Details

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

<p><b>Maurice Bellanger, PhD, </b> is a former Professor of Electronics and Head of the Electronics and Communications Research Team at the Conservatoire National des Arts et Métiers (CNAM), Paris, and past president of the European Association for Signal Processing (EURASIP). He has decades of experience in both industry and academia and has published over one hundred papers on digital signal processing and related subjects.

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