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Understanding Digital Signal Processing,9780137027415
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Understanding Digital Signal Processing



Pub. Date:
Prentice Hall

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This is the 3rd edition with a publication date of 11/1/2010.
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The classic bestseller on digital signal processing -- now 100% updated for the latest techniques, with nearly twice as many real-world tips bull; bull;Readable, intuitive, example-rich, and accurate: helps readers fully grasp the basics and quickly move on to sophisticated techniques. bull;Includes extensive new coverage of FIR and IIR filter analysis, multirate processing, digital differentiators, integrators, matched filters, and much more bull;Now contains end-of-chapter problems to support college instruction and professional self-study. 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.

Author Biography

Richard G. Lyons is a consulting systems engineer and lecturer with Besser Associates in Mountain View, California. He has been lead hardware engineer for numerous signal processing systems for both the National Security Agency (NSA) and Northrop Grumman Corp. Lyons has taught DSP at the University of California Santa Cruz Extension and authored numerous articles on DSP. As associate editor for IEEE Signal Processing Magazine, he created, edits, and contributes to the magazine’s “DSP Tips & Tricks” column.

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

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