DIGITAL SIGNAL PROCESSING : theory and practice, 10 th edition

Signal processing is required and deployed in almost all engineering fields, not only electronics and communications but also biology, mechanics, chemistry, and geophysics. Moreover, signal processing algorithms are exploited for data analysis and modelling in business and finance and are also at the core of artificial intelligence systems. Delivering on the promise of 'theory and practice' throughout, the author ensures that the chapters and exercises meet the requirements of both students and industry practitioners, with more advanced topics appearing in the second half of the book. Mathematical concepts are explained, and merge well with the text, allowing the reader to follow the narrative instead of breaking off into tough mathematical diversions. The book has been updated throughout and includes a brand-new section on neural networks. This book series, published originally in French, has not been available in English for many years, and readers will find that it stands alone as a complete text, with no earlier edition knowledge required. Cover Title Page Copyright Contents Foreword (Historical Perspective) Preface Introduction Chapter 1 Signal Digitizing – Sampling and Coding 1.1 Fourier Analysis 1.1.1 Fourier Series Expansion of a Periodic Function 1.1.2 Fourier Transform of a Function 1.2 Distributions 1.2.1 Definition 1.2.2 Differentiation of Distributions 1.2.2.1 The Fourier Transform of a Distribution 1.3 Some Commonly Studied Signals 1.3.1 Deterministic Signals 1.3.2 Random Signals 1.3.3 Gaussian Signals 1.3.3.1 Peak Factor of a Random Signal 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 1.8.1 Sinusoidal Signals 1.8.2 Discrete Random Signals 1.8.3 Discrete Noise Generation 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 Exercises References Chapter 2 The Discrete Fourier Transform 2.1 Definition and Properties of the Discrete Fourier Transform 2.2 Fast Fourier Transform (FFT) 2.2.1 Decimation‐in‐time Fast Fourier Transform 2.2.2 Decimation‐in‐frequency Fast Fourier Transform 2.2.3 Radix‐4 FFT Algorithm 2.2.4 Split‐radix FFT Algorithm 2.3 Degradation Arising from Wordlength Limitation Effects 2.4 Calculation of a Spectrum Using the DFT 2.4.1 The Filtering Function of the DFT 2.4.2 Spectral Resolution 2.5 Fast Convolution 2.6 Calculations of a DFT Using Convolution 2.7 Implementation Exercises References 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 3.3.1 Transform of Real Data and Odd DFT 3.3.2 The Odd‐time Odd‐frequency DFT 3.3.3 Sine and Cosine Transforms 3.3.4 The Two‐dimensional DCT 3.4 Lapped Transform 3.5 Other Fast Algorithms 3.6 Binary Fourier Transform – Hadamard 3.7 Number‐Theoretic Transforms Exercises References 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 Exercises References 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 Exercises References 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 Coefficient Wordlength Limitation 6.6 Internal Data Wordlength Limitation 6.7 Stability and Limit Cycles Exercises References 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 7.2.1 Impulse Invariance 7.2.2 Bilinear Transform 7.2.2.1 Butterworth Filters 7.2.2.2 Elliptic Filters 7.2.2.3 Calculating any Filter by Transformation of a Low‐pass Filter 7.2.3 Iterative Techniques for Calculating IIR Filter with Frequency 7.2.3.1 Minimizing the Mean Square Error 7.2.3.2 Chebyshev Approximation 7.2.4 Filters Based on Spheroidal Sequences 7.2.5 Structures Representing the Transfer Function 7.2.6 Limiting the Coefficient Wordlength 7.2.7 Round‐Off Noise 7.2.8 Comparison of IIR and FIR Filters Exercises References 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 Exercises References 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 Exercises References 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 Exercises References 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 Exercises References 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 Exercises References 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 13.7.1 Sensor Networks – Antenna Processing 13.8 Multiple Sources – MIMO 13.9 Conclusion Appendix: Estimation Bounds Exercises References 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 Exercises References 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 Exercises References Chapter 16 Error‐Correcting Codes 16.1 Reed–Solomon Codes 16.1.1 Predictable Signals 16.1.2 Reed–Solomon Codes in the Frequency Domain 16.1.3 Reed–Solomon Codes in the Time Domain 16.1.4 Computing in a Finite Field 16.1.5 Performance of Reed–Solomon Codes 16.2 Convolutional Codes 16.2.1 Channel Capacity 16.2.2 Approaching the Capacity Limit 16.2.3 A Simple Convolutional Code 16.2.4 Coding Gain and Error Probability 16.2.5 Decoding and Output Signals 16.2.6 Recursive Systematic Coding (RSC) 16.2.7 Principle of Turbo Codes 16.2.8 Trellis‐Coded Modulations 16.3 Conclusion Exercises References 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 17.5.1 Data Echo Canceller 17.5.1.1 Two‐wire Line 17.5.2 Acoustic Echo Canceler 17.6 Television Image Processing 17.7 Multicarrier Transmission – OFDM 17.8 Mobile Radiocommunications References Exercises: Solutions and Hints Index EULA