Digital Signal Processing

Maurice Bellanger, PhD, 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.

• Foreword (Historical Perspective) xiPreface xiiiIntroduction xv1 Signal Digitizing - Sampling and Coding 11.1 Fourier Analysis 11.2 Distributions 41.3 Some Commonly Studied Signals 61.4 The Norms of a Function 121.5 Sampling 131.6 Frequency Sampling 141.7 The Sampling Theorem 151.8 Sampling of Sinusoidal and Random Signals 161.9 Quantization 201.10 The Coding Dynamic Range 221.11 Nonlinear Coding with the 13-segment A-law 241.12 Optimal Coding 261.13 Quantity of Information and Channel Capacity 281.14 Binary Representations 292 The Discrete Fourier Transform 352.1 Definition and Properties of the Discrete Fourier Transform 362.2 Fast Fourier Transform (FFT) 382.3 Degradation Arising fromWordlength Limitation Effects 452.4 Calculation of a Spectrum Using the DFT 462.5 Fast Convolution 502.6 Calculations of a DFT Using Convolution 512.7 Implementation 523 Other Fast Algorithms for the FFT 553.1 Kronecker Product of Matrices 553.2 Factorizing the Matrix of a Decimation-in-Frequency Algorithm 563.3 Partial Transforms 583.4 Lapped Transform 663.5 Other Fast Algorithms 673.6 Binary Fourier Transform - Hadamard 713.7 Number-Theoretic Transforms 714 Time-Invariant Discrete Linear Systems 774.1 Definition and Properties 774.2 The Z-Transform 784.3 Energy and Power of Discrete Signals 804.4 Filtering of Random Signals 824.5 Systems Defined by Difference Equations 834.6 State Variable Analysis 855 Finite Impulse Response (FIR) Filters 895.1 FIR Filters 895.2 Practical Transfer Functions and Linear Phase Filters 915.3 Calculation of Coefficients by Fourier Series Expansion for Frequency Specifications 945.4 Calculation of Coefficients by the Least-Squares Method 975.5 Calculation of Coefficient by Discrete Fourier Transform 995.6 Calculation of Coefficients by Chebyshev Approximation 1005.7 Relationships Between the Number of Coefficients and the Filter Characteristic 1025.8 Raised-Cosine Transition Filter 1045.9 Structures for Implementing FIR Filters 1065.10 Limitation of the Number of Bits for Coefficients 1075.11 Z-Transfer Function of an FIR Filter 1095.12 Minimum-Phase Filters 1115.13 Design of Filters with a Large Number of Coefficients 1135.14 Two-Dimensional FIR Filters 1145.15 Coefficients of Two-Dimensional FIR Filters by the Least-Squares Method 1186 Infinite Impulse Response (IIR) Filter Sections 1236.1 First-Order Section 1236.2 Purely Recursive Second-Order Section 1276.3 General Second-Order Section 1346.4 Structures for Implementation 1386.5 CoefficientWordlength Limitation 1406.6 Internal DataWordlength Limitation 1416.7 Stability and Limit Cycles 1427 Infinite Impulse Response Filters 1477.1 General Expressions for the Properties of IIR Filters 1477.2 Direct Calculations of the Coefficients Using Model Functions 1488 Digital Ladder Filters 1738.1 Properties of Two-Port Circuits 1738.2 Simulated Ladder Filters 1768.3 Switched-Capacitor Filters 1808.4 Lattice Filters 1838.5 Comparison Elements 1879 Complex Signals - Quadrature Filters - Interpolators 1899.1 The Fourier Transform of a Real and Causal Set 1899.2 Analytic Signals 1929.3 Calculating the Coefficients of an FIR Quadrature Filter 1959.4 Recursive 90° Phase Shifters 1979.5 Single Side-Band Modulation 1999.6 Minimum-Phase Filters 2009.7 Differentiator 2019.8 Interpolation Using FIR Filters 2029.9 Lagrange Interpolation 2039.10 Interpolation by Blocks - Splines 2049.11 Interpolations and Signal Restoration 2069.12 Conclusion 20810 Multirate Filtering 21310.1 Decimation and Z-Transform 21310.2 Decomposition of a Low-Pass FIR Filter 21710.3 Half-Band FIR Filters 22010.4 Decomposition with Half-Band Filters 22210.5 Digital Filtering by Polyphase Network 22410.6 Multirate Filtering with IIR Elements 22710.7 Filter Banks Using Polyphase Networks and DFT 22710.8 Conclusion 22911 QMF Filters and Wavelets 23311.1 Decomposition into Two Sub-Bands and Reconstruction 23311.2 QMF Filters 23311.3 Perfect Decomposition and Reconstruction 23611.4 Wavelets 23811.5 Lattice Structures 24212 Filter Banks 24512.1 Decomposition and Reconstruction 24512.2 Analyzing the Elements of the Polyphase Network 24712.3 Determining the Inverse Functions 24812.4 Banks of Pseudo-QMF Filters 24912.5 Determining the Coefficients of the Prototype Filter 25312.6 Realizing a Bank of Real Filters 25413 Signal Analysis and Modeling 25913.1 Autocorrelation and Intercorrelation 25913.2 Correlogram Spectral Analysis 26113.3 Single-Frequency Estimation 26213.4 Correlation Matrix 26413.5 Modeling 26613.6 Linear Prediction 26813.7 Predictor Structures 27013.8 Multiple Sources - MIMO 27313.9 Conclusion 27514 Adaptive Filtering 27914.1 Principle of Adaptive Filtering 27914.2 Convergence Conditions 28214.3 Time Constant 28414.4 Residual Error 28514.5 Complexity Parameters 28614.6 Normalized Algorithms and Sign Algorithms 28814.7 Adaptive FIR Filtering in Cascade Form 28914.8 Adaptive IIR Filtering 29114.9 Conclusion 29315 Neural Networks 29715.1 Classification 29715.2 Multilayer Perceptron 29915.3 The Backpropagation Algorithm 30015.4 Examples of Application 30315.5 Convolution Neural Networks 30615.6 Recurrent/Recursive Neural Networks 30715.7 Neural Network and Signal Processing 30815.8 On Activation Functions 30915.9 Conclusion 31016 Error-Correcting Codes 31316.1 Reed-Solomon Codes 31316.2 Convolutional Codes 31916.3 Conclusion 33117 Applications 33517.1 Frequency Detection 33517.2 Phase-locked Loop 33717.3 Differential Coding of Speech 33817.4 Coding of Sound 33917.5 Echo Cancelation 34017.6 Television Image Processing 34217.7 Multicarrier Transmission - OFDM 34417.8 Mobile Radiocommunications 347References 349Exercises: Solutions and Hints 351Index 363