Understanding Digital Signal Processing

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.

• 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