Discrete Communication Systems
- Length: 992 pages
- Edition: 1
- Language: English
- Publisher: Oxford University Press
- Publication Date: 2021-09-19
- ISBN-10: 019886079X
- ISBN-13: 9780198860792
- Sales Rank: #2015663 (See Top 100 Books)
This is the first textbook which presents the theory of pure discrete communication systems and its relation to the existing theory of digital and analog communications at a graduate level.
Based on the orthogonality principles and theory of discrete time stochastic processes, a generic structure of communication systems, based on correlation demodulation and optimum detection, is developed and presented in the form of mathematical operators with precisely defined inputs and outputs
and related functions. Based on this generic structure, the traditionally defined phase shift keying (PSK), frequency shift keying (FSK), quadrature amplitude modulation (QAM), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) systems are deduced as its
special cases. The main chapters, presenting the theory of communications, are supported by a set of supplementary chapters containing the theory of deterministic and stochastic signal processing, which makes the book a self-contained presentation of the subject.
The book uses unified notation and unified terminology, which allows a clear distinction between deterministic and stochastic signals, power signals and energy signals, discrete time signals and processes and continuous time signals and processes, and an easy way of understanding the differences in
defining the correlation functions, power and energy spectral densities, and amplitudes and power spectra of the mentioned signals and processes.
In addition to solved examples in the text, about 300 solved problems are available to readers in the supplementary material that aim to enhance the understanding of the theory in the text. In addition, five research Projects are added to be used by lecturers or instructors that aim to enhance the
understanding of theory and to establish its relation to the practice.
Cover Discrete Communication Systems Copyright Dedication Preface Acknowlegements Contents List of Symbols, Functions, Operators, and Abbreviations Symbols Greek and Cyrillic Symbols Defined Functions Operators Abbreviations 1: Introduction to Communication Systems 1.1 Communication Systems and Networks 1.2 Classification of Signals and Systems 1.2.1 Classification of Signals with Respect to Time and Value 1.2.2 Periodic and Symmetric Signals 1.2.3 Deterministic and Stochastic Signals 1.2.4 Classification of Signals with Respect to Power and Energy 1.2.5 Classification of Signals with Respect to Realizability 1.2.6 Classification of Systems 1.3 Conversions of Analogue and Digital Signals 1.3.1 Analogue-to-Digital Conversion 1.3.2 Digital-to-Analogue Conversion 1.3.3 Application of Signals in Digital and Discrete Communication Systems 2: Orthogonal Signals and the Orthogonalization Procedure 2.1 Introduction 2.2 Geometric Representation of Signals 2.2.1 Orthonormal Basis Functions 2.2.2 Vector Representation of Signals 2.3 The Gram–Schmidt Orthogonalization Procedure 2.4 Continuous-Time Orthogonal Signals 2.4.1 Continuous-Time Versus Discrete-Time Basis Signals 2.4.2 Orthonormal Signals 2.4.3 The Gram–Schmidt Orthogonalization Procedure 2.5 Orthogonal Signals in Code Division Multiple Access Communication Systems Problems 3: Discrete-Time Stochastic Processes 3.1 Definition and Analysis of Discrete-Time Stochastic Processes 3.1.1 Introduction 3.1.2 Definition of a Stochastic Process 3.1.3 Mathematical Analysis of Stochastic Processes 3.2 Statistical Properties of Stochastic Processes 3.2.1 First-Order Statistics 3.2.2 Second-Order Statistics 3.2.3 Higher-Order Statistics 3.2.4 Types of Discrete-Time Stochastic Processes 3.3 The Stationarity of Discrete-Time Stochastic Processes 3.3.1 The Stationarity of One Discrete-Time Stochastic Process 3.3.2 Properties of the Autocorrelation Function 3.3.3 The Stationarity of Two Discrete-Time Stochastic Processes 3.4 Ergodic Processes 3.4.1 Ensemble Averages and Time Averages 3.4.2 Ergodic Processes 3.4.3 Estimate of the Mean across the Ensemble of Realizations of X(n) 3.4.4 Estimate of the Mean across a realization of X(n) 3.4.5 Estimate of the Mean of an Ergodic Process X(n) 3.4.6 Summary of Ergodic Stochastic Processes 3.5 The Frequency-Domain Representation of Discrete-Time Stochastic Processes 3.5.1 Continuous-Time Stochastic Processes in the Frequency Domain 3.5.2 Discrete-Time Stochastic Processes in the Frequency Domain 3.5.3 Cross-Spectrum Functions 3.6 Typical Stochastic Processes 3.6.1 Noise Processes 3.6.2 General Gaussian Noise Processes 3.6.3 Harmonic Processes 3.6.4 Stochastic Binary Processes 3.7 Linear Systems with Stationary Random Inputs 3.7.1 An LTI System with Stationary Random Inputs in the Time Domain 3.7.2 Frequency-Domain Analysis of an LTI System 3.8 Summary Problems 4 Noise Processes in Discrete Communication Systems 4.1 Gaussian Noise Processes in the Continuous-Time Domain 4.1.1 Continuous White Gaussian Noise Processes 4.1.2 The Entropy of White Gaussian Noise Processes 4.1.3 Truncated Gaussian Noise Processes 4.1.4 Concluding Notes on Gaussian Noise Processes 4.2 Gaussian Noise Processes in the Discrete-Time Domain 4.2.1 White Gaussian Noise Processes with Discrete-Time and Continuous-Valued Samples 4.2.2 Discrete-Time White Gaussian Noise Processes with Discrete-Valued Samples 4.2.3 White Gaussian Noise Processes with Quantized Samples in a Strictly Limited Interval 4.2.4 Band-Limited Continuous- and Discrete-Time Signals and Noise 4.3 Operation of a Baseband Noise Generator 4.3.1 Band-Limited Continuous-Time Noise Generators 4.3.2 Band-Limited Discrete-Time Noise Generators 4.3.3 Spectral Analysis of Continuous-Time Baseband Noise 4.3.4 Spectral Analysis of Discrete-Time Baseband Noise 4.4 Operation of a Bandpass Noise Generator 4.4.1 Ideal Bandpass Continuous-Time Gaussian Noise 4.4.2 Ideal Bandpass Discrete Gaussian Noise 4.4.3 Modulators and Demodulators of Ideal Bandpass Discrete Gaussian Noise 4.5 Practical Design of a Band-Limited Discrete-Time Noise Modulator 4.6 Design of an Ordinary Band-Limited Discrete-Time Noise Modulator Problems 5: Operation of a Discrete Communication System 5.1 Structure of a Discrete System 5.2 Operation of a Discrete Message Source 5.3 Operation of a Discrete Modulator 5.4 Additive White Gaussian Noise Channels in a Discrete-Time Domain 5.5 Correlation Demodulators 5.5.1 Operation of a Correlator 5.5.2 Statistical Characterization of Correlator Output 5.5.3 Signal Constellation 5.6 Optimum Detectors 5.6.1 The Maximum Likelihood Estimator of a Transmitted Signal 5.6.2 Application of the Maximum Likelihood Rule 5.6.3 Design of an Optimum Detector 5.6.4 Generic Structure of a Discrete Communication System 5.7 Multilevel Systems with a Binary Source 5.7.1 Transmitter Operation 5.7.2 Radio Frequency Blocks and Additive White Gaussian Noise Waveform Channels 5.7.3 Operation of a Bandpass Noise Generator 5.7.4 Intermediate-Frequency Optimum Receivers 5.7.5 Intermediate-Frequency Optimum Detectors 5.8 Operation of a Digital Communication System 5.8.1 Digital versus Discrete Communication Systems 5.8.2 Generic Structure of a Digital Communication System Appendix: Operation of a Correlator in the Presence of Discrete White Gaussian Noise 6: Digital Bandpass Modulation Methods 6.1 Introduction 6.2 Coherent Binary Phase-Shift Keying Systems 6.2.1 Operation of a Binary Phase-Shift Keying System 6.2.2 Transmitter Operation 6.2.2.1 Modulating Signal Presentation 6.2.2.2 Modulated Signals in Time and Frequency Domains 6.2.3 Receiver Operation 6.2.3.1 Correlation Demodulator Operation 6.2.3.2 Operation of the Optimum Detector, and Structure of the Receiver 6.2.3.3 Bit Error Probability Calculation 6.3 Quadriphase-Shift Keying 6.3.1 Operation of a Quadrature Phase-Shift Keying System 6.3.2 Transmitter Operation 6.3.2.1 Modulating Signals in Time and Frequency Domains 6.3.2.2 Modulated Signals in the Time Domain 6.3.2.3 Modulated Signals in the Frequency Domain 6.3.2.4 The Power Spectral Density of Signals in a Quadriphase-Shift Keying System 6.3.3 Receiver Operation 6.3.3.1 Operation of the Correlation Demodulator and the Optimum Detector 6.3.3.2 Bit Error Probability Calculation 6.3.3.3 Signal Analysis and Transceiver Structure in a Quadrature Phase-Shift Keying System 6.4 Coherent Binary Frequency-Shift Keying with a Continuous Phase 6.4.1 Operation of a Binary Frequency-Shift Keying System 6.4.2 Transmitter Operation 6.4.2.1 Modulating Signals in Time and Frequency Domains 6.4.2.2 Modulated Signals in the Time Domain and the Signal-Space Diagram 6.4.2.3 Modulating and Modulated Signals in Time and Frequency Domains 6.4.2.4 Modulated Signals in the Frequency Domain 6.4.3 Receiver Operation 6.4.3.1 Operation of a Correlation Demodulator 6.4.3.2 Operation of an Optimum Detector 6.4.3.3 Calculation of the Bit Error Probability 6.4.3.4 Design of a Transceiver for a Binary Frequency-Shift Keying Signal 6.5 M-ary Quadrature Amplitude Modulation 6.5.1 System Operation 6.5.2 Transmitter Operation 6.5.3 Receiver Operation Appendix A: Densities of the Correlation Variables X1 and X2 in a Quadrature Phase-Shift Keying System Appendix B: Derivatives of Density Functions for a Binary Frequency-Shift Keying System Appendix C: Precise Derivation of the Bit Error Probability for a Binary Frequency-Shift Keying System Appendix D: Power Spectral Density of a Quadrature Component in a Frequency-Shift Keying Signal Problems 7: Discrete Bandpass Modulation Methods 7.1 Introduction 7.2 Coherent Binary Phase-Shift Keying Systems 7.2.1 Operation of a Binary Phase-Shift Keying System 7.2.2 Transmitter Operation 7.2.2.1 Presentation of a Modulating Signal 7.2.2.2 Modulated Signals in Time and Frequency Domains 7.2.2.3 The Power Spectral Density of Binary Phase-Shift Keying Modulated Signals 7.2.3 Receiver Operation 7.2.3.1 Operation of a Correlation Demodulator 7.2.3.2 Operation of an Optimum Detector, and Structure of a Receiver 7.2.3.3 Calculation of the Bit Error Probability 7.3 Quadriphase-Shift Keying 7.3.1 System Operation 7.3.2 Transmitter Operation 7.3.2.1 Modulating Signals in Time and Frequency Domains 7.3.2.2 Modulated Signals in the Time Domain 7.3.2.3 Modulated Signals in the Frequency Domain 7.3.3 Receiver Operation 7.3.3.1 Operation of the Correlation Demodulator and the Optimum Detector 7.3.3.2 Calculation of the Bit Error Probability 7.3.3.3 Signal Analysis and Structure of the Transceiver in a Quadriphase-Shift Keying System 7.4 Coherent Binary Frequency-Shift Keying with Continuous Phase 7.4.1 Operation of a Binary Frequency-Shift Keying System 7.4.2 Transmitter Operation 7.4.2.1 Modulating Signals in Time and Frequency Domains 7.4.2.2 Modulated Signal Analysis in the Time Domain and a Signal-Space Diagram 7.4.2.3 Modulated Signal Analysis in Time and Frequency Domains 7.4.2.4 Modulated Signals in the Frequency Domain 7.4.3 Receiver Operation 7.4.3.1 Operation of the Correlation Demodulator 7.4.3.2 Operation of the Optimum Detector 7.4.3.3 Calculation of the Bit Error Probability 7.4.3.4 Transceiver Design for a Binary Frequency-Shift Keying Signal 7.5 M-ary Discrete Quadrature Amplitude Modulation 7.5.1 Operation of a Discrete M-ary Quadrature Amplitude Modulation System 7.5.2 Transmitter Operation 7.5.3 Operation of a Correlation Demodulator 7.5.4 Operation of an Optimum Detector Appendix A: Power Spectral Density of a Quadriphase-Shift Keying Modulating Signal Appendix B: Probability Density Functions for a Quadriphase-Shift Keying System Appendix C: Density Functions for X1 and X2 in a Frequency-Shift Keying System Appendix D: Statistics of the Decision Variable X = X1 – X2 Problems 8: Orthogonal Frequency Division Multiplexing and Code Division Multiple Access Systems 8.1 Introduction 8.2 Digital Orthogonal Frequency Division Multiplexing Systems 8.2.1 Introduction 8.2.2 Transmitter Operation 8.2.3 Receiver Operation 8.2.4 Operation of a Receiver in the Presence of Noise 8.3 Discrete Orthogonal Frequency Division Multiple Access Systems 8.3.1 Principles of Discrete Signal Processing in an Orthogonal Frequency Division Multiple Access System 8.3.2 A Discrete Baseband Orthogonal Frequency Division Multiple Access System Based on Binary Phase-Shift Keying 8.3.3 Structure and Operation of a Discrete Orthogonal Frequency Division Multiple Access System 8.3.4 Operation of the Receiver in an Orthogonal Frequency Division Multiple Access System 8.3.5 Operation of the Receiver in the Presence of Noise 8.4 Discrete Code Division Multiple Access Systems 8.4.1 Principles of Operation of a Discrete Code Division Multiple Access System 8.4.2 Derivation of the Probability of Error Problems 9: Information Theory and Channel Coding 9.1 Characterization of a Discrete Source 9.2 Characterization of a Discrete Channel 9.2.1 A Discrete Memoryless Channel 9.2.2 Discrete Binary Channels with and without Memory 9.2.2.1 Discrete Binary Channels 9.2.2.2 Discrete Binary Memoryless Channels 9.2.2.3 Discrete Binary Channels with Memory 9.2.3 Capacity of a Discrete Memoryless Channel 9.2.3.1 Capacity of a Discrete Channel 9.2.3.2 Example of the Capacity of a Binary Memoryless Channel 9.3 Characterization of Continuous Channels 9.3.1 Differential Entropy 9.3.2 Channel Information for Random Vectors 9.3.3 Definition of the Capacity of a Continuous Channel 9.3.4 Proof of the Channel Capacity Theorem 9.4 Capacity Limits and the Coding Theorem 9.4.1 Capacity Limits 9.4.2 The Coding Theorem and Coding Channel Capacity 9.5 Information and Entropy of Uniform Density Functions 9.5.1 Continuous Uniform Density Functions 9.5.2 Discrete Uniform Density Functions 9.6 Information and Entropy of Gaussian Density Functions 9.6.1 Continuous Gaussian Density Functions 9.6.2 Discrete Gaussian Density Functions 9.7 Block Error Control Codes 9.7.1 Theoretical Basis and Definitions of Block Code Terms 9.7.2 Coding Procedure Using a Generator Matrix 9.7.3 Error Detection Using a Parity Check Matrix 9.7.4 Standard Array Decoding 9.7.5 Syndrome Table Decoding 9.8 Convolutional Codes 9.8.1 Linear Convolutional Codes 9.8.2 Operation of a Coding Communication System 9.8.3 Operation of a Decoder 9.8.4 Decoding Algorithms 9.9 Introduction to Iterative Decoding and Turbo Decoding 9.9.1 Coding Models for Communication Systems 9.9.2 The Hard-Output Viterbi Algorithm 9.9.3 Iterative Algorithms and Turbo Coding Appendix A: Derivation of Mutual Information Appendix B: Entropy of a Truncated Discrete Gaussian Density Function Problems Problems 10: Designing Discrete and Digital Communication Systems 10.1 Introduction 10.2 Designing Quadriphase-Shift Keying Transceivers 10.2.1 Quadriphase-Shift Keying Systems with Digital-to-Analogue and Analogue-to-Digital Conversion of Modulating Signals 10.2.1.1 Quadriphase-Shift Keying Transmitters with Baseband Discrete-Time Signal Processing 10.2.1.2 Designing a Quadriphase-Shift Keying Receiver 10.2.1.3 Practical Design of a Quadriphase-Shift Keying Receiver 10.2.2 Quadriphase-Shift Keying Systems with Digital-to-Analogue and Analogue-to-Digital Conversion of Intermediate-Frequency Signals 10.2.2.1 Designing a Digital Quadriphase-Shift Keying Transmitter at Intermediate Frequency 10.2.2.2 Design of a Digital Quadriphase-Shift Keying Receiver at Intermediate Frequency 10.2.2.3 Practical Design of a Discrete Quadriphase-Shift Keying Receiver at Intermediate Frequency 10.3 Designing Quadrature Amplitude Modulation Transceivers 10.3.1 Quadrature Amplitude Modulation Systems with Digital-to-Analogue and Analogue-to-Digital Conversion of Modulating Signals 10.3.1.1 Quadrature Amplitude Modulation Transmitters with Baseband Discrete-Time Signal Processing 10.3.1.2 Designing a Quadrature Amplitude Modulation Receiver 10.3.1.3 Practical Design of a Quadrature Amplitude Modulation Receiver 10.3.2 Quadrature Amplitude Modulation Systems with Digital-to-Analogue and Analogue-to-Digital Conversion of Intermediate-Frequency Signals 10.3.2.1 Digital Design of a Quadrature Amplitude Modulation Transmitter at Intermediate Frequency 10.3.2.2 Digital Design of a Quadrature Amplitude Modulation Receiver at Intermediate Frequency 10.3.2.3 Practical Design of a Discrete Quadrature Amplitude Modulation Receiver at Intermediate Frequency 10.4 Overview of Discrete Transceiver Design 10.4.1 Introduction 10.4.2 Designing Quadrature Amplitude Modulation Systems 11: Deterministic Continuous-Time Signals and Systems 11.1 Basic Continuous-Time Signals 11.2 Modification of the Independent Variable 11.3 Combined Modifications of the Independent Variable 11.4 Cross-Correlation and Autocorrelation 11.4.1 The Cross-Correlation Function 11.4.2 The Autocorrelation Function 11.5 System Classification 11.6 Continuous-Time Linear-Time-Invariant Systems 11.6.1 Modelling of Systems in the Time Domain 11.6.2 Representation of an Input Signal 11.6.3 Basic Representation of a Linear-Time-Invariant System 11.6.4 Representation of an Output Signal 11.6.5 Properties of Convolution 11.7 Properties of Linear-Time-Invariant Systems Problems 12: Transforms of Deterministic Continuous-Time Signals 12.1 Introduction 12.2 The Fourier Series 12.2.1 The Fourier Series in Trigonometric Form 12.2.2 An Example of Periodic Signal Analysis 12.2.3 The Fourier Series in Complex Exponential Form 12.2.4 Amplitude Spectra, Magnitude Spectra, and Phase Spectra of Periodic Signals 12.2.5 The Power and Energy of Signals, and Parseval’s Theorem 12.2.6 Existence of Fourier Series 12.2.7 Orthogonality Characteristics of the Fourier Series 12.2.8 Table of the Fourier Series 12.3 Fourier Transform of Continuous Signals 12.3.1 Derivative and Application of Fourier Transform Pairs 12.3.2 Convergence Conditions 12.3.3 The Rayleigh Theorem and the Energy of Signals 12.3.4 Properties of the Fourier Transform 12.3.5 Important Problems and Solutions 12.3.6 Tables of the Fourier Transform 12.4 Fourier Transform of Periodic Signals 12.5 Correlation Functions, Power Spectral Densities, and Linear-Time-Invariant Systems 12.5.1 Correlation of Real-Valued Energy Signals 12.5.2 Correlation of Real-Valued Power Signals 12.5.3 Comprehensive Analysis of Linear-Time-Invariant Systems 12.5.3.1 System Presentation 12.5.3.2 Correlation and Energy Spectral Density of Complex Energy Signals 12.5.3.3 Correlation and Power Spectral Density of Complex Power Signals 12.5.3.4 Analysis of a Linear-Time-Invariant System with Deterministic Energy Signals 12.5.4 Tables of Correlation Functions and Related Spectral Densities Problems 13: Sampling and Reconstruction of Continuous-Time Signals 13.1 Introduction 13.2 Sampling of Continuous-Time Signals 13.3 Reconstruction of Analogue Signals 13.4 Operation of a Lowpass Reconstruction Filter 13.5 Generation of Discrete-Time Signals 14: Deterministic Discrete-Time Signals and Systems 14.1 Discrete-Time Signals 14.1.1 Elementary Discrete-Time Signals 14.1.2 Modification of Independent Variables 14.1.3 Cross-Correlation and Autocorrelation Functions 14.2 Discrete-Time Systems 14.2.1 Systems Classification 14.2.2 Discrete-Time Linear-Time-Invariant Systems 14.3 Properties of Linear-Time-Invariant Systems 14.4 Analysis of Linear-Time-Invariant Systems in Time and Frequency Domains Problems 15: Deterministic Discrete-Time Signal Transforms 15.1 Introduction 15.2 The Discrete-Time Fourier Series 15.2.1 Continuous-Time Fourier Series and Transforms 15.2.2 The Discrete-Time Fourier Series 15.2.3 Fourier Series Examples Important for Communication Systems 15.3 The Discrete-Time Fourier Transform 15.3.1 Derivation of the Discrete-Time Fourier Transform Pair 15.3.2 The Problem of Convergence 15.3.3 Properties of the Discrete-Time Fourier Transform 15.3.4 Tables for the Discrete-Time Fourier Transform 15.4 Discrete Fourier Transforms 15.4.1 Fundamentals of Frequency-Domain Sampling 15.4.2 Discrete Fourier Transforms 15.4.3 Inverse Discrete Fourier Transforms 15.4.4 Three Typical Cases of Discrete Fourier Transforms 15.5 Algorithms for Discrete Fourier Transforms 15.5.1 Goertzel’s Algorithm 15.5.2 Discrete Fourier Transforms as Linear Transformations 15.5.3 The Radix-2 Fast Fourier Transform Algorithm 15.6 Correlation and Spectral Densities of Discrete-Time Signals 15.6.1 Cross-Correlation and Correlation of Real-Valued Energy Signals 15.6.2 Cross-Correlation and Correlation of Real-Valued Power Signals 15.6.3 Parseval’s Theorem and the Wiener–Khintchine Theorem 15.6.4 Comprehensive Analysis of Discrete Linear-Time-Invariant Systems 15.6.4.1 System Presentation 15.6.4.2 Correlation and Power Spectral Density of Complex Energy Signals 15.6.4.3 Correlation of Complex Power Signals 15.6.4.4 Analysis of a Linear-Time-Invariant System with Energy Signals 15.6.5 Tables of Correlation Functions and Related Spectral Density Functions 15.7 The z-Transform 15.7.1 Introduction 15.7.2 Derivation of Expressions for the z-Transform 15.7.3 Properties of the z-Transform 15.7.4 The Inverse z-Transform Problems 16: Theory of the Design, and Operation of Digital Filters 16.1 The Basic Concept of Filtering 16.2 Ideal and Real Transfer Functions 16.3 Representation of Digital Filters 16.4 Basic Finite Impulse Response Filters 16.5 Structures of Finite Impulse Response Filters 16.6 Basic Infinite Impulse Response Filters 16.7 Structures of Infinite Impulse Response Filters 16.7.1 Introduction 16.7.2 Conventional Description of Block Diagrams 16.7.3 Direct Forms of Infinite Impulse Response Filters 16.8 Algorithms for the Design of Digital Filters 16.8.1 Ideal and Real Frequency Responses 16.8.2 Basic Methods for the Design of Digital Filters 16.8.3 Algorithms Based on Iterative Optimization 17: Multi-Rate Discrete-Time Signal Processing 17.1 Multi-Rate Signals in Time and Frequency Domains 17.1.1 Time-Domain Analysis 17.1.2 Frequency-Domain Analysis 17.1.3 Complex Multi-Rate Systems 17.1.4 Complexity Reduction 17.2 Multi-Rate Systems 17.2.1 Basic System Structures 17.2.2 System Analysis in Time and Frequency Domains 17.3 Reduction of Computational Complexity 17.3.1 Multistage Decimators and Interpolators 17.3.2 Polyphase Decomposition of a Decimation Filter 17.3.3 Polyphase Decomposition of a Finite Impulse Response Transfer Function 17.3.4 Polyphase Decomposition of an Infinite Impulse Response Transfer Function Problems 18: Multi-Rate Filter Banks 18.1 Digital Filter Banks 18.2 Two-Channel Quadrature Mirror Filter Banks 18.2.1 Basic Theory 18.2.2 Elimination of Aliasing in Two-Channel Quadrature Mirror Filter Banks 18.3 Perfect Reconstruction of Two-Channel Filter Banks 18.4 Multichannel Quadrature Mirror Filter Banks 18.5 Multilevel Filter Banks and Adaptive Filter Banks 18.5.1 Banks with Equal or Unequal Passband Widths 18.5.2 Adaptive Filter Banks Problems 19: Continuous-Time Stochastic Processes 19.1 Continuous-Time Stochastic Processes 19.1.1 Probability, Random Variables, and Stochastic Processes 19.1.2 Statistical Analysis of Stochastic Processes 19.2 Statistical Properties of Stochastic Processes 19.2.1 First- and Second-Order Properties of Stochastic Processes 19.2.2 Types of Stochastic Processes 19.2.3 Entropy of Stochastic Processes and White Noise 19.3 Stationary and Ergodic Stochastic Processes 19.3.1 Stationary Stochastic Processes in Time and Frequency Domains 19.3.1.1 Time Domain Analysis 19.3.1.2 Frequency Domain Analysis 19.3.2 Ergodic Stochastic Processes 19.3.3 Characterization of White Noise Processes 19.3.4 Gaussian Correlated Processes 19.4 Linear-Time Invariant Systems with StationaryStochastic Inputs 19.4.1 Analysis of Linear-Time Invariant Systems in Time and Frequency Domains 19.4.2 Definition of a System Correlation Function for Stochastic Input 19.4.3 Application of the Theory of Linear-Time-Invariant Systems to the Analysis of the Operation of a Lowpass Filter 19.4.4 Analysis of the Operation of a Bandpass Filter Problems Bibliography Index
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