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**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 Cover 1 Contents 8 Preface 16 About The Author 24 1 Discrete Sequences And Systems 26 1.1 Discrete Sequences And Their Notation 27 1.2 Signal Amplitude, Magnitude, Power 33 1.3 Signal Processing Operational Symbols 35 1.4 Introduction To Discrete Linear Time-Invariant Systems 37 1.5 Discrete Linear Systems 37 1.6 Time-Invariant Systems 42 1.7 The Commutative Property Of Linear Time-Invariant Systems 43 1.8 Analyzing Linear Time-Invariant Systems 44 References 46 Chapter 1 Problems 48 2 Periodic Sampling 58 2.1 Aliasing: Signal Ambiguity In The Frequency Domain 58 2.2 Sampling Lowpass Signals 63 2.3 Sampling Bandpass Signals 67 2.4 Practical Aspects Of Bandpass Sampling 70 References 74 Chapter 2 Problems 75 3 The Discrete Fourier Transform 84 3.1 Understanding The Dft Equation 85 3.2 Dft Symmetry 98 3.3 Dft Linearity 100 3.4 Dft Magnitudes 100 3.5 Dft Frequency Axis 102 3.6 Dft Shifting Theorem 102 3.7 Inverse Dft 105 3.8 Dft Leakage 106 3.9 Windows 114 3.10 Dft Scalloping Loss 121 3.11 Dft Resolution, Zero Padding, And Frequency-Domain Sampling 123 3.12 Dft Processing Gain 127 3.13 The Dft Of Rectangular Functions 130 3.14 Interpreting The Dft Using The Discrete-Time Fourier Transform 145 References 149 Chapter 3 Problems 150 4 The Fast Fourier Transform 160 4.1 Relationship Of The Fft To The Dft 161 4.2 Hints On Using Ffts In Practice 162 4.3 Derivation Of The Radix-2 Fft Algorithm 166 4.4 Fft Input/Output Data Index Bit Reversal 174 4.5 Radix-2 Fft Butterfly Structures 176 4.6 Alternate Single-Butterfly Structures 179 References 183 Chapter 4 Problems 185 5 Finite Impulse Response Filters 194 5.1 An Introduction To Finite Impulse Response (Fir) Filters 195 5.2 Convolution In Fir Filters 200 5.3 Lowpass Fir Filter Design 211 5.4 Bandpass Fir Filter Design 226 5.5 Highpass Fir Filter Design 228 5.6 Parks-Mcclellan Exchange Fir Filter Design Method 229 5.7 Half-Band Fir Filters 232 5.8 Phase Response Of Fir Filters 234 5.9 A Generic Description Of Discrete Convolution 239 5.10 Analyzing Fir Filters 251 References 260 Chapter 5 Problems 263 6 Infinite Impulse Response Filters 278 6.1 An Introduction To Infinite Impulse Response Filters 279 6.2 The Laplace Transform 282 6.3 The Z-Transform 295 6.4 Using The Z-Transform To Analyze Iir Filters 299 6.5 Using Poles And Zeros To Analyze Iir Filters 307 6.6 Alternate Iir Filter Structures 314 6.7 Pitfalls In Building Iir Filters 317 6.8 Improving Iir Filters With Cascaded Structures 320 6.9 Scaling The Gain Of Iir Filters 325 6.10 Impulse Invariance Iir Filter Design Method 328 6.11 Bilinear Transform Iir Filter Design Method 344 6.12 Optimized Iir Filter Design Method 355 6.13 A Brief Comparison Of Iir And Fir Filters 357 References 358 Chapter 6 Problems 361 7 Specialized Digital Networks And Filters 386 7.1 Differentiators 386 7.2 Integrators 395 7.3 Matched Filters 401 7.4 Interpolated Lowpass Fir Filters 406 7.5 Frequency Sampling Filters: The Lost Art 417 References 451 Chapter 7 Problems 454 8 Quadrature Signals 464 8.1 Why Care About Quadrature Signals? 465 8.2 The Notation Of Complex Numbers 465 8.3 Representing Real Signals Using Complex Phasors 471 8.4 A Few Thoughts On Negative Frequency 475 8.5 Quadrature Signals In The Frequency Domain 476 8.6 Bandpass Quadrature Signals In The Frequency Domain 479 8.7 Complex Down-Conversion 481 8.8 A Complex Down-Conversion Example 483 8.9 An Alternate Down-Conversion Method 487 References 489 Chapter 8 Problems 490 9 The Discrete Hilbert Transform 504 9.1 Hilbert Transform Definition 505 9.2 Why Care About The Hilbert Transform? 507 9.3 Impulse Response Of A Hilbert Transformer 512 9.4 Designing A Discrete Hilbert Transformer 514 9.5 Time-Domain Analytic Signal Generation 520 9.6 Comparing Analytical Signal Generation Methods 522 References 523 Chapter 9 Problems 524 10 Sample Rate Conversion 532 10.1 Decimation 533 10.2 Two-Stage Decimation 535 10.3 Properties Of Downsampling 539 10.4 Interpolation 541 10.5 Properties Of Interpolation 543 10.6 Combining Decimation And Interpolation 546 10.7 Polyphase Filters 547 10.8 Two-Stage Interpolation 553 10.9 Z-Transform Analysis Of Multirate Systems 558 10.10 Polyphase Filter Implementations 560 10.11 Sample Rate Conversion By Rational Factors 565 10.12 Sample Rate Conversion With Half-Band Filters 568 10.13 Sample Rate Conversion With Ifir Filters 573 10.14 Cascaded Integrator-Comb Filters 575 References 591 Chapter 10 Problems 593 11 Signal Averaging 614 11.1 Coherent Averaging 615 11.2 Incoherent Averaging 622 11.3 Averaging Multiple Fast Fourier Transforms 625 11.4 Averaging Phase Angles 628 11.5 Filtering Aspects Of Time-Domain Averaging 629 11.6 Exponential Averaging 633 References 640 Chapter 11 Problems 642 12 Digital Data Formats And Their Effects 648 12.1 Fixed-Point Binary Formats 648 12.2 Binary Number Precision And Dynamic Range 657 12.3 Effects Of Finite Fixed-Point Binary Word Length 659 12.4 Floating-Point Binary Formats 677 12.5 Block Floating-Point Binary Format 683 References 683 Chapter 12 Problems 686 13 Digital Signal Processing Tricks 696 13.1 Frequency Translation Without Multiplication 696 13.2 High-Speed Vector Magnitude Approximation 704 13.3 Frequency-Domain Windowing 708 13.4 Fast Multiplication Of Complex Numbers 711 13.5 Efficiently Performing The Fft Of Real Sequences 712 13.6 Computing The Inverse Fft Using The Forward Fft 724 13.7 Simplified Fir Filter Structure 727 13.8 Reducing A/D Converter Quantization Noise 729 13.9 A/D Converter Testing Techniques 734 13.10 Fast Fir Filtering Using The Fft 741 13.11 Generating Normally Distributed Random Data 747 13.12 Zero-Phase Filtering 750 13.13 Sharpened Fir Filters 751 13.14 Interpolating A Bandpass Signal 753 13.15 Spectral Peak Location Algorithm 755 13.16 Computing Fft Twiddle Factors 759 13.17 Single Tone Detection 762 13.18 The Sliding Dft 766 13.19 The Zoom Fft 774 13.20 A Practical Spectrum Analyzer 778 13.21 An Efficient Arctangent Approximation 781 13.22 Frequency Demodulation Algorithms 783 13.23 Dc Removal 786 13.24 Improving Traditional Cic Filters 790 13.25 Smoothing Impulsive Noise 795 13.26 Efficient Polynomial Evaluation 797 13.27 Designing Very High-Order Fir Filters 800 13.28 Time-Domain Interpolation Using The Fft 803 13.29 Frequency Translation Using Decimation 806 13.30 Automatic Gain Control (Agc) 808 13.31 Approximate Envelope Detection 809 13.32 A Quadrature Oscillator 811 13.33 Specialized Exponential Averaging 814 13.34 Filtering Narrowband Noise Using Filter Nulls 817 13.35 Efficient Computation Of Signal Variance 822 13.36 Real-Time Computation Of Signal Averages And Variances 824 13.37 Building Hilbert Transformers From Half-Band Filters 827 13.38 Complex Vector Rotation With Arctangents 830 13.39 An Efficient Differentiating Network 835 13.40 Linear-Phase Dc-Removal Filter 837 13.41 Avoiding Overflow In Magnitude Computations 840 13.42 Efficient Linear Interpolation 840 13.43 Alternate Complex Down-Conversion Schemes 841 13.44 Signal Transition Detection 845 13.45 Spectral Flipping Around Signal Center Frequency 846 13.46 Computing Missing Signal Samples 848 13.47 Computing Large Dfts Using Small Ffts 851 13.48 Computing Filter Group Delay Without Arctangents 855 13.49 Computing A Forward And Inverse Fft Using A Single Fft 856 13.50 Improved Narrowband Lowpass Iir Filters 858 13.51 A Stable Goertzel Algorithm 863 References 865 A: The Arithmetic Of Complex Numbers 872 A.1 Graphical Representation Of Real And Complex Numbers 872 A.2 Arithmetic Representation Of Complex Numbers 873 A.3 Arithmetic Operations Of Complex Numbers 875 A.4 Some Practical Implications Of Using Complex Numbers 881 B: Closed Form Of A Geometric Series 884 C: Time Reversal And The Dft 888 D: Mean,Variance, And Standard Deviation 892 D.1 Statistical Measures 892 D.2 Statistics Of Short Sequences 895 D.3 Statistics Of Summed Sequences 897 D.4 Standard Deviation (Rms) Of A Continuous Sinewave 899 D.5 Estimating Signal-To-Noise Ratios 900 D.6 The Mean And Variance Of Random Functions 904 D.7 The Normal Probability Density Function 907 E: Decibels (Db And Dbm) 910 E.1 Using Logarithms To Determine Relative Signal Power 910 E.2 Some Useful Decibel Numbers 914 E.3 Absolute Power Using Decibels 916 F: Digital Filter Terminology 918 G: Frequency Sampling Filter Derivations 928 G.1 Frequency Response Of A Comb Filter 928 G.2 Single Complex Fsf Frequency Response 929 G.3 Multisection Complex Fsf Phase 930 G.4 Multisection Complex Fsf Frequency Response 931 G.5 Real Fsf Transfer Function 933 G.6 Type-Iv Fsf Frequency Response 935 H: Frequency Sampling Filter Design Tables 938 I: Computing Chebyshev Window Sequences 952 I.1 Chebyshev Windows For Fir Filter Design 952 I.2 Chebyshev Windows For Spectrum Analysis 954 Index 956 A 956 B 957 C 958 D 959 E 961 F 962 G 965 H 965 I 966 J 968 K 968 L 968 M 969 N 970 O 970 P 970 Q 972 R 972 S 973 T 976 U 977 V 977 W 978 Z 978 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

"Understanding Digital Signal Processing, 3/e is simply the best practitioner's resource for mastering DSP technology. Richard Lyons has thoroughly updated and expanded his best-selling second edition, building on the exceptionally readable coverage that has made it a favorite of both professionals and students worldwide. Lyons achieves the perfect balance between practice and math, making DSP accessible to beginners without ever oversimplifying it, and offering systematic practical guidance for day-to-day problem-solving. Down-to-earth, intuitive, and example-rich, this book helps readers thoroughly grasp the basics and quickly move on to more sophisticated DSP techniques. Coverage includes: discrete sequences/systems, DFT, FFT, finite/infinite impulse response filters, quadrature (I/Q) processing, discrete Hilbert transforms, sample rate conversion, signal averaging, and much more. This edition adds extensive new coverage of FIR and IIR filter analysis techniques. The previous multirate processing, and binary number format, material has been significantly updated and expanded. It also provides new coverage of digital differentiators, integrators, and matched filters. Lyons has also doubled the number of DSP tips and tricks as in the previous edition including techniques even seasoned DSP professionals may have overlooked. He has also added end-of-chapter homework problems throughout to support college instruction and professional self-study."--Publisher's website