
		Complex Exponentials and Sinusoids
		Functions with Discontinuities
			The Signum Function
			The Unit-Step Function
			The Unit-Ramp Function
			The Unit Impulse
				The Impulse, the Unit Step, and Generalized Derivatives
				The Equivalence Property of the Impulse
				The Sampling Property of the Impulse
				The Scaling Property of the Impulse
			The Unit Periodic Impulse or Impulse Train
			A Coordinated Notation for Singularity Functions
			The Unit-Rectangle Function
	2.4 Combinations of Functions
	2.5 Shifting and Scaling
		Amplitude Scaling
		Time Shifting
		Time Scaling
		Simultaneous Shifting and Scaling
	2.6 Differentiation and Integration
	2.7 Even and Odd Signals
		Combinations of Even and Odd Signals
		Derivatives and Integrals of Even and Odd Signals
	2.8 Periodic Signals
	2.9 Signal Energy and Power
		Signal Energy
		Signal Power
	2.10 Summary of Important Points
	Exercises
		Exercises with Answers
			Signal Functions
			Shifting and Scaling
			Derivatives and Integrals of Functions
			Generalized Derivative
			Even and Odd Functions
			Periodic Signals
			Signal Energy and Power of Signals
		Exercises without Answers
			Signal Functions
			Scaling and Shifting
			Generalized Derivative
			Derivatives and Integrals of Functions
			Even and Odd Functions
			Periodic Functions
			Signal Energy and Power of Signals
Chapter 3 Discrete-Time Signal Description
	3.1 Introduction and Goals
	3.2 Sampling and Discrete Time
	3.3 Sinusoids and Exponentials
		Sinusoids
		Exponentials
	3.4 Singularity Functions
		The Unit-Impulse Function
		The Unit-Sequence Function
		The Signum Function
		The Unit-Ramp Function
		The Unit Periodic Impulse Function or Impulse Train
	3.5 Shifting and Scaling
		Amplitude Scaling
		Time Shifting
		Time Scaling
			Time Compression
			Time Expansion
	3.6 Differencing and Accumulation
	3.7 Even and Odd Signals
		Combinations of Even and Odd Signals
		Symmetrical Finite Summation of Even and Odd Signals
	3.8 Periodic Signals
	3.9 Signal Energy and Power
		Signal Energy
		Signal Power
	3.10 Summary of Important Points
	Exercises
		Exercises with Answers
			Functions
			Scaling and Shifting Functions
			Differencing and Accumulation
			Even and Odd Functions
			Periodic Functions
			Signal Energy and Power
		Exercises without Answers
			Signal Functions
			Shifting and Scaling Functions
			Differencing and Accumulation
			Even and Odd Functions
			Periodic Signals
			Signal Energy and Power
Chapter 4 Description of Systems
	4.1 Introduction and Goals
	4.2 Continuous-Time Systems
		System Modeling
			Differential Equations
			Block Diagrams
		System Properties
			Introductory Example
			Homogeneity
			Time Invariance
			Additivity
			Linearity and Superposition
			LTI Systems
			Stability
			Causality
			Memory
			Static Nonlinearity
			Invertibility
		Dynamics of Second-Order Systems
		Complex Sinusoid Excitation
	4.3 Discrete-Time Systems
		System Modeling
			Block Diagrams
			Difference Equations
		System Properties
	4.4 Summary of Important Points
	Exercises
		Exercises with Answers
			System Models
			Block Diagrams
			System Properties
		Exercises without Answers
			System Models
			System Properties
Chapter 5 Time-Domain System Analysis
	5.1 Introduction and Goals
	5.2 Continuous Time
		Impulse Response
		Continuous-Time Convolution
			Derivation
			Graphical and Analytical Examples of Convolution
			Convolution Properties
			System Connections
			Step Response and Impulse Response
			Stability and Impulse Response
			Complex Exponential Excitation and the Transfer Function
			Frequency Response
	5.3 Discrete Time
		Impulse Response
		Discrete-Time Convolution
			Derivation
			Graphical and Analytical Examples of Convolution
			Convolution Properties
			Numerical Convolution
				Discrete-Time Numerical Convolution
				Continuous-Time Numerical Convolution
			Stability and Impulse Response
			System Connections
			Unit-Sequence Response and Impulse Response
			Complex Exponential Excitation and the Transfer Function
			Frequency Response
	5.4 Summary of Important Points
	Exercises
		Exercises with Answers
			Continuous Time
			Impulse Response
			Convolution
			Stability
			Frequency Response
			Discrete Time
			Impulse Response
			Convolution
			Stability
		Exercises without Answers
			Continuous Time
			Impulse Response
			Convolution
			Stability
			Discrete Time
			Impulse Response
			Convolution
			Stability
Chapter 6 Continuous-Time Fourier Methods
	6.1 Introduction and Goals
	6.2 The Continuous-Time Fourier Series
		Conceptual Basis
		Orthogonality and the Harmonic Function
		The Compact Trigonometric Fourier Series
		Convergence
			Continuous Signals
			Discontinuous Signals
		Minimum Error of Fourier-Series Partial Sums
		The Fourier Series of Even and Odd Periodic Functions
		Fourier-Series Tables and Properties
		Numerical Computation of the Fourier Series
	6.3 The Continuous-Time Fourier Transform
		Extending the Fourier Series to Aperiodic Signals
		The Generalized Fourier Transform
		Fourier Transform Properties
		Numerical Computation of the Fourier Transform
	6.4 Summary of Important Points
	Exercises
		Exercises with Answers
			Fourier Series
			Orthogonality
			Forward and Inverse Fourier Transforms
			Relation of CTFS to CTFT
			Numerical CTFT
			System Response
		Exercises without Answers
			Fourier Series
			Forward and Inverse Fourier Transforms
			System Response
			Relation of CTFS to CTFT
Chapter 7 Discrete-Time Fourier Methods
	7.1 Introduction and Goals
	7.2 The Discrete-Time Fourier Series and the Discrete Fourier Transform
		Linearity and Complex-Exponential Excitation
		Orthogonality and the Harmonic Function
		Discrete Fourier Transform Properties
		The Fast Fourier Transform
	7.3 The Discrete-Time Fourier Transform
		Extending the Discrete Fourier Transform to Aperiodic Signals
		Derivation and Definition
		The Generalized DTFT
		Convergence of the Discrete-Time Fourier Transform
		DTFT Properties
		Numerical Computation of the Discrete-Time Fourier Transform
	7.4 Fourier Method Comparisons
	7.5 Summary of Important Points
	Exercises
		Exercises with Answers
			Orthogonality
			Discrete Fourier Transform
			Discrete-Time Fourier Transform Definition
			Forward and Inverse Discrete-Time Fourier Transforms
		Exercises without Answers
			Discrete Fourier Transform
			Forward and Inverse Discrete-Time Fourier Transforms
Chapter 8 The Laplace Transform
	8.1 Introduction and Goals
	8.2 Development of the Laplace Transform
		Generalizing the Fourier Transform
		Complex Exponential Excitation and Response
	8.3 The Transfer Function
	8.4 Cascade-Connected Systems
	8.5 Direct Form II Realization
	8.6 The Inverse Laplace Transform
	8.7 Existence of the Laplace Transform
		Time-Limited Signals
		Right- and Left-Sided Signals
	8.8 Laplace-Transform Pairs
	8.9 Partial-Fraction Expansion
	8.10 Laplace-Transform Properties
	8.11 The Unilateral Laplace Transform
		Definition
		Properties Unique to the Unilateral Laplace Transform
		Solution of Differential Equations with Initial Conditions
	8.12 Pole-Zero Diagrams and Frequency Response
	8.13 MATLAB System Objects
	8.14 Summary of Important Points
	Exercises
		Exercises with Answers
			Laplace-Transform Definition
			Direct Form II System Realization
			Forward and Inverse Laplace Transforms
			Unilateral Laplace-Transform Integral
			Solving Differential Equations
		Exercises without Answers
			Region of Convergence
			Existence of the Laplace Transform
			Direct Form II System Realization
			Forward and Inverse Laplace Transforms
			Solution of Differential Equations
			Pole-Zero Diagrams and Frequency Response
Chapter 9 The z Transform
	9.1 Introduction and Goals
	9.2 Generalizing the Discrete-Time Fourier Transform
	9.3 Complex Exponential Excitation and Response
	9.4 The Transfer Function
	9.5 Cascade-Connected Systems
	9.6 Direct Form II System Realization
	9.7 The Inverse z Transform
	9.8 Existence of the z Transform
		Time-Limited Signals
		Right- and Left-Sided Signals
	9.9 z-Transform Pairs
	9.10 z-Transform Properties
	9.11 Inverse z-Transform Methods
		Synthetic Division
		Partial-Fraction Expansion
		Examples of Forward and Inverse z Transforms
	9.12 The Unilateral z Transform
		Properties Unique to the Unilateral z Transform
		Solution of Difference Equations
	9.13 Pole-Zero Diagrams and Frequency Response
	9.14 MATLAB System Objects
		In MATLAB
	9.15 Transform Method Comparisons
	9.16 Summary of Important Points
	Exercises
		Exercises with Answers
			Direct-Form II System Realization
			Existence of the z Transform
			Forward and Inverse z Transforms
			Unilateral z-Transform Properties
			Solution of Difference Equations
			Pole-Zero Diagrams and Frequency Response
		Exercises without Answers
			Direct Form II System Realization
			Existence of the z Transform
			Forward and Inverse z-Transforms
			Pole-Zero Diagrams and Frequency Response
Chapter 10 Sampling and Signal Processing
	10.1 Introduction and Goals
	10.2 Continuous-Time Sampling
		Sampling Methods
		The Sampling Theorem
			Qualitative Concepts
			Sampling Theorem Derivation
		Aliasing
		Time-limited and Bandlimited Signals
		Interpolation
			Ideal Interpolation
			Practical Interpolation
				Zero-Order Hold
				First-Order Hold
		Sampling Bandpass Signals
		Sampling a Sinusoid
		Bandlimited Periodic Signals
		Signal Processing Using the DFT
			CTFT-DFT Relationship
				CTFT-DTFT Relationship
				Sampling and Periodic-Repetition Relationship
			Computing the CTFS Harmonic Function with the DFT
			Approximating the CTFT with the DFT
				Forward CTFT
				Inverse CTFT
			Approximating the DTFT with the DFT
			Approximating Continuous-Time Convolution with the DFT
				Aperiodic Convolution
				Periodic Convolution
			Discrete-Time Convolution with the DFT
				Aperiodic Convolution
				Periodic Convolution
			Summary of Signal Processing Using the DFT
	10.3 Discrete-Time Sampling
		Periodic-Impulse Sampling
		Interpolation
	10.4 Summary of Important Points
	Exercises
		Exercises with Answers
			Pulse Amplitude Modulation
			Sampling
			Impulse Sampling
			Nyquist Rates
			Time-Limited and Bandlimited Signals
			Interpolation
			Aliasing
			Bandlimited Periodic Signals
			CTFT-CTFS-DFT Relationships
			Windows
			DFT
		Exercises without Answers
			Sampling
			Impulse Sampling
			Nyquist Rates
			Aliasing
			Practical Sampling
			Bandlimited Periodic Signals
			DFT
			Discrete-Time Sampling
Chapter 11 Frequency Response Analysis
	11.1 Introduction and Goals
	11.2 Frequency Response
	11.3 Continuous-Time Filters
		Examples of Filters
		Ideal Filters
			Distortion
			Filter Classifications
			Ideal Filter Frequency Responses
			Impulse Responses and Causality
			The Power Spectrum
			Noise Removal
		Bode Diagrams
			The Decibel
				The One-Real-Pole System
				The One-Real-Zero System
				Integrators and Differentiators
				Frequency-Independent Gain
				Complex Pole and Zero Pairs
			Practical Filters
				Passive Filters
					The Lowpass Filter
					The Bandpass Filter
				Active Filters
					Operational Amplifiers
					The Integrator
					The Lowpass Filter
	11.4 Discrete-Time Filters
		Notation
		Ideal Filters
			Distortion
			Filter Classifications
			Frequency Responses
			Impulse Responses and Causality
			Filtering Images
		Practical Filters
			Comparison with Continuous-Time Filters
			Highpass, Bandpass, and Bandstop Filters
			The Moving Average Filter
			The Almost Ideal Lowpass Filter
			Advantages Compared to Continuous-Time Filters
	11.5 Summary of Important Points
	Exercises
		Exercises with Answers
			Continuous-Time Frequency Response
			Continuous-Time Ideal Filters
			Continuous-Time Causality
			Logarithmic Graphs, Bode Diagrams, and Decibels
			Continuous-Time Practical Passive Filters
			Continuous-Time Practical Active Filters
			Discrete-Time Frequency Response
			Discrete-Time Ideal Filters
			Discrete-Time Causality
			Discrete-Time Practical Filters
		Exercises without Answers
			Continuous-Time Frequency Response
			Continuous-Time Ideal Filters
			Continuous-Time Causality
			Bode Diagrams
			Continuous-Time Practical Passive Filters
			Continuous-Time Filters
			Continuous-Time Practical Active Filters
			Discrete-Time Causality
			Discrete-Time Filters
Chapter 12 Laplace System Analysis
	12.1 Introduction and Goals
	12.2 System Representations
	12.3 System Stability
	12.4 System Connections
		Cascade and Parallel Connections
		The Feedback Connection
			Terminology and Basic Relationships
			Feedback Effects on Stability
			Beneficial Effects of Feedback
			Instability Caused by Feedback
			Stable Oscillation Using Feedback
			The Root-Locus Method
			Tracking Errors in Unity-Gain Feedback Systems
	12.5 System Analysis Using MATLAB
	12.6 System Responses to Standard Signals
		Unit-Step Response
		Sinusoid Response
	12.7 Standard Realizations of Systems
		Cascade Realization
		Parallel Realization
	12.8 Summary of Important Points
	Exercises
		Exercises with Answers
			Transfer Functions
			Stability
			Parallel, Cascade, and Feedback Connections
			Root Locus
			Tracking Errors in Unity-Gain Feedback Systems
			System Responses to Standard Signals
			System Realization
		Exercises without Answers
			Stability
			Transfer Functions
			Stability
			Parallel, Cascade, and Feedback Connections
			Root Locus
			Tracking Errors in Unity-Gain Feedback Systems
			Response to Standard Signals
			System Realization
Chapter 13 z-Transform System Analysis
	13.1 Introduction and Goals
	13.2 System Models
		Difference Equations
		Block Diagrams
	13.3 System Stability
	13.4 System Connections
	13.5 System Responses to Standard Signals
		Unit-Sequence Response
		Response to a Causal Sinusoid
	13.6 Simulating Continuous-Time Systems with Discrete-Time Systems
		z-Transform-Laplace-Transform Relationships
		Impulse Invariance
		Sampled-Data Systems
	13.7 Standard Realizations of Systems
		Cascade Realization
		Parallel Realization
	13.8 Summary of Important Points
	Exercises
		Exercises with Answers
			Stability
			Parallel, Cascade, and Feedback Connections
			Response to Standard Signals
			Root Locus
			Laplace-Transform-z-Transform Relationship
			Sampled-Data Systems
			System Realization
		Exercises without Answers
			Stability
			Root Locus
			Parallel, Cascade, and Feedback Connections
			Response to Standard Signals
			Laplace-Transform-z-Transform Relationship
			Sampled-Data Systems
			System Realization
			General
Chapter 14 Filter Analysis and Design
	14.1 Introduction and Goals
	14.2 Analog Filters
		Butterworth Filters
			Normalized Butterworth Filters
			Filter Transformations
			MATLAB Design Tools
		Chebyshev, Elliptic, and Bessel Filters
	14.3 Digital Filters
		Simulation of Analog Filters
		Filter Design Techniques
			IIR Filter Design
			Time-Domain Methods
				Impulse-Invariant Design
				Step-Invariant Design
				Finite-Difference Design
				Frequency-Domain Methods
				The Bilinear Method
			FIR Filter Design
				Truncated Ideal Impulse Response
				Optimal FIR Filter Design
			MATLAB Design Tools
	14.4 Summary of Important Points
	Exercises
		Exercises with Answers
			Continuous-Time Filters
			Finite-Difference Filter Design
			Matched-z Transform and Direct Substitution Filter Design
			Bilinear z-Transform Filter Design
			FIR Filter Design
			Digital Filter Design Method Comparison
		Exercises without Answers
			Analog Filter Design
			Impulse-Invariant and Step-Invariant Filter Design
			Finite-Difference Filter Design
			Matched z-Transform and Direct Substitution Filter Design
			Bilinear z-Transform Filter Design
			FIR Filter Design
			Digital Filter Design Method Comparison
Appendix
	I: Useful Mathematical Relations
	II: Continuous-Time Fourier Series Pairs
	III: Discrete Fourier Transform Pairs
	IV: Continuous-Time Fourier Transform Pairs
	V: Discrete-Time Fourier Transform Pairs
	VI: Tables of Laplace Transform Pairs
	VII: z-Transform Pairs
Bibliography
Index
	A
	B
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	D
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