The Scientist and Engineer's Guide to Digital Signal Processing
By Steven W. Smith, Ph.D.

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FOUNDATIONS

Chapter 1 - The Breadth and Depth of DSP The Roots of DSP Telecommunications Audio Processing Echo Location Image Processing Chapter 2 - Statistics, Probability and Noise Signal and Graph Terminology Mean and Standard Deviation Signal vs. Underlying Process The Histogram, Pmf and Pdf The Normal Distribution Digital Noise Generation Precision and Accuracy Chapter 3 - ADC and DAC Quantization The Sampling Theorem Digital-to-Analog Conversion Analog Filters for Data Conversion Selecting The Antialias Filter Multirate Data Conversion Single Bit Data Conversion Chapter 4 - DSP Software Computer Numbers Fixed Point (Integers) Floating Point (Real Numbers) Number Precision Execution Speed: Program Language Execution Speed: Hardware Execution Speed: Programming Tips

FUNDAMENTALS

Chapter 5 - Linear Systems Signals and Systems Requirements for Linearity Static Linearity and Sinusoidal Fidelity Examples of Linear and Nonlinear Systems Special Properties of Linearity Superposition: the Foundation of DSP Common Decompositions Alternatives to Linearity Chapter 6 - Convolution The Delta Function and Impulse Response Convolution The Input Side Algorithm The Output Side Algorithm The Sum of Weighted Inputs Chapter 7 - Properties of Convolution Common Impulse Responses Mathematical Properties Correlation Speed Chapter 8 - The Discrete Fourier Transform The Family of Fourier Transform Notation and Format of the Real DFT The Frequency Domain's Independent Variable DFT Basis Functions Synthesis, Calculating the Inverse DFT Analysis, Calculating the DFT Duality Polar Notation Polar Nuisances Chapter 9 - Applications of the DFT Spectral Analysis of Signals Frequency Response of Systems Convolution via the Frequency Domain Chapter 10 - Fourier Transform Properties Linearity of the Fourier Transform Characteristics of the Phase Periodic Nature of the DFT Compression and Expansion, Multirate methods Multiplying Signals (Amplitude Modulation) The Discrete Time Fourier Transform Parseval's Relation Chapter 11 - Fourier Transform Pairs Delta Function Pairs The Sinc Function Other Transform Pairs Gibbs Effect Harmonics Chirp Signals Chapter 12 - The Fast Fourier Transform Real DFT Using the Complex DFT How the FFT works FFT Programs Speed and Precision Comparisons Further Speed Increases Chapter 13 - Continuous Signal Processing The Delta Function Convolution The Fourier Transform The Fourier Series

DIGITAL FILTERS

• Chapter 14 - Introduction to Digital Filters
  • Filter Basics
  • How Information is Represented in Signals
  • Time Domain Parameters
  • Frequency Domain Parameters
  • High-Pass, Band-Pass and Band-Reject Filters
  • Filter Classification
• Chapter 15 - Moving Average Filters
  • Implementation by Convolution
  • Noise Reduction vs. Step Response
  • Frequency Response
  • Relatives of the Moving Average Filter
  • Recursive Implementation
• Chapter 16 - Windowed-Sinc Filters
  • Strategy of the Windowed-Sinc
  • Designing the Filter
  • Examples of Windowed-Sinc Filters
  • Pushing it to the Limit
• Chapter 17 - Custom Filters
  • Arbitrary Frequency Response
  • Deconvolution
  • Optimal Filters
• Chapter 18 - FFT Convolution
  • The Overlap-Add Method
  • FFT Convolution
  • Speed Improvements
• Chapter 19 - Recursive Filters
  • The Recursive Method
  • Single Pole Recursive Filters
  • Narrow-band Filters
  • Phase Response
  • Using Integers
• Chapter 20 - Chebyshev Filters
  • The Chebyshev and Butterworth Responses
  • Designing the Filter
  • Step Response Overshoot
  • Stability
• Chapter 21 - Filter Comparison
  • Match #1: Analog vs. Digital Filters
  • Match #2: Windowed-Sinc vs. Chebyshev
  • Match #3: Moving Average vs. Single Pole

APPLICATIONS

• Chapter 22 - Audio Processing
  • Human Hearing
  • Timbre
  • Sound Quality vs. Data Rate
  • High Fidelity Audio
  • Companding
  • Speech Synthesis and Recognition
  • Nonlinear Audio Processing
• Chapter 23 - Image Formation & Display
  • Digital Image Structure
  • Cameras and Eyes
  • Television Video Signals
  • Other Image Acquisition and Display
  • Brightness and Contrast Adjustments
  • Grayscale Transforms
  • Warping
• Chapter 24 - Linear Image Processing
  • Convolution
  • 3x3 Edge Modification
  • Convolution by Separability
  • Example of a Large PSF: Illumination Flattening
  • Fourier Image Analysis
  • FFT Convolution
  • A Closer Look at Image Convolution
• Chapter 25 - Special Imaging Techniques
  • Spatial Resolution
  • Sample Spacing and Sampling Aperture
  • Signal-to-Noise Ratio
  • Morphological Image Processing
  • Computed Tomography
• Chapter 26 - Neural Networks (and more!)
  • Target Detection
  • Neural Network Architecture
  • Why Does it Work?
  • Training the Neural Network
  • Evaluating the Results
  • Recursive Filter Design
• Chapter 27 - Data Compression
  • Data Compression Strategies
  • Run-Length Encoding
  • Huffman Encoding
  • Delta Encoding
  • LZW Compression
  • JPEG (Transform Compression)
  • MPEG
• Chapter 28 - Digital Signal Processors
  • How DSPs are Different from Other Microprocessors
  • Circular Buffering
  • Architecture of the Digital Signal Processor
  • Fixed versus Floating Point
  • C versus Assembly
  • How Fast are DSPs?
  • The Digital Signal Processor Market
• Chapter 29 - Getting Started with DSPs
  • The ADSP-2106x family
  • The SHARC EZ-KIT Lite
  • Design Example: An FIR Audio Filter
  • Analog Measurements on a DSP System
  • Another Look at Fixed versus Floating Point
  • Advanced Software Tools

COMPLEX TECHNIQUES

• Chapter 30 - Complex Numbers
  • The Complex Number System
  • Polar Notation
  • Using Complex Numbers by Substitution
  • Complex Representation of Sinusoids
  • Complex Representation of Systems
  • Electrical Circuit Analysis
• Chapter 31 - The Complex Fourier Transform
  • The Real DFT
  • Mathematical Equivalence
  • The Complex DFT
  • The Family of Fourier Transforms
  • Why the Complex Fourier Transform is Used
• Chapter 32 - The Laplace Transform
  • The Nature of the s-Domain
  • Strategy of the Laplace Transform
  • Analysis of Electric Circuits
  • The Importance of Poles and Zeros
  • Filter Design in the s-Domain
• Chapter 33 - The z-Transform
  • The Nature of the z-Domain
  • Analysis of Recursive Systems
  • Cascade and Parallel Stages
  • Spectral Inversion
  • Gain Changes
  • Chebyshev-Butterworth Filter Design
  • The Best and Worst of DSP
• Chapter 34 - Explaining Benford's Law
  • Frank Benford's Discovery
  • Homomorphic Processing
  • The Ones Scaling Test
  • Writing Benford's Law as a Convolution
  • Solving in the Frequency Domain
  • Solving Mystery #1
  • Solving Mystery #2
  • More on Following Benford's law
  • Analysis of the Log-Normal Distribution
  • The Power of Signal Processing