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9780071454247

Digital Signal Processing Signals, Systems, and Filters

by
  • ISBN13:

    9780071454247

  • ISBN10:

    0071454241

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2005-10-10
  • Publisher: McGraw-Hill Education
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Summary

Digital Signal Processing is a rapidly growing academic discipline the world over. This new text utilizes MATLAB and the CD-based DSP Lab to provide readers with a fully interactive approach to mastering the fundamentals of DSP and filter design. DSP Lab allows readers to work problems without purchasing MATLAB

Author Biography

Andreas Antoniou (Victoria, Canada) is Professor of Electrical and Computer Engineering at the University of Victoria. He has published over 100 technical papers in the fields of signal processing and filter design, and is the author of McGraw-Hill’s Digital Filters.

Table of Contents

Preface xix
Introduction to Digital Signal Processing
1(28)
Introduction
1(1)
Signals
1(3)
Frequency-Domain Representation
4(3)
Notation
7(1)
Signal Processing
8(7)
Analog Filters
15(1)
Applications of Analog Filters
16(3)
Digital Filters
19(4)
Two DSP Applications
23(6)
Processing of EKG signals
23(1)
Processing of Stock-Exchange Data
24(2)
References
26(3)
The Fourier Series and Fourier Transform
29(50)
Introduction
29(1)
Fourier Series
29(17)
Definition
30(1)
Particular Forms
31(4)
Theorems and Properties
35(11)
Fourier Transform
46(33)
Derivation
47(3)
Particular Forms
50(7)
Theorems and Properties
57(16)
References
73(1)
Problems
73(6)
The z Transform
79(52)
Introduction
79(1)
Definition of z Transform
80(1)
Convergence Properties
81(2)
The z Transform as a Laurent Series
83(2)
Inverse z Transform
85(1)
Theorems and Properties
86(9)
Elementary Discrete-Time Signals
95(6)
z-Transform Inversion Techniques
101(18)
Use of Binomial Series
103(5)
Use of Convolution Theorem
108(2)
Use of Long Division
110(3)
Use of Initial-Value Theorem
113(2)
Use of Partial Fractions
115(4)
Spectral Representation of Discrete-Time Signals
119(12)
Frequency Spectrum
119(1)
Periodicity of Frequency Spectrum
120(4)
Interrelations
124(2)
References
126(1)
Problems
126(5)
Discrete-Time Systems
131(70)
Introduction
131(1)
Basic System Properties
132(8)
Linearity
132(2)
Time Invariance
134(2)
Causality
136(4)
Characterization of Discrete-Time Systems
140(2)
Nonrecursive Systems
140(1)
Recursive Systems
140(2)
Discrete-Time System Networks
142(13)
Network Analysis
143(3)
Implementation of Discrete-Time Systems
146(1)
Signal Flow-Graph Analysis
147(8)
Introduction to Time-Domain Analysis
155(8)
Convolution Summation
163(8)
Graphical Interpretation
166(3)
Alternative Classification
169(2)
Stability
171(3)
State-Space Representation
174(27)
Computability
175(1)
Characterization
176(8)
Time-Domain Analysis
184(2)
Applications of State-Space Method
186(1)
References
186(1)
Problems
186(15)
The Application of the z Transform
201(60)
Introduction
201(1)
The Discrete-Time Transfer Function
202(5)
Derivation of H(z) from Difference Equation
202(2)
Derivation of H(z) from System Network
204(1)
Derivation of H(z) from State-Space Characterization
205(2)
Stability
207(16)
Constraint on Poles
207(4)
Constraint on Eigenvalues
211(3)
Stability Criteria
214(1)
Test for Common Factors
215(1)
Schur-Cohn Stability Criterion
216(1)
Schur-Cohn-Fujiwara Stability Criterion
217(2)
Jury-Marden Stability Criterion
219(3)
Lyapunov Stability Criterion
222(1)
Time-Domain Analysis
223(1)
Frequency-Domain Analysis
224(21)
Steady-State Sinusoidal Response
224(3)
Evaluation of Frequency Response
227(1)
Periodicity of Frequency Response
228(1)
Aliasing
229(3)
Frequency Response of Digital Filters
232(13)
Transfer Functions for Digital Filters
245(6)
First-Order Transfer Functions
246(1)
Second-Order Transfer Functions
246(5)
Higher-Order Transfer Functions
251(1)
Amplitude and Delay Distortion
251(10)
References
254(1)
Problems
254(7)
The Sampling Process
261(60)
Introduction
261(2)
Fourier Transform Revisited
263(15)
Impulse Functions
263(9)
Periodic Signals
272(2)
Unit-Step Function
274(1)
Generalized Functions
274(4)
Interrelation Between the Fourier Series and the Fourier Transform
278(6)
Poisson's Summation Formula
284(2)
Impulse-Modulated Signals
286(8)
Interrelation Between the Fourier and z Transforms
288(2)
Spectral Relationship Between Discrete- and Continuous-Time Signals
290(4)
The Sampling Theorem
294(2)
Aliasing
296(1)
Graphical Representation of Interrelations
297(1)
Processing of Continuous-Time Signals Using Digital Filters
298(5)
Practical A/D and D/A Converters
303(18)
References
311(1)
Problems
311(10)
The Discrete Fourier Transform
321(68)
Introduction
321(1)
Definition
322(1)
Inverse DFT
322(1)
Properties
323(2)
Linearity
323(1)
Periodicity
323(1)
Symmetry
323(2)
Interrelation Between the DFT and the z Transform
325(8)
Frequency-Domain Sampling Theorem
328(5)
Time-Domain Aliasing
333(1)
Interrelation Between the DFT and the CFT
333(2)
Time-Domain Aliasing
335(1)
Interrelation Between the DFT and the Fourier Series
335(2)
Window Technique
337(21)
Continuous-Time Windows
337(13)
Discrete-Time Windows
350(2)
Periodic Discrete-Time Windows
352(2)
Application of Window Technique
354(4)
Simplified Notation
358(1)
Periodic Convolutions
358(4)
Time-Domain Periodic Convolution
359(2)
Frequency-Domain Periodic Convolution
361(1)
Fast Fourier-Transform Algorithms
362(14)
Decimation-in-Time Algorithm
362(8)
Decimation-in-Frequency Algorithm
370(5)
Inverse DFT
375(1)
Application of the FFT Approach to Signal Processing
376(13)
Overlap-and-Add Method
377(3)
Overlap-and-Save Method
380(1)
References
381(1)
Problems
382(7)
Realization of Digital Filters
389(36)
Introduction
389(2)
Realization
391(21)
Direct Realization
392(3)
Direct Canonic Realization
395(2)
State-Space Realization
397(4)
Lattice Realization
401(3)
Cascade Realization
404(3)
Parallel Realization
407(3)
Transposition
410(2)
Implementation
412(13)
Design Considerations
412(1)
Systolic Implementations
412(5)
References
417(1)
Problems
417(8)
Design of Nonrecursive (FIR) Filters
425(38)
Introduction
425(1)
Properties of Constant-Delay Nonrecursive Filters
426(5)
Impulse Response Symmetries
426(2)
Frequency Response
428(2)
Location of Zeros
430(1)
Design Using the Fourier Series
431(3)
Use of Window Functions
434(19)
Rectangular Window
435(2)
von Hann and Hamming Windows
437(2)
Blackman Window
439(1)
Dolph-Chebyshev Window
440(5)
Kaiser Window
445(1)
Prescribed Filter Specifications
445(8)
Other Windows
453(1)
Design Based on Numerical-Analysis Formulas
453(10)
References
458(1)
Problems
459(4)
Approximations for Analog Filters
463(66)
Introduction
463(2)
Basic Concepts
465(10)
Characterization
465(1)
Laplace Transform
465(1)
The Transfer Function
466(1)
Time-Domain Response
466(3)
Frequency-Domain Analysis
469(2)
Ideal and Practical Filters
471(3)
Realizability Constraints
474(1)
Butterworth Approximation
475(6)
Derivation
475(1)
Normalized Transfer Function
476(3)
Minimum Filter Order
479(2)
Chebyshev Approximation
481(12)
Derivation
481(4)
Zeros of Loss Function
485(4)
Normalized Transfer Function
489(1)
Minimum Filter Order
490(3)
Inverse-Chebyshev Approximation
493(4)
Normalized Transfer Function
493(1)
Minimum Filter Order
494(3)
Elliptic Approximation
497(16)
Fifth-Order Approximation
497(7)
Nth-Order Approximation (n Odd)
504(1)
Zeros and Poles of L(--s2)
504(3)
Nth-Order Approximation (n Even)
507(1)
Specification Constraint
508(1)
Normalized Transfer Function
509(4)
Bessel-Thomson Approximation
513(3)
Transformations
516(13)
Lowpass-to-Lowpass Transformation
516(1)
Lowpass-to-Bandpass Transformation
516(3)
References
519(1)
Problems
520(9)
Design of Recursive (IIR) Filters
529(34)
Introduction
529(1)
Realizability Constraints
530(1)
Invariant Impulse-Response Method
530(4)
Modified Invariant Impulse-Response Method
534(4)
Matched-z Transformation Method
538(3)
Bilinear-Transformation Method
541(8)
Derivation
541(2)
Mapping Properties of Bilinear Transformation
543(2)
The Warping Effect
545(4)
Digital-Filter Transformations
549(5)
General Transformation
549(2)
Lowpass-to-Lowpass Transformation
551(1)
Lowpass-to-Bandstop Transformation
552(2)
Application
554(1)
Comparison Between Recursive and Nonrecursive Designs
554(9)
References
555(1)
Problems
556(7)
Recursive (IIR) Filters Satisfying Prescribed Specifications
563(30)
Introduction
563(1)
Design Procedure
564(1)
Design Formulas
565(12)
Lowpass and Highpass Filters
565(3)
Bandpass and Bandstop Filters
568(5)
Butterworth Filters
573(2)
Chebyshev Filters
575(1)
Inverse-Chebyshev Filters
576(1)
Elliptic Filters
576(1)
Design Using the Formulas and Tables
577(9)
Constant Group Delay
586(2)
Delay Equalization
586(1)
Zero-Phase Filters
587(1)
Amplitude Equalization
588(5)
References
588(1)
Problems
588(5)
Random Signals
593(24)
Introduction
593(1)
Random Variables
593(5)
Probability-Distribution Function
594(1)
Probability-Density Function
594(1)
Uniform Probability Density
594(1)
Gaussian Probability Density
594(1)
Joint Distributions
594(1)
Mean Values and Moments
595(3)
Random Processes
598(1)
Notation
598(1)
First-and Second-Order Statistics
599(3)
Moments and Autocorrelation
602(2)
Stationary Processes
604(1)
Frequency-Domain Representation
604(5)
Discrete-Time Random Processes
609(1)
Filtering of Discrete-Time Random Signals
610(7)
References
613(1)
Problems
613(4)
Effects of Finite Word Length in Digital Filters
617(56)
Introduction
617(1)
Number Representation
618(9)
Binary System
618(2)
Fixed-Point Arithmetic
620(3)
Floating-Point Arithmetic
623(2)
Number Quantization
625(2)
Coefficient Quantization
627(5)
Low-Sensitivity Structures
632(6)
Case I
635(1)
Case II
636(2)
Product Quantization
638(2)
Signal Scaling
640(7)
Method A
640(1)
Method B
641(2)
Types of Scaling
643(2)
Application of Scaling
645(2)
Minimization of Output Roundoff Noise
647(4)
Application of Error-Spectrum Shaping
651(3)
Limit-Cycle Oscillations
654(19)
Quantization Limit Cycles
654(5)
Overflow Limit Cycles
659(1)
Elimination of Quantization Limit Cycles
660(5)
Elimination of Overflow Limit Cycles
665(2)
References
667(1)
Problems
668(5)
Design of Nonrecursive Filters Using Optimization Methods
673(46)
Introduction
673(1)
Problem Formulation
674(4)
Lowpass and Highpass Filters
675(1)
Bandpass and Bandstop Filters
676(1)
Alternation Theorem
677(1)
Remez Exchange Algorithm
678(5)
Initialization of Extremals
679(1)
Location of Maxima of the Error Function
679(2)
Computation of |E(ω)| and Pc(ω)
681(1)
Rejection of Superfluous Potential Extremals
682(1)
Computation of Impulse Response
683(1)
Improved Search Methods
683(8)
Selective Step-by-Step Search
683(4)
Cubic Interpolation
687(2)
Quadratic Interpolation
689(1)
Improved Formulation
689(2)
Efficient Remez Exchange Algorithm
691(3)
Gradient Information
694(6)
Property 1
695(1)
Property 2
695(1)
Property 3
695(1)
Property 4
696(1)
Property 5
696(4)
Prescribed Specifications
700(3)
Generalization
703(4)
Antisymmetrical Impulse Response and Odd Filter Length
703(2)
Even Filter Length
705(2)
Digital Differentiators
707(5)
Problem Formulation
707(1)
First Derivative
708(1)
Prescribed Specifications
708(4)
Arbitrary Amplitude Responses
712(1)
Multiband Filters
712(7)
References
715(1)
Additional References
716(1)
Problems
716(3)
Design of Recursive Filters Using Optimization Methods
719(54)
Introduction
719(1)
Problem Formulation
720(2)
Newton's Method
722(4)
Quasi-Newton Algorithms
726(12)
Basic Quasi-Newton Algorithm
726(3)
Updating Formulas for Matrix Sk+1
729(1)
Inexact Line Searches
730(4)
Practical Quasi-Newton Algorithm
734(4)
Minimax Algorithms
738(3)
Improved Minimax Algorithms
741(4)
Design of Recursive Filters
745(8)
Objective Function
745(1)
Gradient Information
746(1)
Stability
746(1)
Minimum Filter Order
746(1)
Use of Weighting
747(6)
Design of Recursive Delay Equalizers
753(20)
References
766(1)
Additional References
766(1)
Problems
767(6)
Wave Digital Filters
773(56)
Introduction
773(1)
Sensitivity Considerations
774(1)
Wave Network Characterization
775(2)
Element Realizations
777(14)
Impedances
778(1)
Voltage Sources
779(1)
Series Wire Interconnection
780(2)
Parallel Wire Interconnection
782(1)
2-Port Adaptors
783(1)
Transformers
784(2)
Unit Elements
786(2)
Circulators
788(1)
Resonant Circuits
788(3)
Realizability Constraint
791(1)
Lattice Wave Digital Filters
791(7)
Analysis
791(1)
Alternative Lattice Configuration
792(4)
Digital Realization
796(2)
Ladder Wave Digital Filters
798(4)
Filters Satisfying Prescribed Specifications
802(3)
Frequency-Domain Analysis
805(2)
Scaling
807(1)
Elimination of Limit-Cycle Oscillations
808(2)
Related Synthesis Methods
810(1)
A Cascade Synthesis Based on the Wave Characterization
811(8)
Generalized-Immittance Converters
811(1)
Analog G-CGIC Configuration
811(1)
Digital G-CGIC Configuration
812(2)
Cascade Synthesis
814(3)
Signal Scaling
817(1)
Output Noise
818(1)
Choice of Structure
819(10)
References
820(2)
Problems
822(7)
Digital Signal Processing Applications
829(62)
Introduction
829(1)
Sampling-Frequency Conversion
830(9)
Decimators
830(3)
Interpolators
833(6)
Sampling Frequency Conversion by a Noninteger Factor
839(1)
Design Considerations
839(1)
Quadrature-Mirror-Image Filter Banks
839(12)
Operation
840(4)
Elimination of Aliasing Errors
844(2)
Design Considerations
846(3)
Perfect Reconstruction
849(2)
Hilbert Transformers
851(11)
Design of Hilbert Transformers
854(5)
Single-Sideband Modulation
859(2)
Sampling of Bandpassed Signals
861(1)
Adaptive Digital Filters
862(12)
Wiener Filters
865(2)
Newton Algorithm
867(1)
Steepest-Descent Algorithm
867(3)
Least-Mean-Square Algorithm
870(1)
Recursive Filters
871(1)
Applications
872(2)
Two-Dimensional Digital Filters
874(17)
Two-Dimensional Convolution
875(1)
Two-Dimensional z Transform
875(1)
Two-Dimensional Transfer Function
875(1)
Stability
876(1)
Frequency-Domain Analysis
877(3)
Types of 2-D Filters
880(1)
Approximations
881(1)
Applications
881(1)
References
882(2)
Additional References
884(1)
Problems
884(7)
Appendix A. Complex Analysis
891(34)
A.1 Introduction
891(1)
A.2 Complex Numbers
892(7)
A.2.1 Complex Arithmetic
894(1)
A.2.2 De Moivre's Theorem
894(1)
A.2.3 Euler's Formula
895(1)
A.2.4 Exponential Form
896(1)
A.2.5 Vector Representation
897(1)
A.2.6 Spherical Representation
898(1)
A.3 Functions of a Complex Variable
899(7)
A.3.1 Polynomials
899(1)
A.3.2 Inverse Algebraic Functions
900(1)
A.3.3 Trigonometric Functions and Their Inverses
900(1)
A.3.4 Hyperbolic Functions and Their Inverses
901(1)
A.3.5 Multi-Valued Functions
902(2)
A.3.6 Periodic Functions
904(1)
A.3.7 Rational Algebraic Functions
905(1)
A.4 Basic Principles of Complex Analysis
906(5)
A.4.1 Limit
906(1)
A.4.2 Differentiability
907(1)
A.4.3 Analyticity
907(1)
A.4.4 Zeros
908(1)
A.4.5 Singularities
908(2)
A.4.6 Zero-Pole Plots
910(1)
A.5 Series
911(4)
A.6 Laurent Theorem
915(4)
A.7 Residue Theorem
919(1)
A.8 Analytic Continuation
920(1)
A.9 Conformal Transformations
921(4)
References
924(1)
Appendix B. Elliptic Functions
925(14)
B.1 Introduction
925(1)
B.2 Elliptic Integral of the First Kind
925(2)
B.3 Elliptic Functions
927(3)
B.4 Imaginary Argument
930(2)
B.5 Formulas
932(1)
B.6 Periodicity
932(2)
B.7 Transformation
934(2)
B.8 Series Representation
936(3)
References
937(2)
Index 939

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