Digital Signal Processing Signals, Systems, and Filters

by Antoniou, Andreas

• ISBN13: 9780071454247
• ISBN10: 0071454241
• eBook ISBN(s): 9780071589048
• Additional ISBN(s): 9780071454254, 9780071846035
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-10-10
• Publisher: McGraw-Hill Education
• More Book Details
• Purchase Benefits

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