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# Understanding Digital Signal Processing : United States Edition

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## Description

Amazon.com's Top-Selling DSP Book for Seven Straight Years-Now Fully Updated! Understanding Digital Signal Processing, Third Edition, is quite simply the best resource for engineers and other technical professionals who want to master and apply today's latest DSP techniques. Richard G. Lyons has updated and expanded his best-selling second edition to reflect the newest technologies, building on the exceptionally readable coverage that made it the favorite of DSP professionals worldwide. He has also added hands-on problems to every chapter, giving students even more of the practical experience they need to succeed. Comprehensive in scope and clear in approach, this book achieves the perfect balance between theory and practice, keeps math at a tolerable level, and makes DSP exceptionally accessible to beginners without ever oversimplifying it. Readers can thoroughly grasp the basics and quickly move on to more sophisticated techniques. This edition adds extensive new coverage of FIR and IIR filter analysis techniques, digital differentiators, integrators, and matched filters. Lyons has significantly updated and expanded his discussions of multirate processing techniques, which are crucial to modern wireless and satellite communications. He also presents nearly twice as many DSP Tricks as in the second edition-including techniques even seasoned DSP professionals may have overlooked. Coverage includesNew homework problems that deepen your understanding and help you apply what you've learned Practical, day-to-day DSP implementations and problem-solving throughout Useful new guidance on generalized digital networks, including discrete differentiators, integrators, and matched filters Clear descriptions of statistical measures of signals, variance reduction by averaging, and real-world signal-to-noise ratio (SNR) computation A significantly expanded chapter on sample rate conversion (multirate systems) and associated filtering techniques New guidance on implementing fast convolution, IIR filter scaling, and more Enhanced coverage of analyzing digital filter behavior and performance for diverse communications and biomedical applications Discrete sequences/systems, periodic sampling, DFT, FFT, finite/infinite impulse response filters, quadrature (I/Q) processing, discrete Hilbert transforms, binary number formats, and much more

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## Product details

- Hardback | 984 pages
- 182.88 x 233.68 x 38.1mm | 1,338.09g
- 25 Jan 2011
- Pearson Education (US)
- Prentice Hall
- Upper Saddle River, United States
- English
- 3rd edition
- 0137027419
- 9780137027415
- 189,355

## About Richard G. Lyons

Richard G. Lyons is a consulting Systems Engineer and lecturer with Besser Associates in Mountain View, California. He is author of the book "Understanding Digital Signal Processing", editor and contributor to the book "Streamlining Digital Signal Processing", and has authored numerous articles on DSP. Lyons has taught DSP at the University of California Santa Cruz Extension and recently received the IEEE Signal Processing Society's 2012 Educator of the Year award.

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## Table of contents

Preface xv About the Author xxiii Chapter 1: Discrete Sequences and Systems 11.1 Discrete Sequences and their Notation 21.2 Signal Amplitude, Magnitude, Power 81.3 Signal Processing Operational Symbols 101.4 Introduction to Discrete Linear Time-Invariant Systems 121.5 Discrete Linear Systems 121.6 Time-Invariant Systems 171.7 The Commutative Property of Linear Time-Invariant Systems 181.8 Analyzing Linear Time-Invariant Systems 19References 21Chapter 1 Problems 23 Chapter 2: Periodic Sampling 332.1 Aliasing: Signal Ambiguity in the Frequency Domain 332.2 Sampling Lowpass Signals 382.3 Sampling Bandpass Signals 422.4 Practical Aspects of Bandpass Sampling 45References 49Chapter 2 Problems 50 Chapter 3: The Discrete Fourier Transform 593.1 Understanding the DFT Equation 603.2 DFT Symmetry 733.3 DFT Linearity 753.4 DFT Magnitudes 753.5 DFT Frequency Axis 773.6 DFT Shifting Theorem 773.7 Inverse DFT 803.8 DFT Leakage 813.9 Windows 893.10 DFT Scalloping Loss 963.11 DFT Resolution, Zero Padding, and Frequency-Domain Sampling 983.12 DFT Processing Gain 1023.13 The DFT of Rectangular Functions 1053.14 Interpreting the DFT Using the Discrete-Time Fourier Transform 120References 124Chapter 3 Problems 125 Chapter 4: The Fast Fourier Transform 1354.1 Relationship of the FFT to the DFT 1364.2 Hints on Using FFTs in Practice 1374.3 Derivation of the Radix-2 FFT Algorithm 1414.4 FFT Input/Output Data Index Bit Reversal 1494.5 Radix-2 FFT Butterfly Structures 1514.6 Alternate Single-Butterfly Structures 154References 158Chapter 4 Problems 160 Chapter 5: Finite Impulse Response Filters 1695.1 An Introduction to Finite Impulse Response (FIR) Filters 1705.2 Convolution in FIR Filters 1755.3 Lowpass FIR Filter Design 1865.4 Bandpass FIR Filter Design 2015.5 Highpass FIR Filter Design 2035.6 Parks-McClellan Exchange FIR Filter Design Method 2045.7 Half-band FIR Filters 2075.8 Phase Response of FIR Filters 2095.9 A Generic Description of Discrete Convolution 2145.10 Analyzing FIR Filters 226References 235Chapter 5 Problems 238 Chapter 6: Infinite Impulse Response Filters 2536.1 An Introduction to Infinite Impulse Response Filters 2546.2 The Laplace Transform 2576.3 The z-Transform 2706.4 Using the z-Transform to Analyze IIR Filters 2746.5 Using Poles and Zeros to Analyze IIR Filters 2826.6 Alternate IIR Filter Structures 2896.7 Pitfalls in Building IIR Filters 2926.8 Improving IIR Filters with Cascaded Structures 2956.9 Scaling the Gain of IIR Filters 3006.10 Impulse Invariance IIR Filter Design Method 3036.11 Bilinear Transform IIR Filter Design Method 3196.12 Optimized IIR Filter Design Method 3306.13 A Brief Comparison of IIR and FIR Filters 332References 333Chapter 6 Problems 336 Chapter 7: Specialized Digital Networks and Filters 3617.1 Differentiators 3617.2 Integrators 3707.3 Matched Filters 3767.4 Interpolated Lowpass FIR Filters 3817.5 Frequency Sampling Filters: The Lost Art 392References 426Chapter 7 Problems 429 Chapter 8: Quadrature Signals 4398.1 Why Care about Quadrature Signals? 4408.2 The Notation of Complex Numbers 4408.3 Representing Real Signals Using Complex Phasors 4468.4 A Few Thoughts on Negative Frequency 4508.5 Quadrature Signals in the Frequency Domain 4518.6 Bandpass Quadrature Signals in the Frequency Domain 4548.7 Complex Down-Conversion 4568.8 A Complex Down-Conversion Example 4588.9 An Alternate Down-Conversion Method 462References 464Chapter 8 Problems 465 Chapter 9: The Discrete Hilbert Transform 4799.1 Hilbert Transform Definition 4809.2 Why Care about the Hilbert Transform? 4829.3 Impulse Response of a Hilbert Transformer 4879.4 Designing a Discrete Hilbert Transformer 4899.5 Time-Domain Analytic Signal Generation 4959.6 Comparing Analytical Signal Generation Methods 497References 498Chapter 9 Problems 499 Chapter 10: Sample Rate Conversion 50710.1 Decimation 50810.2 Two-Stage Decimation 51010.3 Properties of Downsampling 51410.4 Interpolation 51610.5 Properties of Interpolation 51810.6 Combining Decimation and Interpolation 52110.7 Polyphase Filters 52210.8 Two-Stage Interpolation 52810.9 z-Transform Analysis of Multirate Systems 53310.10 Polyphase Filter Implementations 53510.11 Sample Rate Conversion by Rational Factors 54010.12 Sample Rate Conversion with Half-band Filters 54310.13 Sample Rate Conversion with IFIR Filters 54810.14 Cascaded Integrator-Comb Filters 550References 566Chapter 10 Problems 568 Chapter 11: Signal Averaging 58911.1 Coherent Averaging 59011.2 Incoherent Averaging 59711.3 Averaging Multiple Fast Fourier Transforms 60011.4 Averaging Phase Angles 60311.5 Filtering Aspects of Time-Domain Averaging 60411.6 Exponential Averaging 608References 615Chapter 11 Problems 617 Chapter 12: Digital Data Formats and their Effects 62312.1 Fixed-Point Binary Formats 62312.2 Binary Number Precision and Dynamic Range 63212.3 Effects of Finite Fixed-Point Binary Word Length 63412.4 Floating-Point Binary Formats 65212.5 Block Floating-Point Binary Format 658References 658Chapter 12 Problems 661 Chapter 13: Digital Signal Processing Tricks 67113.1 Frequency Translation without Multiplication 67113.2 High-Speed Vector Magnitude Approximation 67913.3 Frequency-Domain Windowing 68313.4 Fast Multiplication of Complex Numbers 68613.5 Efficiently Performing the FFT of Real Sequences 68713.6 Computing the Inverse FFT Using the Forward FFT 69913.7 Simplified FIR Filter Structure 70213.8 Reducing A/D Converter Quantization Noise 70413.9 A/D Converter Testing Techniques 70913.10 Fast FIR Filtering Using the FFT 71613.11 Generating Normally Distributed Random Data 72213.12 Zero-Phase Filtering 72513.13 Sharpened FIR Filters 72613.14 Interpolating a Bandpass Signal 72813.15 Spectral Peak Location Algorithm 73013.16 Computing FFT Twiddle Factors 73413.17 Single Tone Detection 73713.18 The Sliding DFT 74113.19 The Zoom FFT 74913.20 A Practical Spectrum Analyzer 75313.21 An Efficient Arctangent Approximation 75613.22 Frequency Demodulation Algorithms 75813.23 DC Removal 76113.24 Improving Traditional CIC Filters 76513.25 Smoothing Impulsive Noise 77013.26 Efficient Polynomial Evaluation 77213.27 Designing Very High-Order FIR Filters 77513.28 Time-Domain Interpolation Using the FFT 77813.29 Frequency Translation Using Decimation 78113.30 Automatic Gain Control (AGC) 78313.31 Approximate Envelope Detection 78413.32 AQuadrature Oscillator 78613.33 Specialized Exponential Averaging 78913.34 Filtering Narrowband Noise Using Filter Nulls 79213.35 Efficient Computation of Signal Variance 79713.36 Real-time Computation of Signal Averages and Variances 79913.37 Building Hilbert Transformers from Half-band Filters 80213.38 Complex Vector Rotation with Arctangents 80513.39 An Efficient Differentiating Network 81013.40 Linear-Phase DC-Removal Filter 81213.41 Avoiding Overflow in Magnitude Computations 81513.42 Efficient Linear Interpolation 81513.43 Alternate Complex Down-conversion Schemes 81613.44 Signal Transition Detection 82013.45 Spectral Flipping around Signal Center Frequency 82113.46 Computing Missing Signal Samples 82313.47 Computing Large DFTs Using Small FFTs 82613.48 Computing Filter Group Delay without Arctangents 83013.49 Computing a Forward and Inverse FFT Using a Single FFT 83113.50 Improved Narrowband Lowpass IIR Filters 83313.51 A Stable Goertzel Algorithm 838References 840 Appendix A: The Arithmetic of Complex Numbers 847A.1 Graphical Representation of Real and Complex Numbers 847A.2 Arithmetic Representation of Complex Numbers 848A.3 Arithmetic Operations of Complex Numbers 850A.4 Some Practical Implications of Using Complex Numbers 856 Appendix B: Closed Form of a Geometric Series 859 Appendix C: Time Reversal and the DFT 863 Appendix D: Mean, Variance, and Standard Deviation 867D.1 Statistical Measures 867D.2 Statistics of Short Sequences 870D.3 Statistics of Summed Sequences 872D.4 Standard Deviation (RMS) of a Continuous Sinewave 874D.5 Estimating Signal-to-Noise Ratios 875D.6 The Mean and Variance of Random Functions 879D.7 The Normal Probability Density Function 882 Appendix E: Decibels (DB and DBM) 885E.1 Using Logarithms to Determine Relative Signal Power 885E.2 Some Useful Decibel Numbers 889E.3 Absolute Power Using Decibels 891 Appendix F: Digital Filter Terminology 893 Appendix G: Frequency Sampling Filter Derivations 903G.1 Frequency Response of a Comb Filter 903G.2 Single Complex FSF Frequency Response 904G.3 Multisection Complex FSF Phase 905G.4 Multisection Complex FSF Frequency Response 906G.5 Real FSF Transfer Function 908G.6 Type-IV FSF Frequency Response 910 Appendix H: Frequency Sampling Filter Design Tables 913 Appendix I: Computing Chebyshev Window Sequences 927I.1 Chebyshev Windows for FIR Filter Design 927I.2 Chebyshev Windows for Spectrum Analysis 929 Index 931

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