Foreword (Historical Perspective) xi -- Preface xiii -- Introduction xv -- 1 Signal Digitizing - Sampling and Coding 1 -- 1.1 Fourier Analysis 1 -- 1.2 Distributions 4 -- 1.3 Some Commonly Studied Signals 6 -- 1.4 The Norms of a Function 12 -- 1.5 Sampling 13 -- 1.6 Frequency Sampling 14 -- 1.7 The Sampling Theorem 15 -- 1.8 Sampling of Sinusoidal and Random Signals 16 -- 1.9 Quantization 20 -- 1.10 The Coding Dynamic Range 22 -- 1.11 Nonlinear Coding with the 13-segment A-law 24 -- 1.12 Optimal Coding 26 -- 1.13 Quantity of Information and Channel Capacity 28 -- 1.14 Binary Representations 29 -- 2 The Discrete Fourier Transform 35 -- 2.1 Definition and Properties of the Discrete Fourier Transform 36 -- 2.2 Fast Fourier Transform (FFT) 38 -- 2.3 Degradation Arising fromWordlength Limitation Effects 45 -- 2.4 Calculation of a Spectrum Using the DFT 46 -- 2.5 Fast Convolution 50 -- 2.6 Calculations of a DFT Using Convolution 51 -- 2.7 Implementation 52 -- 3 Other Fast Algorithms for the FFT 55 -- 3.1 Kronecker Product of Matrices 55 -- 3.2 Factorizing the Matrix of a Decimation-in-Frequency Algorithm 56 -- 3.3 Partial Transforms 58 -- 3.4 Lapped Transform 66 -- 3.5 Other Fast Algorithms 67 -- 3.6 Binary Fourier Transform - Hadamard 71 -- 3.7 Number-Theoretic Transforms 71 -- 4 Time-Invariant Discrete Linear Systems 77 -- 4.1 Definition and Properties 77 -- 4.2 The Z-Transform 78 -- 4.3 Energy and Power of Discrete Signals 80 -- 4.4 Filtering of Random Signals 82 -- 4.5 Systems Defined by Difference Equations 83 -- 4.6 State Variable Analysis 85 -- 5 Finite Impulse Response (FIR) Filters 89 -- 5.1 FIR Filters 89 -- 5.2 Practical Transfer Functions and Linear Phase Filters 91 -- 5.3 Calculation of Coefficients by Fourier Series Expansion for Frequency Specifications 94 -- 5.4 Calculation of Coefficients by the Least-Squares Method 97 -- 5.5 Calculation of Coefficient by Discrete Fourier Transform 99 -- 5.6 Calculation of Coefficients by Chebyshev Approximation 100 -- 5.7 Relationships Between the Number of Coefficients and the Filter Characteristic 102 -- 5.8 Raised-Cosine Transition Filter 104 -- 5.9 Structures for Implementing FIR Filters 106 -- 5.10 Limitation of the Number of Bits for Coefficients 107 -- 5.11 Z-Transfer Function of an FIR Filter 109 -- 5.12 Minimum-Phase Filters 111 -- 5.13 Design of Filters with a Large Number of Coefficients 113 -- 5.14 Two-Dimensional FIR Filters 114 -- 5.15 Coefficients of Two-Dimensional FIR Filters by the Least-Squares Method 118 -- 6 Infinite Impulse Response (IIR) Filter Sections 123 -- 6.1 First-Order Section 123 -- 6.2 Purely Recursive Second-Order Section 127 -- 6.3 General Second-Order Section 134 -- 6.4 Structures for Implementation 138 -- 6.5 CoefficientWordlength Limitation 140 -- 6.6 Internal DataWordlength Limitation 141 -- 6.7 Stability and Limit Cycles 142 -- 7 Infinite Impulse Response Filters 147 -- 7.1 General Expressions for the Properties of IIR Filters 147 -- 7.2 Direct Calculations of the Coefficients Using Model Functions 148 -- 8 Digital Ladder Filters 173 -- 8.1 Properties of Two-Port Circuits 173 -- 8.2 Simulated Ladder Filters 176 -- 8.3 Switched-Capacitor Filters 180 -- 8.4 Lattice Filters 183 -- 8.5 Comparison Elements 187 -- 9 Complex Signals - Quadrature Filters - Interpolators 189 -- 9.1 The Fourier Transform of a Real and Causal Set 189 -- 9.2 Analytic Signals 192 -- 9.3 Calculating the Coefficients of an FIR Quadrature Filter 195 -- 9.4 Recursive 90° Phase Shifters 197 -- 9.5 Single Side-Band Modulation 199 -- 9.6 Minimum-Phase Filters 200 -- 9.7 Differentiator 201 -- 9.8 Interpolation Using FIR Filters 202 -- 9.9 Lagrange Interpolation 203 -- 9.10 Interpolation by Blocks - Splines 204 -- 9.11 Interpolations and Signal Restoration 206 -- 9.12 Conclusion 208 -- 10 Multirate Filtering 213 -- 10.1 Decimation and Z-Transform 213 -- 10.2 Decomposition of a Low-Pass FIR Filter 217 -- 10.3 Half-Band FIR Filters 220 -- 10.4 Decomposition with Half-Band Filters 222 -- 10.5 Digital Filtering by Polyphase Network 224 -- 10.6 Multirate Filtering with IIR Elements 227 -- 10.7 Filter Banks Using Polyphase Networks and DFT 227 -- 10.8 Conclusion 229 -- 11 QMF Filters and Wavelets 233 -- 11.1 Decomposition into Two Sub-Bands and Reconstruction 233 -- 11.2 QMF Filters 233 -- 11.3 Perfect Decomposition and Reconstruction 236 -- 11.4 Wavelets 238 -- 11.5 Lattice Structures 242 -- 12 Filter Banks 245 -- 12.1 Decomposition and Reconstruction 245 -- 12.2 Analyzing the Elements of the Polyphase Network 247 -- 12.3 Determining the Inverse Functions 248 -- 12.4 Banks of Pseudo-QMF Filters 249 -- 12.5 Determining the Coefficients of the Prototype Filter 253 -- 12.6 Realizing a Bank of Real Filters 254 -- 13 Signal Analysis and Modeling 259 -- 13.1 Autocorrelation and Intercorrelation 259 -- 13.2 Correlogram Spectral Analysis 261 -- 13.3 Single-Frequency Estimation 262 -- 13.4 Correlation Matrix 264 -- 13.5 Modeling 266 -- 13.6 Linear Prediction 268 -- 13.7 Predictor Structures 270 -- 13.8 Multiple Sources - MIMO 273 -- 13.9 Conclusion 275 -- 14 Adaptive Filtering 279 -- 14.1 Principle of Adaptive Filtering 279 -- 14.2 Convergence Conditions 282 -- 14.3 Time Constant 284 -- 14.4 Residual Error 285 -- 14.5 Complexity Parameters 286 -- 14.6 Normalized Algorithms and Sign Algorithms 288 -- 14.7 Adaptive FIR Filtering in Cascade Form 289 -- 14.8 Adaptive IIR Filtering 291 -- 14.9 Conclusion 293 -- 15 Neural Networks 297 -- 15.1 Classification 297 -- 15.2 Multilayer Perceptron 299 -- 15.3 The Backpropagation Algorithm 300 -- 15.4 Examples of Application 303 -- 15.5 Convolution Neural Networks 306 -- 15.6 Recurrent/Recursive Neural Networks 307 -- 15.7 Neural Network and Signal Processing 308 -- 15.8 On Activation Functions 309 -- 15.9 Conclusion 310 -- 16 Error-Correcting Codes 313 -- 16.1 Reed-Solomon Codes 313 -- 16.2 Convolutional Codes 319 -- 16.3 Conclusion 331 -- 17 Applications 335 -- 17.1 Frequency Detection 335 -- 17.2 Phase-locked Loop 337 -- 17.3 Differential Coding of Speech 338 -- 17.4 Coding of Sound 339 -- 17.5 Echo Cancelation 340 -- 17.6 Television Image Processing 342 -- 17.7 Multicarrier Transmission - OFDM 344 -- 17.8 Mobile Radiocommunications 347 -- References 349 -- Exercises: Solutions and Hints 351 -- Index 363.