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Digital Signal Processing, 10th Edition

Name: Digital Signal Processing, 10th Edition
ISBN: 9781394182664

by Maurice Bellanger, Benjamin A. Engel

April 2024

Intermediate to advanced

400 pages

12h 28m

English

Wiley

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Cover
Table of Contents
Title Page
Copyright
Foreword (Historical Perspective)
Preface
Introduction
1 Signal Digitizing – Sampling and Coding
1.1 Fourier Analysis1.2 Distributions1.3 Some Commonly Studied Signals1.4 The Norms of a Function1.5 Sampling1.6 Frequency Sampling1.7 The Sampling Theorem1.8 Sampling of Sinusoidal and Random Signals1.9 Quantization1.10 The Coding Dynamic Range1.11 Nonlinear Coding with the 13-segment A-law1.12 Optimal Coding1.13 Quantity of Information and Channel Capacity1.14 Binary Representations1.A Appendix 1: The Function I(x)1.B Appendix 2: The Reduced Normal DistributionExercisesReferences
2 The Discrete Fourier Transform
2.1 Definition and Properties of the Discrete Fourier Transform2.2 Fast Fourier Transform (FFT)2.3 Degradation Arising from Wordlength Limitation Effects2.4 Calculation of a Spectrum Using the DFT2.5 Fast Convolution2.6 Calculations of a DFT Using Convolution2.7 ImplementationExercisesReferences
3 Other Fast Algorithms for the FFT
3.1 Kronecker Product of Matrices3.2 Factorizing the Matrix of a Decimation-in-Frequency Algorithm3.3 Partial Transforms3.4 Lapped Transform3.5 Other Fast Algorithms3.6 Binary Fourier Transform – Hadamard3.7 Number-Theoretic TransformsExercisesReferences

4 Time-Invariant Discrete Linear Systems
4.1 Definition and Properties4.2 The Z-Transform4.3 Energy and Power of Discrete Signals4.4 Filtering of Random Signals4.5 Systems Defined by Difference Equations4.6 State Variable AnalysisExercisesReferences
5 Finite Impulse Response (FIR) Filters
5.1 FIR Filters5.2 Practical Transfer Functions and Linear Phase Filters5.3 Calculation of Coefficients by Fourier Series Expansion for Frequency Specifications5.4 Calculation of Coefficients by the Least-Squares Method5.5 Calculation of Coefficient by Discrete Fourier Transform5.6 Calculation of Coefficients by Chebyshev Approximation5.7 Relationships Between the Number of Coefficients and the Filter Characteristic5.8 Raised-Cosine Transition Filter5.9 Structures for Implementing FIR Filters5.10 Limitation of the Number of Bits for Coefficients5.11 Z–Transfer Function of an FIR Filter5.12 Minimum-Phase Filters5.13 Design of Filters with a Large Number of Coefficients5.14 Two-Dimensional FIR Filters5.15 Coefficients of Two-Dimensional FIR Filters by the Least-Squares MethodExercisesReferences
6 Infinite Impulse Response (IIR) Filter Sections
6.1 First-Order Section6.2 Purely Recursive Second-Order Section6.3 General Second-Order Section6.4 Structures for Implementation6.5 Coefficient Wordlength Limitation6.6 Internal Data Wordlength Limitation6.7 Stability and Limit CyclesExercisesReferences
7 Infinite Impulse Response Filters
7.1 General Expressions for the Properties of IIR Filters7.2 Direct Calculations of the Coefficients Using Model FunctionsExercisesReferences
8 Digital Ladder Filters
8.1 Properties of Two-Port Circuits8.2 Simulated Ladder Filters8.3 Switched-Capacitor Filters8.4 Lattice Filters8.5 Comparison ElementsExercisesReferences
9 Complex Signals – Quadrature Filters – Interpolators
9.1 The Fourier Transform of a Real and Causal Set9.2 Analytic Signals9.3 Calculating the Coefficients of an FIR Quadrature Filter9.4 Recursive 90° Phase Shifters9.5 Single Side-Band Modulation9.6 Minimum-Phase Filters9.7 Differentiator9.8 Interpolation Using FIR Filters9.9 Lagrange Interpolation9.10 Interpolation by Blocks – Splines9.11 Interpolations and Signal Restoration9.12 ConclusionExercisesReferences
10 Multirate Filtering
10.1 Decimation and Z-Transform10.2 Decomposition of a Low-Pass FIR Filter10.3 Half-Band FIR Filters10.4 Decomposition with Half-Band Filters10.5 Digital Filtering by Polyphase Network10.6 Multirate Filtering with IIR Elements10.7 Filter Banks Using Polyphase Networks and DFT10.8 ConclusionExercisesReferences
11 QMF Filters and Wavelets
11.1 Decomposition into Two Sub-Bands and Reconstruction11.2 QMF Filters11.3 Perfect Decomposition and Reconstruction11.4 Wavelets11.5 Lattice StructuresExercisesReferences
12 Filter Banks
12.1 Decomposition and Reconstruction12.2 Analyzing the Elements of the Polyphase Network12.3 Determining the Inverse Functions12.4 Banks of Pseudo-QMF Filters12.5 Determining the Coefficients of the Prototype Filter12.6 Realizing a Bank of Real FiltersExercisesReferences
13 Signal Analysis and Modeling
13.1 Autocorrelation and Intercorrelation13.2 Correlogram Spectral Analysis13.3 Single-Frequency Estimation13.4 Correlation Matrix13.5 Modeling13.6 Linear Prediction13.7 Predictor Structures13.8 Multiple Sources – MIMO13.9 ConclusionAppendix: Estimation BoundsExercisesReferences
14 Adaptive Filtering
14.1 Principle of Adaptive Filtering14.2 Convergence Conditions14.3 Time Constant14.4 Residual Error14.5 Complexity Parameters14.6 Normalized Algorithms and Sign Algorithms14.7 Adaptive FIR Filtering in Cascade Form14.8 Adaptive IIR Filtering14.9 ConclusionExercisesReferences
15 Neural Networks
15.1 Classification15.2 Multilayer Perceptron15.3 The Backpropagation Algorithm15.4 Examples of Application15.5 Convolution Neural Networks15.6 Recurrent/Recursive Neural Networks15.7 Neural Network and Signal Processing15.8 On Activation Functions15.9 ConclusionExercisesReferences
16 Error-Correcting Codes
16.1 Reed–Solomon Codes16.2 Convolutional Codes16.3 ConclusionExercisesReferences
17 Applications
17.1 Frequency Detection17.2 Phase-locked Loop17.3 Differential Coding of Speech17.4 Coding of Sound17.5 Echo Cancelation17.6 Television Image Processing17.7 Multicarrier Transmission – OFDM17.8 Mobile RadiocommunicationsReferences
Exercises: Solutions and Hints
Chapter 1Chapter 2Chapter 3Chapter 4Chapter 5Chapter 6Chapter 7Chapter 8Chapter 9Chapter 10Chapter 11Chapter 12Chapter 13Chapter 14Chapter 15Chapter 16
Index
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Content preview from Digital Signal Processing, 10th Edition

2The Discrete Fourier Transform

The discrete Fourier transform (DFT) is introduced when the Fourier transform of a function is to be calculated using a digital computer. This type of processor can handle only numbers and, in a quantity limited by the size of its memory. It follows that the Fourier transform:

$upper S left-parenthesis f right-parenthesis equals integral Subscript minus infinity Superscript infinity Baseline s left-parenthesis t right-parenthesis e Superscript minus normal j Baseline 2 pi italic f t Baseline normal d t$

must be adapted, by replacing the signal s(t) with the numbers s(nT) which represent a sample of the signal, and by limiting to a finite value N the set of numbers on which the calculations are carried out. The calculation then provides numbers S*(f) defined by

$upper S asterisk left-parenthesis f right-parenthesis equals sigma-summation Underscript n equals 0 Overscript upper N minus 1 Endscripts s left-parenthesis italic n upper T right-parenthesis e Superscript minus normal j Baseline 2 italic pi fnT$

As the computer has limited processing power, it can only provide results for a limited number of values of the frequency f, and it is natural to choose multiples of a certain frequency step Δf. Thus,

$upper S asterisk left-parenthesis k normal upper Delta f right-parenthesis equals sigma-summation Underscript n equals 0 Overscript upper N minus 1 Endscripts s left-parenthesis italic n upper T right-parenthesis e Superscript minus normal j Baseline 2 pi italic n k normal upper Delta italic fT$

The conditions under which the calculated values form a good approximation to the required values are examined below. An interesting simplifying choice is to take Δf = 1/NT. Then there are only N different values of S*(k/NT), which is a periodic set of period N since:

$upper S asterisk left-bracket left-parenthesis k plus upper N right-parenthesis slash italic upper N upper T right-bracket equals upper S asterisk left-parenthesis k slash italic upper N upper T right-parenthesis$

On the other hand, the transform thus calculated ...

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Digital Signal Processing, 10th Edition

by Maurice Bellanger, Benjamin A. Engel

2The Discrete Fourier Transform

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.