Digital Signal Processing Using MATLAB and Wavelets, 2/e (With CD)

Contents:

Chapter 1: Introduction • Numbers • Why Do We Use a Base 10 Number System? • Why Do Computers Use Binary? • Why Do Programmers Sometimes Use Base 16 (Hexadecimal)? • Other Number Concepts • Converting Between Representations • Converting Binary to Decimal • Converting Decimal to Binary • Floating-Point Storage • Complex Numbers • What Is a Signal? • Analog Versus Digital • What Is a System? • What Is a Transform? • The Plus/Minus Transform • Working with Sinusoids • Plotting Sinusoids • Sampling Real Signals • Time and Frequency • Summations

Chapter 2: MATLAB • Working with Variables • Getting Help and Writing Comments • MATLAB Programming Basics • Scalars, Vectors, and Matrices • Number Ranges • Output • Conditional Statements (if) • Loops • Continuing a Line • Arithmetic Examples • Functions • How NOT to Plot a Sinusoid • Plotting a Sinusoid • Plotting Sinusoids a Little at a Time • Calculating Error • Sometimes 0 Is Not Exactly 0 • Comparing Numbers with a Tolerance • Rounding and Truncating • MATLAB Programming Tips • MATLAB Programming Exercises • Other Useful MATLAB Commands

Chapter 3: Filters • Parts of a Filter • FIR Filter Structures • Causality, Linearity, and Time-Invariance • Multiply Accumulate Cells • Frequency Response of Filters • IIR Filters • Trends of a Simple IIR Filter • Correlation • A Concise Expression for an Approximate Correlation Value • Finding Cross-Covariance as a Simple Correlation Example • Correlation Examples • Cross-Correlation • Concerning the Shift of a Signal • A Cross-Correlation Program

Chapter 4: Sinusoids • Review of Geometry and Trigonometry • The Number p • Unit Circles • Principal Value of the Phase Shift • Amplitudes • Reviewing Complex Numbers • Some Interesting Properties of j • Rotating Counterclockwise • Rotating Clockwise • Removing j from  v-a • Where Does e Come from? • Euler's Formula • Alternate Form of Euler's Equation • Euler's Inverse Formula • Manipulating Complex Numbers • Adding Two Complex Numbers • Adding Complex Numbers in General • Adding Rotating Phasors • Adding Sinusoids of the Same Frequency • Multiplying Complex Numbers • Adding Rotating Phasors: An Example • Multiplying Phasors • Harmonic Signals • Representing a Digital Signal as a Sum of Sinusoids • Spectrum

Chapter 5: Sampling • Sampling • Reconstruction • Sampling and High-Frequency Noise • Aliasing • Aliasing Example • Folding • Locations of Replications After Sampling • Nyquist Rate • Bandpass Sampling

Chapter 6: The Fourier Transform • Fast Fourier Transform Versus the Discrete Fourier Transform • The Discrete Fourier Transform • Plotting the Spectrum • Zero Padding • DFT Shifting Theory • The Inverse Discrete Fourier Transform • Forward and Inverse DFT • Leakage • Harmonics and Fourier Transform • Sampling Frequency and the Spectrum • Understanding the DFT • When Analysis Matches the Actual Frequency • When Analysis Does Not Match the Actual Frequency • One More Detail • Showing the DFT as Angles on Unit Vector Graphs • Finding the Forward and Inverse DFT as Matrix Operations • A Program for Finding the DFT as Matrix Operations

Chapter 7: The z-Transform • The z-Transform • Replacing Two FIR Filters in Series • Revisiting Sequential Filter Combination with z • Why Is z-1 the Same as a Delay by One Unit? • How the z-Transform Reduces to the Fourier Transform • Powers of -z • Showing that Time-Domain Convolution Is Equivalent to Frequency-Domain Multiplication • Frequency Response of Filters • Trends of a Simple IIR Filter, Part II

Chapter 8: The Discrete Wavelet Transform • The Two-Channel Filter Bank • Quadrature Mirror Filters and Conjugate Quadrature Filters • How the Haar Transform Is a 450 Rotation • How The Haar Transform Affects a Point's Radius • How The Haar Transform Affects a Point's Angle • Daubechies Four-Coefficient Wavelet • Down-Sampling and Up-Sampling • Example Using Down-/Up-Samplers • Down-Sampling and Up-Sampling with Two Coefficients • Down-Sampling and Up-Sampling with Daubechies • Breaking a Signal Into Waves • Wavelet Filter Design???Filters with Four Coefficients • Orthonormal Bases • Multiresolution • Biorthogonal Wavelets • Wavelet Transform Theory • Performing the DWT with Matrices • A Brief Review of Matrix Multiplication • Applying the DWT • Down-Sampling with Matrices • Combining Lowpass and Highpass into One Matrix • Generalizing the DWT with Matrices • Frequency Magnitude Response for a Wavelet

Chapter 9: The Continuous Wavelet Transform • The Mexican Hat Wavelet • Shifting the Hat • Scaling the Hat • Shifting and Scaling: Wavelets • Evaluating Integrals • Multiplying a Function by the Mexican Hat • Example of the CWT • Analytical Example of the CWT on a Function • Analytical Example of the CWT on an Impulse Function • The CWT on a Square Function • A Program to Compute the CWT • Convolution • Another Way to Approach the CWT Function • Undoing the Continuous Wavelet Transform

Chapter 10: Applications • Examples of Working with Sound • Examples of Working with Images • Shrinking a Picture • A Bottom-Up Approach • Abstracting One Level Up • Batch Processing • Using the Smaller Images in a Web Page • Performing the Two-Dimensional Discrete Wavelet Transform on an Image • Two-Dimensional DWT of a Grayscale Image • Two-Dimensional DWT of a Color Image • Doing and Undoing the Discrete Wavelet Transform • Edge Detection • Recursively Solving a Sudoku Puzzle • Frequency Magnitude Response of Sound • Filter Design • Windowing Methods • Designing an FIR Filter • Compression • Experimenting with Compression • Compressing an Image Ourselves

A. Constants and Variables Used in This Book • Constants • Variables • Symbols Common in DSP Literature

B. Equations • Convolution • Correlation • Euler's Formula • Fourier Transform • Continuous Fourier Transform • Discrete Fourier Transform • Inverse Discrete Fourier Transform • Magnitudes, Phases, and Analysis Frequencies • Integral Approximation • Sampling • Statistics • Trigonometric Identities and Other Math Notes • Wavelet Transform • Discrete Wavelet Transform • Continuous Wavelet Transform • z-Transform • DSP Project Ideas • About the CD-ROM • Answers to Selected Exercises • Glossary • References • Index

About the Author: 

Michael Weeks-Georgia State University

Michael Weeks is an associate professor at Georgia State University where he teaches courses in Digital Signal Processing. He holds a PhD in computer engineering from University of Louisiana and has authored or co-authored numerous journal and conference papers.