Digital Signal Processing SIGNALS SYSTEMS AND FILTERS by Andreas Antoniou

Book Name:Digital Signal Processing SIGNALS SYSTEMS AND FILTERS 

Author: Andreas Antoniou

Pages: 991

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Preface
Chapter 1. Introduction to Digital Signal Processing  
1.1 Introduction
1.2 Signals
1.3 Frequency-Domain Representation
1.4 Notation
1.5 Signal Processing
1.6 Analog Filters
1.7 Applications of Analog Filters
1.8 Digital Filters
1.9 Two DSP Applications
1.9.1 Processing of EKG signals
1.9.2 Processing of Stock-Exchange Data
References
Chapter 2. The Fourier Series and Fourier Transform
2.1 Introduction
2.2 Fourier Series
2.2.1 Definition
2.2.2 Particular Forms
2.2.3 Theorems and Properties
2.3 Fourier Transform
2.3.1 Derivation
2.3.2 Particular Forms
2.3.3 Theorems and Properties
References
Problems
Chapter 3. The z Transform 
3.1 Introduction
3.2 Definition of z Transform
3.3 Convergence Properties
3.4 The z Transform as a Laurent Series
3.5 Inverse z Transform
3.6 Theorems and Properties
3.7 Elementary Discrete-Time Signals
3.8 z-Transform Inversion Techniques
3.8.1 Use of Binomial Series
3.8.2 Use of Convolution Theorem
3.8.3 Use of Long Division
3.8.4 Use of Initial-Value Theorem
3.8.5 Use of Partial Fractions
3.9 Spectral Representation of Discrete-Time Signals
3.9.1 Frequency Spectrum
3.9.2 Periodicity of Frequency Spectrum
3.9.3 Interrelations
References
Problems
Chapter 4. Discrete-Time Systems 
4.1 Introduction
4.2 Basic System Properties
4.2.1 Linearity
4.2.2 Time Invariance
4.2.3 Causality
4.3 Characterization of Discrete-Time Systems
4.3.1 Nonrecursive Systems
4.3.2 Recursive Systems
4.4 Discrete-Time System Networks
4.4.1 Network Analysis
4.4.2 Implementation of Discrete-Time Systems
4.4.3 Signal Flow-Graph Analysis
4.5 Introduction to Time-Domain Analysis
4.6 Convolution Summation
4.6.1 Graphical Interpretation
4.6.2 Alternative Classification
4.7 Stability
4.8 State-Space Representation
4.8.1 Computability
4.8.2 Characterization
4.8.3 Time-Domain Analysis
4.8.4 Applications of State-Space Method
References
Problems
Chapter 5. The Application of the z Transform 
5.1 Introduction
5.2 The Discrete-Time Transfer Function
5.2.1 Derivation of H(z) from Difference Equation
5.2.2 Derivation of H(z) from System Network
5.2.3 Derivation of H(z) from State-Space Characterization
5.3 Stability
5.3.1 Constraint on Poles
5.3.2 Constraint on Eigenvalues
5.3.3 Stability Criteria
5.3.4 Test for Common Factors
5.3.5 Schur-Cohn Stability Criterion
5.3.6 Schur-Cohn-Fujiwara Stability Criterion
5.3.7 Jury-Marden Stability Criterion
5.3.8 Lyapunov Stability Criterion
5.4 Time-Domain Analysis
5.5 Frequency-Domain Analysis
5.5.1 Steady-State Sinusoidal Response
5.5.2 Evaluation of Frequency Response
5.5.3 Periodicity of Frequency Response
5.5.4 Aliasing
5.5.5 Frequency Response of Digital Filters
5.6 Transfer Functions for Digital Filters
5.6.1 First-Order Transfer Functions
5.6.2 Second-Order Transfer Functions
5.6.3 Higher-Order Transfer Functions
5.7 Amplitude and Delay Distortion
References
Problems
Chapter 6. The Sampling Process 
6.1 Introduction
6.2 Fourier Transform Revisited
6.2.1 Impulse Functions
6.2.2 Periodic Signals
6.2.3 Unit-Step Function
6.2.4 Generalized Functions
6.3 Interrelation Between the Fourier Series and the Fourier Transform
6.4 Poisson’s Summation Formula
6.5 Impulse-Modulated Signals
6.5.1 Interrelation Between the Fourier and z Transforms
6.5.2 Spectral Relationship Between Discrete- and Continuous-Time Signals
6.6 The Sampling Theorem
6.7 Aliasing
6.8 Graphical Representation of Interrelations
6.9 Processing of Continuous-Time Signals Using Digital Filters
6.10 Practical A/D and D/A Converters
References
Problems
Chapter 7. The Discrete Fourier Transform 
7.1 Introduction
7.2 Definition
7.3 Inverse DFT
7.4 Properties
7.4.1 Linearity
7.4.2 Periodicity
7.4.3 Symmetry
7.5 Interrelation Between the DFT and the z Transform
7.5.1 Frequency-Domain Sampling Theorem
7.5.2 Time-Domain Aliasing
7.6 Interrelation Between the DFT and the CFT
7.6.1 Time-Domain Aliasing
7.7 Interrelation Between the DFT and the Fourier Series
7.8 Window Technique
7.8.1 Continuous-Time Windows
7.8.2 Discrete-Time Windows
7.8.3 Periodic Discrete-Time Windows
7.8.4 Application of Window Technique
7.9 Simplified Notation
7.10 Periodic Convolutions
7.10.1 Time-Domain Periodic Convolution
7.10.2 Frequency-Domain Periodic Convolution
7.11 Fast Fourier-Transform Algorithms
7.11.1 Decimation-in-Time Algorithm
7.11.2 Decimation-in-Frequency Algorithm
7.11.3 Inverse DFT
7.12 Application of the FFT Approach to Signal Processing
7.12.1 Overlap-and-Add Method
7.12.2 Overlap-and-Save Method
References
Problems
Chapter 8. Realization of Digital Filters 
8.1 Introduction
8.2 Realization
8.2.1 Direct Realization
8.2.2 Direct Canonic Realization
8.2.3 State-Space Realization
8.2.4 Lattice Realization
8.2.5 Cascade Realization
8.2.6 Parallel Realization
8.2.7 Transposition
8.3 Implementation
8.3.1 Design Considerations
8.3.2 Systolic Implementations
References
Problems
Chapter 9. Design of Nonrecursive (FIR) Filters 
9.1 Introduction
9.2 Properties of Constant-Delay Nonrecursive Filters
9.2.1 Impulse Response Symmetries
9.2.2 Frequency Response
9.2.3 Location of Zeros
9.3 Design Using the Fourier Series
9.4 Use of Window Functions
9.4.1 Rectangular Window
9.4.2 von Hann and Hamming Windows
9.4.3 Blackman Window
9.4.4 Dolph-Chebyshev Window
9.4.5 Kaiser Window
9.4.6 Prescribed Filter Specifications
9.4.7 Other Windows
9.5 Design Based on Numerical-Analysis Formulas
References
Problems
Chapter 10. Approximations for Analog Filters 
10.1 Introduction
10.2 Basic Concepts
10.2.1 Characterization
10.2.2 Laplace Transform
10.2.3 The Transfer Function
10.2.4 Time-Domain Response
10.2.5 Frequency-Domain Analysis
10.2.6 Ideal and Practical Filters
10.2.7 Realizability Constraints
10.3 Butterworth Approximation
10.3.1 Derivation
10.3.2 Normalized Transfer Function
10.3.3 Minimum Filter Order
10.4 Chebyshev Approximation
10.4.1 Derivation
10.4.2 Zeros of Loss Function
10.4.3 Normalized Transfer Function
10.4.4 Minimum Filter Order
10.5 Inverse-Chebyshev Approximation
10.5.1 Normalized Transfer Function
10.5.2 Minimum Filter Order
10.6 Elliptic Approximation
10.6.1 Fifth-Order Approximation
10.6.2 Nth-Order Approximation (n Odd)
10.6.3 Zeros and Poles of L(−s2)
10.6.4 Nth-Order Approximation (n Even)
10.6.5 Specification Constraint
10.6.6 Normalized Transfer Function
10.7 Bessel-Thomson Approximation
10.8 Transformations
10.8.1 Lowpass-to-Lowpass Transformation
10.8.2 Lowpass-to-Bandpass Transformation
References
Problems
Chapter 11. Design of Recursive (IIR) Filters 
11.1 Introduction
11.2 Realizability Constraints
11.3 Invariant Impulse-Response Method
11.4 Modified Invariant Impulse-Response Method
11.5 Matched-z Transformation Method
11.6 Bilinear-Transformation Method
11.6.1 Derivation
11.6.2 Mapping Properties of Bilinear Transformation
11.6.3 The Warping Effect
11.7 Digital-Filter Transformations
11.7.1 General Transformation
11.7.2 Lowpass-to-Lowpass Transformation
11.7.3 Lowpass-to-Bandstop Transformation
11.7.4 Application
11.8 Comparison Between Recursive and Nonrecursive Designs
References
Problems
Chapter 12. Recursive (IIR) Filters Satisfying Prescribed Specifications
12.1 Introduction
12.2 Design Procedure
12.3 Design Formulas
12.3.1 Lowpass and Highpass Filters
12.3.2 Bandpass and Bandstop Filters
12.3.3 Butterworth Filters
12.3.4 Chebyshev Filters
12.3.5 Inverse-Chebyshev Filters
12.3.6 Elliptic Filters
12.4 Design Using the Formulas and Tables
12.5 Constant Group Delay
12.5.1 Delay Equalization
12.5.2 Zero-Phase Filters
12.6 Amplitude Equalization
References
Problems
Chapter 13. Random Signals 
13.1 Introduction
13.2 Random Variables
13.2.1 Probability-Distribution Function
13.2.2 Probability-Density Function
13.2.3 Uniform Probability Density
13.2.4 Gaussian Probability Density
13.2.5 Joint Distributions
13.2.6 Mean Values and Moments
13.3 Random Processes
13.3.1 Notation
13.4 First- and Second-Order Statistics
13.5 Moments and Autocorrelation
13.6 Stationary Processes
13.7 Frequency-Domain Representation
13.8 Discrete-Time Random Processes
13.9 Filtering of Discrete-Time Random Signals
References
Problems
Chapter 14. Effects of FiniteWord Length in Digital Filters 
14.1 Introduction
14.2 Number Representation
14.2.1 Binary System
14.2.2 Fixed-Point Arithmetic
14.2.3 Floating-Point Arithmetic
14.2.4 Number Quantization
14.3 Coefficient Quantization
14.4 Low-Sensitivity Structures
14.4.1 Case I
14.4.2 Case II
14.5 Product Quantization
14.6 Signal Scaling
14.6.1 Method A
14.6.2 Method B
14.6.3 Types of Scaling
14.6.4 Application of Scaling
14.7 Minimization of Output Roundoff Noise
14.8 Application of Error-Spectrum Shaping
14.9 Limit-Cycle Oscillations
14.9.1 Quantization Limit Cycles
14.9.2 Overflow Limit Cycles
14.9.3 Elimination of Quantization Limit Cycles
14.9.4 Elimination of Overflow Limit Cycles
References
Problems
Chapter 15. Design of Nonrecursive Filters Using Optimization Methods
15.1 Introduction
15.2 Problem Formulation
15.2.1 Lowpass and Highpass Filters
15.2.2 Bandpass and Bandstop Filters
15.2.3 Alternation Theorem
15.3 Remez Exchange Algorithm
15.3.1 Initialization of Extremals
15.3.2 Location of Maxima of the Error Function
15.3.3 Computation of |E(ω)| and Pc(ω)
15.3.4 Rejection of Superfluous Potential Extremals
15.3.5 Computation of Impulse Response
15.4 Improved Search Methods
15.4.1 Selective Step-by-Step Search
15.4.2 Cubic Interpolation
15.4.3 Quadratic Interpolation
15.4.4 Improved Formulation
15.5 Efficient Remez Exchange Algorithm
15.6 Gradient Information
15.6.1 Property 1
15.6.2 Property 2
15.6.3 Property 3
15.6.4 Property 4
15.6.5 Property 5
15.7 Prescribed Specifications
15.8 Generalization
15.8.1 Antisymmetrical Impulse Response and Odd Filter Length
15.8.2 Even Filter Length
15.9 Digital Differentiators
15.9.1 Problem Formulation
15.9.2 First Derivative
15.9.3 Prescribed Specifications
15.10 Arbitrary Amplitude Responses
15.11 Multiband Filters
References
Additional References
Problems
Chapter 16. Design of Recursive Filters Using Optimization Methods
16.1 Introduction
16.2 Problem Formulation
16.3 Newton’s Method
16.4 Quasi-Newton Algorithms
16.4.1 Basic Quasi-Newton Algorithm
16.4.2 Updating Formulas for Matrix Sk+1
16.4.3 Inexact Line Searches
16.4.4 Practical Quasi-Newton Algorithm
16.5 Minimax Algorithms
16.6 Improved Minimax Algorithms
16.7 Design of Recursive Filters
16.7.1 Objective Function
16.7.2 Gradient Information
16.7.3 Stability
16.7.4 Minimum Filter Order
16.7.5 Use of Weighting
16.8 Design of Recursive Delay Equalizers
References
Additional References
Problems
Chapter 17. Wave Digital Filters 
17.1 Introduction
17.2 Sensitivity Considerations
17.3 Wave Network Characterization
17.4 Element Realizations
17.4.1 Impedances
17.4.2 Voltage Sources
17.4.3 Series Wire Interconnection
17.4.4 Parallel Wire Interconnection
17.4.5 2-Port Adaptors
17.4.6 Transformers
17.4.7 Unit Elements
17.4.8 Circulators
17.4.9 Resonant Circuits
17.4.10 Realizability Constraint
17.5 Lattice Wave Digital Filters
17.5.1 Analysis
17.5.2 Alternative Lattice Configuration
17.5.3 Digital Realization
17.6 Ladder Wave Digital Filters
17.7 Filters Satisfying Prescribed Specifications
17.8 Frequency-Domain Analysis
17.9 Scaling
17.10 Elimination of Limit-Cycle Oscillations
17.11 Related Synthesis Methods
17.12 A Cascade Synthesis Based on the Wave Characterization
17.12.1 Generalized-Immittance Converters
17.12.2 Analog G-CGIC Configuration
17.12.3 Digital G-CGIC Configuration
17.12.4 Cascade Synthesis
17.12.5 Signal Scaling
17.12.6 Output Noise
17.13 Choice of Structure
References
Problems
Chapter 18. Digital Signal Processing Applications 
18.1 Introduction
18.2 Sampling-Frequency Conversion
18.2.1 Decimators
18.2.2 Interpolators
18.2.3 Sampling Frequency Conversion by a Noninteger Factor
18.2.4 Design Considerations
18.3 Quadrature-Mirror-Image Filter Banks
18.3.1 Operation
18.3.2 Elimination of Aliasing Errors
18.3.3 Design Considerations
18.3.4 Perfect Reconstruction
18.4 Hilbert Transformers
18.4.1 Design of Hilbert Transformers
18.4.2 Single-Sideband Modulation
18.4.3 Sampling of Bandpassed Signals
18.5 Adaptive Digital Filters
18.5.1 Wiener Filters
18.5.2 Newton Algorithm
18.5.3 Steepest-Descent Algorithm
18.5.4 Least-Mean-Square Algorithm
18.5.5 Recursive Filters
18.5.6 Applications
18.6 Two-Dimensional Digital Filters
18.6.1 Two-Dimensional Convolution
18.6.2 Two-Dimensional z Transform
18.6.3 Two-Dimensional Transfer Function
18.6.4 Stability
18.6.5 Frequency-Domain Analysis
18.6.6 Types of 2-D Filters
18.6.7 Approximations
18.6.8 Applications
References
Additional References
Problems
Appendix A. Complex Analysis
A.1 Introduction
A.2 Complex Numbers
A.2.1 Complex Arithmetic
A.2.2 De Moivre’s Theorem
A.2.3 Euler’s Formula
A.2.4 Exponential Form
A.2.5 Vector Representation
A.2.6 Spherical Representation
A.3 Functions of a Complex Variable
A.3.1 Polynomials
A.3.2 Inverse Algebraic Functions
A.3.3 Trigonometric Functions and Their Inverses
A.3.4 Hyperbolic Functions and Their Inverses
A.3.5 Multi-Valued Functions
A.3.6 Periodic Function
A.3.7 Rational Algebraic Functions
A.4 Basic Principles of Complex Analysis
A.4.1 Limit
A.4.2 Differentiability
A.4.3 Analyticity
A.4.4 Zeros
A.4.5 Singularities
A.4.6 Zero-Pole Plots
A.5 Series
A.6 Laurent Theorem
A.7 Residue Theorem
A.8 Analytic Continuation
A.9 Conformal Transformations
References
Appendix B. Elliptic Functions
B.1 Introduction
B.2 Elliptic Integral of the First Kind
B.3 Elliptic Functions
B.4 Imaginary Argument
B.5 Formulas
B.6 Periodicity
B.7 Transformation
B.8 Series Representation
References
Index