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

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Chapter33.pdf

Table of contents

• 1: The Breadth and Depth of DSP
  • The Roots of DSP
  • Telecommunications
  • Audio Processing
  • Echo Location
  • Image Processing
• 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
• 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
• 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
• 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
• 6: Convolution
  • The Delta Function and Impulse Response
  • Convolution
  • The Input Side Algorithm
  • The Output Side Algorithm
  • The Sum of Weighted Inputs
• 7: Properties of Convolution
  • Common Impulse Responses
  • Mathematical Properties
  • Correlation
  • Speed
• 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
• 9: Applications of the DFT
  • Spectral Analysis of Signals
  • Frequency Response of Systems
  • Convolution via the Frequency Domain
• 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
• 11: Fourier Transform Pairs
  • Delta Function Pairs
  • The Sinc Function
  • Other Transform Pairs
  • Gibbs Effect
  • Harmonics
  • Chirp Signals
• 12: The Fast Fourier Transform
  • Real DFT Using the Complex DFT
  • How the FFT works
  • FFT Programs
  • Speed and Precision Comparisons
  • Further Speed Increases
• 13: Continuous Signal Processing
  • The Delta Function
  • Convolution
  • The Fourier Transform
  • The Fourier Series
• 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
• 15: Moving Average Filters
  • Implementation by Convolution
  • Noise Reduction vs. Step Response
  • Frequency Response
  • Relatives of the Moving Average Filter
  • Recursive Implementation
• 16: Windowed-Sinc Filters
  • Strategy of the Windowed-Sinc
  • Designing the Filter
  • Examples of Windowed-Sinc Filters
  • Pushing it to the Limit
• 17: Custom Filters
  • Arbitrary Frequency Response
  • Deconvolution
  • Optimal Filters
• 18: FFT Convolution
  • The Overlap-Add Method
  • FFT Convolution
  • Speed Improvements
• 19: Recursive Filters
  • The Recursive Method
  • Single Pole Recursive Filters
  • Narrow-band Filters
  • Phase Response
  • Using Integers
• 20: Chebyshev Filters
  • The Chebyshev and Butterworth Responses
  • Designing the Filter
  • Step Response Overshoot
  • Stability
• 21: Filter Comparison
  • Match #1: Analog vs. Digital Filters
  • Match #2: Windowed-Sinc vs. Chebyshev
  • Match #3: Moving Average vs. Single Pole
• 22: Audio Processing
  • Human Hearing
  • Timbre
  • Sound Quality vs. Data Rate
  • High Fidelity Audio
  • Companding
  • Speech Synthesis and Recognition
  • Nonlinear Audio Processing
• 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
• 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
• 25: Special Imaging Techniques
  • Spatial Resolution
  • Sample Spacing and Sampling Aperture
  • Signal-to-Noise Ratio
  • Morphological Image Processing
  • Computed Tomography
• 26: Neural Networks (and more!)
  • Target Detection
  • Neural Network Architecture
  • Why Does it Work?
  • Training the Neural Network
  • Evaluating the Results
  • Recursive Filter Design
• 27: Data Compression
  • Data Compression Strategies
  • Run-Length Encoding
  • Huffman Encoding
  • Delta Encoding
  • LZW Compression
  • JPEG (Transform Compression)
  • MPEG
• 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
• 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
• 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
• 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
• 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
• 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
• 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

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