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 includes New 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

Table of Contents:
Preface      xv About the Author      xxiii   Chapter 1: Discrete Sequences and Systems      1 1.1 Discrete Sequences and their Notation   2 1.2 Signal Amplitude, Magnitude, Power   8 1.3 Signal Processing Operational Symbols   10 1.4 Introduction to Discrete Linear Time-Invariant Systems   12 1.5 Discrete Linear Systems   12 1.6 Time-Invariant Systems   17 1.7 The Commutative Property of Linear Time-Invariant Systems   18 1.8 Analyzing Linear Time-Invariant Systems   19 References   21 Chapter 1 Problems   23   Chapter 2: Periodic Sampling      33 2.1 Aliasing: Signal Ambiguity in the Frequency Domain   33 2.2 Sampling Lowpass Signals   38 2.3 Sampling Bandpass Signals   42 2.4 Practical Aspects of Bandpass Sampling   45 References   49 Chapter 2 Problems   50   Chapter 3: The Discrete Fourier Transform     59 3.1 Understanding the DFT Equation   60 3.2 DFT Symmetry   73 3.3 DFT Linearity   75 3.4 DFT Magnitudes   75 3.5 DFT Frequency Axis   77 3.6 DFT Shifting Theorem   77 3.7 Inverse DFT   80 3.8 DFT Leakage   81 3.9 Windows   89 3.10 DFT Scalloping Loss   96 3.11 DFT Resolution, Zero Padding, and Frequency-Domain Sampling   98 3.12 DFT Processing Gain   102 3.13 The DFT of Rectangular Functions   105 3.14 Interpreting the DFT Using the Discrete-Time Fourier Transform   120 References   124 Chapter 3 Problems   125   Chapter 4: The Fast Fourier Transform      135 4.1 Relationship of the FFT to the DFT 136 4.2 Hints on Using FFTs in Practice 137 4.3 Derivation of the Radix-2 FFT Algorithm 141 4.4 FFT Input/Output Data Index Bit Reversal 149 4.5 Radix-2 FFT Butterfly Structures 151 4.6 Alternate Single-Butterfly Structures 154 References 158 Chapter 4 Problems 160   Chapter 5: Finite Impulse Response Filters      169 5.1 An Introduction to Finite Impulse Response (FIR) Filters   170 5.2 Convolution in FIR Filters   175 5.3 Lowpass FIR Filter Design   186 5.4 Bandpass FIR Filter Design   201 5.5 Highpass FIR Filter Design   203 5.6 Parks-McClellan Exchange FIR Filter Design Method   204 5.7 Half-band FIR Filters   207 5.8 Phase Response of FIR Filters   209 5.9 A Generic Description of Discrete Convolution   214 5.10 Analyzing FIR Filters   226 References   235 Chapter 5 Problems   238   Chapter 6: Infinite Impulse Response Filters      253 6.1 An Introduction to Infinite Impulse Response Filters   254 6.2 The Laplace Transform   257 6.3 The z-Transform   270 6.4 Using the z-Transform to Analyze IIR Filters   274 6.5 Using Poles and Zeros to Analyze IIR Filters   282 6.6 Alternate IIR Filter Structures   289 6.7 Pitfalls in Building IIR Filters   292 6.8 Improving IIR Filters with Cascaded Structures   295 6.9 Scaling the Gain of IIR Filters   300 6.10 Impulse Invariance IIR Filter Design Method   303 6.11 Bilinear Transform IIR Filter Design Method   319 6.12 Optimized IIR Filter Design Method   330 6.13 A Brief Comparison of IIR and FIR Filters   332 References   333 Chapter 6 Problems   336   Chapter 7: Specialized Digital Networks and Filters      361 7.1 Differentiators   361 7.2 Integrators   370 7.3 Matched Filters   376 7.4 Interpolated Lowpass FIR Filters   381 7.5 Frequency Sampling Filters: The Lost Art   392 References   426 Chapter 7 Problems   429   Chapter 8: Quadrature Signals       439 8.1 Why Care about Quadrature Signals?   440 8.2 The Notation of Complex Numbers   440 8.3 Representing Real Signals Using Complex Phasors   446 8.4 A Few Thoughts on Negative Frequency   450 8.5 Quadrature Signals in the Frequency Domain   451 8.6 Bandpass Quadrature Signals in the Frequency Domain   454 8.7 Complex Down-Conversion   456 8.8 A Complex Down-Conversion Example   458 8.9 An Alternate Down-Conversion Method   462 References   464 Chapter 8 Problems   465   Chapter 9: The Discrete Hilbert Transform       479 9.1 Hilbert Transform Definition   480 9.2 Why Care about the Hilbert Transform?   482 9.3 Impulse Response of a Hilbert Transformer   487 9.4 Designing a Discrete Hilbert Transformer   489 9.5 Time-Domain Analytic Signal Generation   495 9.6 Comparing Analytical Signal Generation Methods   497 References   498 Chapter 9 Problems   499   Chapter 10: Sample Rate Conversion       507 10.1 Decimation   508 10.2 Two-Stage Decimation   510 10.3 Properties of Downsampling   514 10.4 Interpolation   516 10.5 Properties of Interpolation   518 10.6 Combining Decimation and Interpolation   521 10.7 Polyphase Filters   522 10.8 Two-Stage Interpolation   528 10.9 z-Transform Analysis of Multirate Systems   533 10.10 Polyphase Filter Implementations   535 10.11 Sample Rate Conversion by Rational Factors   540 10.12 Sample Rate Conversion with Half-band Filters   543 10.13 Sample Rate Conversion with IFIR Filters   548 10.14 Cascaded Integrator-Comb Filters   550 References   566 Chapter 10 Problems   568   Chapter 11: Signal Averaging      589 11.1 Coherent Averaging   590 11.2 Incoherent Averaging   597 11.3 Averaging Multiple Fast Fourier Transforms   600 11.4 Averaging Phase Angles   603 11.5 Filtering Aspects of Time-Domain Averaging   604 11.6 Exponential Averaging   608 References   615 Chapter 11 Problems   617   Chapter 12: Digital Data Formats and their Effects      623 12.1 Fixed-Point Binary Formats   623 12.2 Binary Number Precision and Dynamic Range   632 12.3 Effects of Finite Fixed-Point Binary Word Length   634 12.4 Floating-Point Binary Formats   652 12.5 Block Floating-Point Binary Format   658 References   658 Chapter 12 Problems   661   Chapter 13: Digital Signal Processing Tricks        671 13.1 Frequency Translation without Multiplication   671 13.2 High-Speed Vector Magnitude Approximation   679 13.3 Frequency-Domain Windowing   683 13.4 Fast Multiplication of Complex Numbers   686 13.5 Efficiently Performing the FFT of Real Sequences   687 13.6 Computing the Inverse FFT Using the Forward FFT   699 13.7 Simplified FIR Filter Structure   702 13.8 Reducing A/D Converter Quantization Noise   704 13.9 A/D Converter Testing Techniques   709 13.10 Fast FIR Filtering Using the FFT   716 13.11 Generating Normally Distributed Random Data   722 13.12 Zero-Phase Filtering   725 13.13 Sharpened FIR Filters   726 13.14 Interpolating a Bandpass Signal   728 13.15 Spectral Peak Location Algorithm   730 13.16 Computing FFT Twiddle Factors   734 13.17 Single Tone Detection   737 13.18 The Sliding DFT   741 13.19 The Zoom FFT   749 13.20 A Practical Spectrum Analyzer   753 13.21 An Efficient Arctangent Approximation   756 13.22 Frequency Demodulation Algorithms   758 13.23 DC Removal   761 13.24 Improving Traditional CIC Filters   765 13.25 Smoothing Impulsive Noise   770 13.26 Efficient Polynomial Evaluation   772 13.27 Designing Very High-Order FIR Filters   775 13.28 Time-Domain Interpolation Using the FFT   778 13.29 Frequency Translation Using Decimation   781 13.30 Automatic Gain Control (AGC)   783 13.31 Approximate Envelope Detection   784 13.32 AQuadrature Oscillator   786 13.33 Specialized Exponential Averaging   789 13.34 Filtering Narrowband Noise Using Filter Nulls   792 13.35 Efficient Computation of Signal Variance   797 13.36 Real-time Computation of Signal Averages and Variances   799 13.37 Building Hilbert Transformers from Half-band Filters   802 13.38 Complex Vector Rotation with Arctangents   805 13.39 An Efficient Differentiating Network   810 13.40 Linear-Phase DC-Removal Filter   812 13.41 Avoiding Overflow in Magnitude Computations   815 13.42 Efficient Linear Interpolation   815 13.43 Alternate Complex Down-conversion Schemes   816 13.44 Signal Transition Detection   820 13.45 Spectral Flipping around Signal Center Frequency   821 13.46 Computing Missing Signal Samples   823 13.47 Computing Large DFTs Using Small FFTs   826 13.48 Computing Filter Group Delay without Arctangents   830 13.49 Computing a Forward and Inverse FFT Using a Single FFT   831 13.50 Improved Narrowband Lowpass IIR Filters   833 13.51 A Stable Goertzel Algorithm   838 References   840   Appendix A: The Arithmetic of Complex Numbers       847 A.1 Graphical Representation of Real and Complex Numbers   847 A.2 Arithmetic Representation of Complex Numbers   848 A.3 Arithmetic Operations of Complex Numbers   850 A.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       867 D.1 Statistical Measures   867 D.2 Statistics of Short Sequences   870 D.3 Statistics of Summed Sequences   872 D.4 Standard Deviation (RMS) of a Continuous Sinewave   874 D.5 Estimating Signal-to-Noise Ratios   875 D.6 The Mean and Variance of Random Functions   879 D.7 The Normal Probability Density Function   882   Appendix E: Decibels (DB and DBM)       885 E.1 Using Logarithms to Determine Relative Signal Power   885 E.2 Some Useful Decibel Numbers   889 E.3 Absolute Power Using Decibels   891   Appendix F: Digital Filter Terminology       893   Appendix G: Frequency Sampling Filter Derivations       903 G.1 Frequency Response of a Comb Filter   903 G.2 Single Complex FSF Frequency Response   904 G.3 Multisection Complex FSF Phase   905 G.4 Multisection Complex FSF Frequency Response   906 G.5 Real FSF Transfer Function   908 G.6 Type-IV FSF Frequency Response   910   Appendix H: Frequency Sampling Filter Design Tables      913   Appendix I: Computing Chebyshev Window Sequences        927 I.1 Chebyshev Windows for FIR Filter Design   927 I.2 Chebyshev Windows for Spectrum Analysis   929   Index        931