Table Of Contents:
Preface xxi

Introduction 1(28)

Numbers 1(9)

Why Do We Use a Base 10 Number System? 2(1)

Why Do Computers Use Binary? 2(1)

Why Do Programmers Sometimes Use Base 16 (Hexadecimal)? 3(1)

Other Number Concepts 4(1)

Complex Numbers 5(5)

What Is a Signal? 10(4)

Analog Versus Digital 14(5)

What Is a System? 19(1)

What Is a Transform? 20(2)

Why Do We Study Sinusoids? 22(2)

Sinusoids and Frequency Plots 24(2)

Summations 26(1)

Summary 27(1)

Review Questions 27(2)

MATLAB 29(56)

Working with Variables 30(1)

Getting Help and Writing Comments 31(1)

MATLAB Programming Basics 32(7)

Scalars, Vectors, and Matrices 33(2)

Number Ranges 35(1)

Output 35(1)

Conditional Statements (if) 36(3)

Loops 39(1)

Continuing a Line 39(1)

Arithmetic Examples 39(13)

Functions 52(1)

How NOT to Plot a Sinusoid 53(3)

Plotting a Sinusoid 56(4)

Plotting Sinusoids a Little at a Time 60(3)

Calculating Error 63(1)

Sometimes 0 Is Not Exactly 0 64(6)

Comparing Numbers with a Tolerance 65(4)

Rounding and Truncating 69(1)

MATLAB Programming Tips 70(1)

MATLAB Programming Exercises 71(10)

Other Useful MATLAB Commands 81(2)

Summary 83(1)

Review Questions 83(2)

Filters 85(48)

Parts of a Filter 89(2)

FIR Filter Structures 91(7)

Causality, Linearity, and Time-Invariance 98(5)

Multiply Accumulate Cells 103(1)

Frequency Response of Filters 104(7)

IIR Filters 111(2)

Trends of a Simple IIR Filter 113(2)

Correlation 115(13)

Summary 128(2)

Review Questions 130(3)

Sinusoids 133(26)

Review of Geometry and Trigonometry 133(1)

The Number π 134(2)

Unit Circles 136(2)

Principal Value of the Phase Shift 138(1)

Amplitudes 139(1)

Harmonic Signals 140(5)

Representing a Digital Signal as a Sum of Sinusoids 145(7)

Spectrum 152(4)

Summary 156(1)

Review Questions 156(3)

Sampling 159(28)

Sampling 160(2)

Reconstruction 162(1)

Sampling and High-Frequency Noise 162(2)

Aliasing 164(11)

Aliasing Example 165(3)

Folding 168(3)

Locations of Replications After Sampling 171(4)

Nyquist Rate 175(1)

Bandpass Sampling 176(6)

Summary 182(1)

Review Questions 183(4)

The Fourier Transform 187(38)

Fast Fourier Transform Versus the Discrete Fourier Transform 190(1)

The Discrete Fourier Transform 191(5)

Plotting the Spectrum 196(6)

Zero Padding 202(1)

DFT Shifting Theory 203(1)

The Inverse Discrete Fourier Transform 204(3)

Forward and Inverse DFT 207(5)

Leakage 212(2)

Harmonics and Fourier Transform 214(5)

Sampling Frequency and the Spectrum 219(2)

Summary 221(1)

Review Questions 221(4)

The Number e 225(28)

Reviewing Complex Numbers 225(3)

Some Interesting Properties of j 228(2)

Rotating Counterclockwise 228(1)

Rotating Clockwise 229(1)

Removing j from √--a 230(1)

Where Does e Come from? 230(3)

Euler's Formula 233(2)

Alternate Form of Euler's Equation 235(1)

Euler's Inverse Formula 236(2)

Manipulating Vectors 238(5)

Adding Two Vectors 238(1)

Adding Vectors in General 239(1)

Adding Rotating Phasors 240(1)

Adding Sinusoids of the Same Frequency 240(1)

Multiplying Complex Numbers 240(3)

Adding Rotating Phasors: an Example 243(6)

Multiplying Phasors 249(1)

Summary 250(1)

Review Questions 250(3)

The z-Transform 253(22)

The z-Transform 254(1)

Replacing Two FIR Filters in Series 255(2)

Revisiting Sequential Filter Combination with z 257(2)

Why Is z-1 the Same as a Delay by One Unit? 259(1)

What Is z? 260(1)

How the z-Transform Reduces to the Fourier Transform 261(1)

Powers of --z 261(1)

Showing that x[n] * h[n] ↔ X(z)H(z) 262(1)

Frequency Response of Filters 263(8)

Trends of a Simple IIR Filter, Part II 271(1)

Summary 271(1)

Review Questions 272(3)

The Wavelet Transform 275(64)

The Two-Channel Filter Bank 277(2)

Quadrature Mirror Filters and Conjugate Quadrature Filters 279(1)

How the Haar Transform Is a 45-Degree Rotation 280(4)

How The Haar Transform Affects a Point's Radius 281(1)

How The Haar Transform Affects a Point's Angle 282(2)

Daubechies Four-Coefficient Wavelet 284(4)

Down-Sampling and Up-Sampling 288(7)

Example Using Down/Up-Samplers 288(2)

Down-Sampling and Up-Sampling with 2 Coefficients 290(2)

Down-Sampling and Up-Sampling with Daubechies 4 292(3)

Breaking a Signal Into Waves 295(14)

Wavelet Filter Design---Filters with Four Coefficients 309(2)

Orthonormal Bases 311(3)

Multiresolution 314(6)

Biorthogonal Wavelets 320(4)

Wavelet Transform Theory 324(12)

Summary 336(1)

Review Questions 336(3)

Applications 339(60)

Examples Working with Sound 339(3)

Examples Working with Images 342(2)

Performing the 2D Discrete Wavelet Transform on an Image 344(6)

2D DWT of a Grayscale Image 347(1)

2D DWT of a Color Image 348(2)

The Plus/Minus Transform 350(2)

Doing and Undoing the Discrete Wavelet Transform 352(5)

Wavelet Transform with Matrices 357(4)

Recursively Solving a Su Doku Puzzle 361(8)

Converting Decimal to Binary 369(4)

Frequency Magnitude Response of Sound 373(3)

Filter Design 376(9)

Windowing Methods 376(4)

Designing an FIR Filter 380(5)

Compression 385(11)

Experimenting with Compression 387(6)

Compressing an Image Ourselves 393(3)

Summary 396(1)

Review Questions 396(3)

A. Constants and Variables Used in This Book 399(4)

Constants 399(1)

Variables 399(2)

Symbols Common in DSP Literature 401(2)

B. Equations 403(8)

Euler's Formula 403(1)

Trigonometric Identities and Other Math Notes 404(1)

Sampling 405(1)

Fourier Transform (FT) 405(2)

Convolution 407(1)

Statistics 407(2)

Wavelet Transform 409(1)

z-Transform 409(2)

C. DSP Project Ideas 411(4)

D. About the CD-ROM 415(2)

E. Answers to Selected Review Questions 417(22)

F. Glossary 439(6)
Bibliography 445(4)
Index 449