Understanding Digital Signal Processing

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2004-01-01
  • Publisher: Prentice Hall
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& bull; New chapter added covering specialized digital filters, and two new chapters included to discuss the quadrature signals used in modern cell phones, satellite communications, and wireless devices. & lt;br/ & gt; & bull; Teaches engineers how to incorporate DSP into their work. & lt;br/ & gt; & bull; 1st Edition is the best-selling book on the topic.

Author Biography

Richard G. Lyons is consulting systems engineer and lecturer with Besser Associates in Mountain View, CA.

Table of Contents

Prefacep. xi
Discrete Sequences and Systemsp. 1
Discrete Sequences and Their Notationp. 2
Signal Amplitude, Magnitude, Powerp. 8
Signal Processing Operational Symbolsp. 9
Introduction to Discrete Linear Time-Invariant Systemsp. 12
Discrete Linear Systemsp. 12
Time-Invariant Systemsp. 17
The Commutative Property of Linear Time-Invariant Systemsp. 18
Analyzing Linear Time-Invariant Systemsp. 19
Periodic Samplingp. 21
Aliasing: Signal Ambiquity in the Frequency Domainp. 21
Sampling Low-Pass Signalsp. 26
Sampling Bandpass Signalsp. 30
Spectral Inversion in Bandpass Samplingp. 39
The Discrete Fourier Transformp. 45
Understanding the DFT Equationp. 46
DFT Symmetryp. 58
DFT Linearityp. 60
DFT Magnitudesp. 61
DFT Frequency Axisp. 62
DFT Shifting Theoremp. 63
Inverse DFTp. 65
DFT Leakagep. 66
Windowsp. 74
DFT Scalloping Lossp. 82
DFT Resolution, Zero Padding, and Frequency-Domain Samplingp. 83
DFT Processing Gainp. 88
The DFT of Rectangular Functionsp. 91
The DFT Frequency Response to a Complex Inputp. 112
The DFT Frequency Response to a Real Cosine Inputp. 116
The DFT Single-Bin Frequency Response to a Real Cosine Inputp. 117
Interpreting the DFTp. 120
The Fast Fourier Transformp. 125
Relationship of the FFT to the DFTp. 126
Hints on Using FFTs in Practicep. 127
FFT Software Programsp. 131
Derivation of the Radix-2 FFT Algorithmp. 132
FFT Input/Output Data Index Bit Reversalp. 139
Radix-2 FFT Butterfly Structuresp. 141
Finite Impulse Response Filtersp. 151
An Introduction to Finite Impulse Response FIR Filtersp. 152
Convolution in FIR Filtersp. 157
Low-Pass FIR Filter Designp. 167
Bandpass FIR Filter Designp. 183
Highpass FIR Filter Designp. 184
Remez Exchange FIR Filter Design Methodp. 186
Half-Band FIR Filtersp. 188
Phase Response of FIR Filtersp. 190
A Generic Description of Discrete Convolutionp. 195
Infinite Impulse Response Filtersp. 211
An Introduction to Infinite Impulse Response Filtersp. 212
The Laplace Transformp. 215
The z-Transformp. 228
Impulse Invariance IIR Filter Design Methodp. 243
Bilinear Transform IIR Filter Design Methodp. 259
Optimized IIR Filter Design Methodp. 270
Pitfalls in Building IIR Digital Filtersp. 272
Improving IIR Filters with Cascaded Structuresp. 274
A Brief Comparison of IIR and FIR Filtersp. 279
Specialized Lowpass Fir Filtersp. 283
Frequency Sampling Filters: The Lost Artp. 284
Interpolated Lowpass FIR Filtersp. 319
Quadrature Signalsp. 335
Why Care About Quadrature Signalsp. 336
The Notation of Complex Numbersp. 336
Representing Real Signals Using Complex Phasorsp. 342
A Few Thoughts on Negative Frequencyp. 346
Quadrature Signals in the Frequency Domainp. 347
Bandpass Quadrature Signals in the Frequency Domainp. 350
Complex Down-Conversionp. 352
A Complex Down-Conversion Examplep. 354
An Alternate Down-Conversion Methodp. 358
The Discrete Hilbert Transformp. 361
Hilbert Transform Definitionp. 362
Why Care About the Hilbert Transform?p. 364
Impulse Response of a Hilbert Transformerp. 369
Designing a Discrete Hilbert Transformerp. 371
Time-Domain Analytic Signal Generationp. 377
Comparing Analytical Signal Generation Methodsp. 379
Sample Rate Conversionp. 381
Decimationp. 382
Interpolationp. 387
Combining Decimation and Interpolationp. 389
Polyphase Filtersp. 391
Cascaded Integrator-Comb Filtersp. 397
Signal Averagingp. 411
Coherent Averagingp. 412
Incoherent Averagingp. 419
Averaging Multiple Fast Fourier Transformsp. 422
Filtering Aspects of Time-Domain Averagingp. 430
Exponential Averagingp. 432
Digital Data Formats and Their Effectsp. 439
Fixed-Point Binary Formatsp. 439
Binary Number Precision and Dynamic Rangep. 445
Effects of Finite Fixed-Point Binary Word Lengthp. 446
Floating-Point Binary Formatsp. 462
Block Floating-Point Binary Formatp. 468
Digital Signal Processing Tricksp. 471
Frequency Translation without Multiplicationp. 471
High-Speed Vector-Magnitude Approximationp. 479
Frequency-Domain Windowingp. 484
Fast Multiplication of Complex Numbersp. 487
Efficiently Performing the FFT of Real Sequencesp. 488
Computing the Inverse FFT Using the Forward FFTp. 500
Simplified FIR Filter Structurep. 503
Reducing A/D Converter Quantization Noisep. 503
A/D Converter Testing Techniquesp. 510
Fast FIR Filtering Using the FFTp. 515
Generating Normally Distributed Random Datap. 516
Zero-Phase Filteringp. 518
Sharpened FIR Filtersp. 519
Interpolating a Bandpass Signalp. 521
Spectral Peak Location Algorithmp. 523
Computing FFT Twiddle Factorsp. 525
Single Tone Detectionp. 528
The Sliding DFTp. 532
The Zoom FFTp. 541
A Practical Spectrum Analyzerp. 544
An Efficient Arctangent Approximationp. 547
Frequency Demodulation Algorithmsp. 549
DC Removalp. 552
Improving Traditional CIC Filtersp. 556
Smoothing Impulsive Noisep. 561
Efficient Polynomial Evaluationp. 563
Designing Very High-Order FIR Filtersp. 564
Time-Domain Interpolation Using the FFTp. 568
Frequency Translation Using Decimationp. 571
Automatic Gain Control (AGC)p. 571
Approximate Envelope Detectionp. 574
A Quadrature Oscillatorp. 576
Dual-Mode Averagingp. 578
The Arithmetic of Complex Numbersp. 585
Graphical Representation of Real and Complex Numbersp. 585
Arithmetic Representation of Complex Numbersp. 586
Arithmetic Operations of Complex Numbersp. 588
Some Practical Implications of Using Complex Numbersp. 593
Closed Form of a Geometric Seriesp. 595
Time Reversal and the DFTp. 599
Mean, Variance, and Standard Deviationp. 603
Statistical Measuresp. 603
Standard Deviation, or RMS, of a Continuous Sinewavep. 606
The Mean and Variance of Random Functionsp. 607
The Normal Probability Density Functionp. 610
Decibels (DB and DBM)p. 613
Using Logarithms to Determine Relative Signal Powerp. 613
Some Useful Decibel Numbersp. 617
Absolute Power Using Decibelsp. 619
Digital Filter Terminologyp. 621
Frequency Sampling Filter Derivationsp. 633
Frequency Response of a Comb Filterp. 633
Single Complex FSF Frequency Responsep. 634
Multisection Complex FSF Phasep. 635
Multisection Complex FSF Frequency Responsep. 636
Real FSF Transfer Functionp. 638
Type-IV FSF Frequency Responsep. 640
Frequency Sampling Filter Design Tablesp. 643
Indexp. 657
About the Authorp. 667
Table of Contents provided by Rittenhouse. All Rights Reserved.


Preface This book is an expansion of the original Understanding Digital Signal Processing textbook published in 1997 and, like the first edition, its goal is to help beginners understand this relatively new technology of digital signal processing (DSP). Additions to this second edition include: Expansion and clarification of selected spectrum analysis and digital filtering topics covered in the first edition making that material more valuable to the DSP beginner. Expanded coverage of quadrature (complex I/Q) signals. In many cases we used three-dimension time and frequency plots to enhance the description of, and give physical meaning to, these two-dimensional signals. With the new emphasis on quadrature signals, material was added describing the Hilbert transform and how it's used in practice to generate quadrature signals. Discussions of Frequency Sampling, Interpolated FIR, and CIC filters; giving these important filters greater exposure than they've received in past DSP textbooks. A significant expansion of the popular "Digital Signal Processing Tricks" chapter. Revision of the terminology making it more consistent with the modern day language of DSP. It's traditional at this point in the preface of a DSP textbook for the author to tell readers why they should learn DSP. I don't need to tell you how important DSP is in our modern engineering world, you already know that. I'll just say that the future of electronics is DSP, and with this book you will not be left behind. Learning Digital Signal Processing Learning the fundamentals, and how to speak the language, of digital signal processing does not require profound analytical skills or an extensive background in mathematics. All you need is a little experience with elementary algebra, knowledge of what a sinewave is, this book, and enthusiasm. This may sound hard to believe, particularly if you've just flipped through the pages of this book and seen figures and equations that look rather complicated. The content here, you say, looks suspiciously like the material in technical journals and textbooks that, in the past, have successfully resisted your attempts to understand. Well, this is not just another book on digital signal processing. This book's goal is to gently provide explanation followed by illustration, not so that you may understand the material, but that you must understand the material. Remember the first time you saw two people playing chess? The game probably appeared to be mysterious and confusing. As you now know, no individual chess move is complicated. Given a little patience, the various chess moves are easy to learn. The game's complexity comes from deciding what combinations of moves to make and when to make them. So it is with Understanding Digital Signal Processing . First we learn the fundamental rules and processes, and then practice using them in combination. If learning digital signal processing is so easy, then why does the subject have the reputation of being hard to understand? The answer lies partially in how the material is typically presented in the literature. It's difficult to convey technical information, with its mathematical subtleties, in written form. It's one thing to write equations, but it's another matter altogether to explain what those equations really mean from a practical standpoint, and that's the goal of this book. Too often, written explanation of digital signal processing theory appears in one of two forms: either mathematical miracles occur and the reader is simply given a short and sweet equation without further explanation, or the reader is engulfed in a flood of complex variable equations and phrases such as "it is obvious that,"

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