Digital Signal Processing

Chapter 1: Signal Digitizing - Sampling and Coding

• • 1.1 Fourier Analysis
• • 1.2 Distributions
• • 1.3 Some Commonly Studied Signals
• • 1.4 The Norms of a Function
• • 1.5 Sampling
• • 1.6 Frequency Sampling
• • 1.7 The Sampling Theorem
• • 1.8 Sampling of Sinusoidal and Random Signals
• • 1.9 Quantization
• • 1.10 The Coding Dynamic Range
• • 1.11 Nonlinear Coding with the 13-segment A-law
• • 1.12 Optimal Coding
• • 1.13 Quantity of Information and Channel Capacity
• • 1.14 Binary Representations

Chapter 2: The Discrete Fourier Transform

• • 2.1 Definition and Properties of the Discrete Fourier Transform
• • 2.2 Fast Fourier Transform (FFT)
• • 2.3 Degradation Arising fromWordlength Limitation Effects
• • 2.4 Calculation of a Spectrum Using the DFT
• • 2.5 Fast Convolution
• • 2.6 Calculations of a DFT Using Convolution
• • 2.7 Implementation

Chapter 3: Other Fast Algorithms for the FFT

• • 3.1 Kronecker Product of Matrices
• • 3.2 Factorizing the Matrix of a Decimation-in-Frequency Algorithm
• • 3.3 Partial Transforms
• • 3.4 Lapped Transform
• • 3.5 Other Fast Algorithms
• • 3.6 Binary Fourier Transform - Hadamard
• • 3.7 Number-Theoretic Transforms

Chapter 4: Time-Invariant Discrete Linear Systems

• • 4.1 Definition and Properties
• • 4.2 The Z-Transform
• • 4.3 Energy and Power of Discrete Signals
• • 4.4 Filtering of Random Signals
• • 4.5 Systems Defined by Difference Equations
• • 4.6 State Variable Analysis

Chapter 5: Finite Impulse Response (FIR) Filters

• • 5.1 FIR Filters
• • 5.2 Practical Transfer Functions and Linear Phase Filters
• • 5.3 Calculation of Coefficients by Fourier Series Expansion for Frequency Specifications
• • 5.4 Calculation of Coefficients by the Least-Squares Method
• • 5.5 Calculation of Coefficient by Discrete Fourier Transform
• • 5.6 Calculation of Coefficients by Chebyshev Approximation
• • 5.7 Relationships Between the Number of Coefficients and the Filter Characteristic
• • 5.8 Raised-Cosine Transition Filter
• • 5.9 Structures for Implementing FIR Filters
• • 5.10 Limitation of the Number of Bits for Coefficients
• • 5.11 Z-Transfer Function of an FIR Filter
• • 5.12 Minimum-Phase Filters
• • 5.13 Design of Filters with a Large Number of Coefficients
• • 5.14 Two-Dimensional FIR Filters
• • 5.15 Coefficients of Two-Dimensional FIR Filters by the Least-Squares Method

Chapter 6: Infinite Impulse Response (IIR) Filter Sections

• • 6.1 First-Order Section
• • 6.2 Purely Recursive Second-Order Section
• • 6.3 General Second-Order Section
• • 6.4 Structures for Implementation
• • 6.5 CoefficientWordlength Limitation
• • 6.6 Internal DataWordlength Limitation
• • 6.7 Stability and Limit Cycles

Chapter 7: Infinite Impulse Response Filters

• • 7.1 General Expressions for the Properties of IIR Filters
• • 7.2 Direct Calculations of the Coefficients Using Model Functions

Chapter 8: Digital Ladder Filters

• • 8.1 Properties of Two-Port Circuits
• • 8.2 Simulated Ladder Filters
• • 8.3 Switched-Capacitor Filters
• • 8.4 Lattice Filters
• • 8.5 Comparison Elements

Chapter 9: Complex Signals - Quadrature Filters - Interpolators

• • 9.1 The Fourier Transform of a Real and Causal Set
• • 9.2 Analytic Signals
• • 9.3 Calculating the Coefficients of an FIR Quadrature Filter
• • 9.4 Recursive 90° Phase Shifters
• • 9.5 Single Side-Band Modulation
• • 9.6 Minimum-Phase Filters
• • 9.7 Differentiator
• • 9.8 Interpolation Using FIR Filters
• • 9.9 Lagrange Interpolation
• • 9.10 Interpolation by Blocks - Splines
• • 9.11 Interpolations and Signal Restoration
• • 9.12 Conclusion

Chapter 10: Multirate Filtering

• • 10.1 Decimation and Z-Transform
• • 10.2 Decomposition of a Low-Pass FIR Filter
• • 10.3 Half-Band FIR Filters
• • 10.4 Decomposition with Half-Band Filters
• • 10.5 Digital Filtering by Polyphase Network
• • 10.6 Multirate Filtering with IIR Elements
• • 10.7 Filter Banks Using Polyphase Networks and DFT
• • 10.8 Conclusion

Chapter 11: QMF Filters and Wavelets

• • 11.1 Decomposition into Two Sub-Bands and Reconstruction
• • 11.2 QMF Filters
• • 11.3 Perfect Decomposition and Reconstruction
• • 11.4 Wavelets
• • 11.5 Lattice Structures

Chapter 12: Filter Banks

• • 12.1 Decomposition and Reconstruction
• • 12.2 Analyzing the Elements of the Polyphase Network
• • 12.3 Determining the Inverse Functions
• • 12.4 Banks of Pseudo-QMF Filters
• • 12.5 Determining the Coefficients of the Prototype Filter
• • 12.6 Realizing a Bank of Real Filters

Chapter 13: Signal Analysis and Modeling

• • 13.1 Autocorrelation and Intercorrelation
• • 13.2 Correlogram Spectral Analysis
• • 13.3 Single-Frequency Estimation
• • 13.4 Correlation Matrix
• • 13.5 Modeling
• • 13.6 Linear Prediction
• • 13.7 Predictor Structures
• • 13.8 Multiple Sources - MIMO
• • 13.9 Conclusion

Chapter 14: Adaptive Filtering

• • 14.1 Principle of Adaptive Filtering
• • 14.2 Convergence Conditions
• • 14.3 Time Constant
• • 14.4 Residual Error
• • 14.5 Complexity Parameters
• • 14.6 Normalized Algorithms and Sign Algorithms
• • 14.7 Adaptive FIR Filtering in Cascade Form
• • 14.8 Adaptive IIR Filtering
• • 14.9 Conclusion

Chapter 15: Neural Networks

• • 15.1 Classification
• • 15.2 Multilayer Perceptron
• • 15.3 The Backpropagation Algorithm
• • 15.4 Examples of Application
• • 15.5 Convolution Neural Networks
• • 15.6 Recurrent/Recursive Neural Networks
• • 15.7 Neural Network and Signal Processing
• • 15.8 On Activation Functions
• • 15.9 Conclusion

Chapter 16: Error-Correcting Codes

• • 16.1 Reed-Solomon Codes
• • 16.2 Convolutional Codes
• • 16.3 Conclusion

Chapter 17: Applications

• • 17.1 Frequency Detection
• • 17.2 Phase-locked Loop
• • 17.3 Differential Coding of Speech
• • 17.4 Coding of Sound
• • 17.5 Echo Cancelation
• • 17.6 Television Image Processing
• • 17.7 Multicarrier Transmission - OFDM
• • 17.8 Mobile Radiocommunications