book

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

9Complex Signals – Quadrature Filters – Interpolators

Complex signals in the form of sets of complex numbers are currently used in digital signal analysis. Some examples of these sets are presented in the chapters on discrete Fourier transforms. In this chapter, analytic signals – a particular category of complex signal – will be studied. Such signals exhibit some interesting properties and occur primarily in modulation and multiplexing. The properties of the Fourier transforms of real causal sets will be examined first [1–3].

9.1 The Fourier Transform of a Real and Causal Set

Consider a set of elements x(n) whose Z-transform is written as:

$upper X left-parenthesis upper Z right-parenthesis equals sigma-summation Underscript n equals minus infinity Overscript infinity Endscripts x left-parenthesis n right-parenthesis upper Z Superscript negative n$

The Fourier transform of this set is obtained by replacing Z with e^j2πf in X(Z):

$upper X left-parenthesis f right-parenthesis equals sigma-summation Underscript n equals minus infinity Overscript infinity Endscripts x left-parenthesis n right-parenthesis e Superscript minus normal j Baseline 2 Baseline Superscript pi italic n f$

If the elements x(n) are real numbers, we obtain:

(9.1) $upper X left-parenthesis negative f right-parenthesis equals ModifyingAbove upper X left-parenthesis f right-parenthesis With bar$

The values of X(f) at negative frequencies are complex conjugates of the values at positive frequencies. The supplementary condition of causality can be imposed on the set x(n) and the consequences for X(f) will now be examined.

The function X(f) can be separated into real and imaginary parts:

(9.2) $upper X left-parenthesis f right-parenthesis equals upper X Subscript upper R Baseline left-parenthesis f right-parenthesis plus j normal upper X Subscript upper I Baseline left-parenthesis f right-parenthesis$

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Digital Signal Processing, 10th Edition

by Maurice Bellanger, Benjamin A. Engel

9Complex Signals – Quadrature Filters – Interpolators

9.1 The Fourier Transform of a Real and Causal Set

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,
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