Yarlagadda Analog and Digital Signals and Systems

1. Auflage 2010
ISBN: 978-1-4419-0034-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 555 Seiten

This book presents a systematic, comprehensive treatment of analog, discrete signal analysis and synthesis and an introduction to analog communication theory. The material is divided into five parts. The first part (Chapters 1-3) is mathematically oriented and deals with continuous-time (analog) signals. The second part (Chapters 4-5) is again mathematically based and deals with Fourier transforms, Hartley transforms, Laplace and Hilbert transforms. The third part (Chapters 6-7) presents basic system analysis, approximations, and analog filter circuits using op-amps. The fourth part (Chapters 8-9) deals with discrete signals, fast algorithms and digital filters. The fifth part deals with an introduction to analog communication systems.

Autoren/Hrsg.

Yarlagadda, R. K. Rao

Inhaltsverzeichnis

1;Analog and Digital Signals and Systems;1
1.1;Note to Instructors;5
1.2;Preface;6
1.2.1;Summary of the Chapters;6
1.2.2;Suggested Course Content;7
1.3;Acknowledgements;9
1.4;Contents;10
1.5;List of Tables;22
2;Basic Concepts in Signals;24
2.1;1.1 Introduction to the Book and Signals;24
2.1.1;1.1.1 Different Ways of Looking at a Signal;24
2.1.2;1.1.2 Continuous-Time and Discrete-Time Signals;26
2.1.3;1.1.3 Analog Versus Digital Signal Processing;28
2.1.4;1.1.4 Examples of Simple Functions;29
2.2;1.2 Useful Signal Operations;31
2.2.1;1.2.1 Time Shifting;31
2.2.2;1.2.2 Time Scaling;31
2.2.3;1.2.3 Time Reversal;31
2.2.4;1.2.4 Amplitude Shift;31
2.2.5;1.2.5 Simple Symmetries: Even and Odd Functions;32
2.2.6;1.2.6 Products of Even and Odd Functions;32
2.2.7;1.2.7 Signum (or sgn) Function;33
2.2.8;1.2.8 Sinc and Sinc2 Functions;33
2.2.9;1.2.9 Sine Integral Function;33
2.3;1.3 Derivatives and Integrals of Functions;34
2.3.1;1.3.1 Integrals of Functions with Symmetries;35
2.3.2;1.3.2 Useful Functions from Unit Step Function;35
2.3.3;1.3.3 Leibniz’s Rule;36
2.3.4;1.3.4 Interchange of a Derivative and an Integral;36
2.3.5;1.3.5 Interchange of Integrals;36
2.4;1.4 Singularity Functions;37
2.4.1;1.4.1 Unit Impulse as the Limit of a Sequence;38
2.4.2;1.4.2 Step Function and the Impulse Function;39
2.4.3;1.4.3 Functions of Generalized Functions;40
2.4.4;1.4.4 Functions of Impulse Functions;41
2.4.5;1.4.5 Functions of Step Functions;42
2.5;1.5 Signal Classification Based on Integrals;42
2.5.1;1.5.1 Effects of Operations on Signals;44
2.5.2;1.5.2 Periodic Functions;44
2.5.3;1.5.3 Sum of Two Periodic Functions;46
2.6;1.6 Complex Numbers, Periodic, and Symmetric Periodic Functions;47
2.6.1;1.6.1 Complex Numbers;48
2.6.2;1.6.2 Complex Periodic Functions;50
2.6.3;1.6.3 Functions of Periodic Functions;50
2.6.4;1.6.4 Periodic Functions with Additional Symmetries;51
2.7;1.7 Examples of Probability Density Functions and their Moments;52
2.8;1.8 Generation of Periodic Functions from Aperiodic Functions;54
2.9;1.9 Decibel;55
2.10;1.10 Summary;57
2.11;Problems;58
3;Convolution and Correlation;61
3.1;2.1 Introduction;61
3.1.1;2.1.1 Scalar Product and Norm;62
3.2;2.2 Convolution;63
3.2.1;2.2.1 Properties of the Convolution Integral;63
3.2.2;2.2.2 Existence of the Convolution Integral;66
3.3;2.3 Interesting Examples;66
3.4;2.4 Convolution and Moments;72
3.4.1;2.4.1 Repeated Convolution and the Central Limit Theorem;74
3.4.2;2.4.2 Deconvolution;75
3.5;2.5 Convolution Involving Periodic and Aperiodic Functions;76
3.5.1;2.5.1 Convolution of a Periodic Function with an Aperiodic Function;76
3.5.2;2.5.2 Convolution of Two Periodic Functions;77
3.6;2.6 Correlation;78
3.6.1;2.6.1 Basic Properties of Cross-Correlation Functions;79
3.6.2;2.6.2 Cross-Correlation and Convolution;79
3.6.3;2.6.3 Bounds on the Cross-Correlation Functions;80
3.6.4;2.6.4 Quantitative Measures of Cross-Correlation;81
3.7;2.7 Autocorrelation Functions of Energy Signals;85
3.8;2.8 Cross- and Autocorrelation of Periodic Functions;87
3.9;2.9 Summary;90
3.10;Problems;90
4;Fourier Series;92
4.1;3.1 Introduction;92
4.2;3.2 Orthogonal Basis Functions;93
4.2.1;3.2.1 Gram-Schmidt Orthogonalization;95
4.3;3.3 Approximation Measures;96
4.3.1;3.3.1 Computation of c[k] Based on Partials;98
4.3.2;3.3.2 Computation of c[k] Using the Method of Perfect Squares;98
4.3.3;3.3.3 Parseval’s Theorem;99
4.4;3.4 Fourier Series;101
4.4.1;3.4.1 Complex Fourier Series;101
4.4.2;3.4.2 Trigonometric Fourier Series;104
4.4.3;3.4.3 Complex F-series and the Trigonometric F-series Coefficients-Relations;104
4.4.4;3.4.4 Harmonic Form of Trigonometric Fourier Series;104
4.4.5;3.4.5 Parseval’s Theorem Revisited;105
4.4.6;3.4.6 Advantages and Disadvantages of the Three Forms of Fourier Series;106
4.5;3.5 Fourier Series of Functions with Simple Symmetries;106
4.5.1;3.5.1 Simplification of the Fourier Series Coefficient Integral;107
4.6;3.6 Operational Properties of Fourier Series;108
4.6.1;3.6.1 Principle of Superposition;108
4.6.2;3.6.2 Time Shift;108
4.6.3;3.6.3 Time and Frequency Scaling;109
4.6.4;3.6.4 Fourier Series Using Derivatives;110
4.6.5;3.6.5 Bounds and Rates of Fourier Series Convergence by the Derivative Method;112
4.6.6;3.6.6 Integral of a Function and Its Fourier Series;114
4.6.7;3.6.7 Modulation in Time;114
4.6.8;3.6.8 Multiplication in Time;115
4.6.9;3.6.9 Frequency Modulation;116
4.6.10;3.6.10 Central Ordinate Theorems;116
4.6.11;3.6.11 Plancherel’s Relation (or Theorem);116
4.6.12;3.6.12 Power Spectral Analysis;116
4.7;3.7 Convergence of the Fourier Series and the Gibbs Phenomenon;117
4.7.1;3.7.1 Fourier’s Theorem;117
4.7.2;3.7.2 Gibbs Phenomenon;118
4.7.3;3.7.3 Spectral Window Smoothing;120
4.8;3.8 Fourier Series Expansion of Periodic Functions with Special Symmetries;121
4.8.1;3.8.1 Half-Wave Symmetry;121
4.8.2;3.8.2 Quarter-Wave Symmetry;123
4.8.3;3.8.3 Even Quarter-Wave Symmetry;123
4.8.4;3.8.4 Odd Quarter-Wave Symmetry;123
4.8.5;3.8.5 Hidden Symmetry;124
4.9;3.9 Half-Range Series Expansions;124
4.10;3.10 Fourier Series Tables;125
4.11;3.11 Summary;125
4.12;Problems;127
5;Fourier Transform Analysis;130
5.1;4.1 Introduction;130
5.2;4.2 Fourier Series to Fourier Integral;130
5.2.1;4.2.1 Amplitude and Phase Spectra;133
5.2.2;4.2.2 Bandwidth-Simplistic Ideas;135
5.3;4.3 Fourier Transform Theorems, Part 1;135
5.3.1;4.3.1 Rayleigh’s Energy Theorem;135
5.3.2;4.3.2 Superposition Theorem;136
5.3.3;4.3.3 Time Delay Theorem;137
5.3.4;4.3.4 Scale Change Theorem;137
5.3.5;4.3.5 Symmetry or Duality Theorem;139
5.3.6;4.3.6 Fourier Central Ordinate Theorems;140
5.4;4.4 Fourier Transform Theorems, Part 2;140
5.4.1;4.4.1 Frequency Translation Theorem;141
5.4.2;4.4.2 Modulation Theorem;141
5.4.3;4.4.3 Fourier Transforms of Periodic and Some Special Functions;142
5.4.4;4.4.4 Time Differentiation Theorem;145
5.4.5;4.4.5 Times-t Property: Frequency Differentiation Theorem;147
5.4.6;4.4.6 Initial Value Theorem;149
5.4.7;4.4.7 Integration Theorem;149
5.5;4.5 Convolution and Correlation;150
5.5.1;4.5.1 Convolution in Time;150
5.5.2;4.5.2 Proof of the Integration Theorem;153
5.5.3;4.5.3 Multiplication Theorem (Convolution in Frequency);154
5.5.4;4.5.4 Energy Spectral Density;156
5.6;4.6 Autocorrelation and Cross-Correlation;157
5.6.1;4.6.1 Power Spectral Density;159
5.7;4.7 Bandwidth of a Signal;160
5.7.1;4.7.1 Measures Based on Areas of the Time and Frequency Functions;160
5.7.2;4.7.2 Measures Based on Moments;161
5.7.3;4.7.3 Uncertainty Principle in Fourier Analysis;162
5.8;4.8 Moments and the Fourier Transform;164
5.9;4.9 Bounds on the Fourier Transform;165
5.10;4.10 Poisson’s Summation Formula;166
5.11;4.11 Interesting Examples and a Short Fourier Transform Table;166
5.11.1;4.11.1 Raised-Cosine Pulse Function;167
5.12;4.12 Tables of Fourier Transforms Properties and Pairs;168
5.13;4.13 Summary;168
5.14;Problems;168
6;Relatives of Fourier Transforms;175
6.1;5.1 Introduction;175
6.2;5.2 Fourier Cosine and Sine Transforms;176
6.3;5.3 Hartley Transform;179
6.4;5.4 Laplace Transforms;181
6.4.1;5.4.1 Region of Convergence (ROC);183
6.4.2;5.4.2 Inverse Transform of Two-Sided Laplace Transform;184
6.4.3;5.4.3 Region of Convergence (ROC) of Rational Functions - Properties;185
6.5;5.5 Basic Two-Sided Laplace Transform Theorems;185
6.5.1;5.5.1 Linearity;185
6.5.2;5.5.2 Time Shift;185
6.5.3;5.5.3 Shift in s;185
6.5.4;5.5.4 Time Scaling;185
6.5.5;5.5.5 Time Reversal;186
6.5.6;5.5.6 Differentiation in Time;186
6.5.7;5.5.7 Integration;186
6.5.8;5.5.8 Convolution;186
6.6;5.6 One-Sided Laplace Transform;186
6.6.1;5.6.1 Properties of the One-Sided Laplace Transform;187
6.6.2;5.6.2 Comments on the Properties (or Theorems) of Laplace Transforms;187
6.7;5.7 Rational Transform Functions and Inverse Laplace Transforms;194
6.7.1;5.7.1 Rational Functions, Poles, and Zeros;195
6.7.2;5.7.2 Return to the Initial and Final Value Theorems and Their Use;196
6.8;5.8 Solutions of Constant Coefficient Differential Equations Using Laplace Transforms;198
6.8.1;5.8.1 Inverse Laplace Transforms;199
6.8.2;5.8.2 Partial Fraction Expansions;199
6.9;5.9 Relationship Between Laplace Transforms and Other Transforms;203
6.9.1;5.9.1 Laplace Transforms and Fourier Transforms;204
6.9.2;5.9.2 Hartley Transforms and Laplace Transforms;205
6.10;5.10 Hilbert Transform;206
6.10.1;5.10.1 Basic Definitions;206
6.10.2;5.10.2 Hilbert Transform of Signals with Non-overlapping Spectra;208
6.10.3;5.10.3 Analytic Signals;209
6.11;5.11 Summary;210
6.12;Problems;210
7;Systems and Circuits;213
7.1;6.1 Introduction;213
7.2;6.2 Linear Systems, an Introduction;213
7.3;6.3 Ideal Two-Terminal Circuit Components and Kirchhoff ’s Laws;214
7.3.1;6.3.1 Two-Terminal Component Equations;215
7.3.2;6.3.2 Kirchhoff’s Laws;217
7.4;6.4 Time-Invariant and Time-Varying Systems;218
7.5;6.5 Impulse Response;219
7.5.1;6.5.1 Eigenfunctions;222
7.5.2;6.5.2 Bounded-Input/Bounded-Output (BIBO) Stability;222
7.5.3;6.5.3 Routh-Hurwitz Criterion (R-H criterion);223
7.5.4;6.5.4 Eigenfunctions in the Fourier Domain;226
7.6;6.6 Step Response;228
7.7;6.7 Distortionless Transmission;233
7.7.1;6.7.1 Group Delay and Phase Delay;233
7.8;6.8 System Bandwidth Measures;236
7.8.1;6.8.1 Bandwidth Measures Using the Impulse Response $ \curr h({\rm t})$ and Its Transform $\curr{ H({\rm j}\omega )}$;236
7.8.2;6.8.2 Half-Power or 3 dB Bandwidth;237
7.8.3;6.8.3 Equivalent Bandwidth or Noise Bandwidth;237
7.8.4;6.8.4 Root Mean-Squared (RMS) Bandwidth;238
7.9;6.9 Nonlinear Systems;239
7.9.1;6.9.1 Distortion Measures;240
7.9.2;6.9.2 Output Fourier Transform of a Nonlinear System;240
7.9.3;6.9.3 Linearization of Nonlinear System Functions;241
7.10;6.10 Ideal Filters;241
7.10.1;6.10.1 Low-Pass, High-Pass, Band-Pass, and Band-Elimination Filters;242
7.11;6.11 Real and Imaginary Parts of the Fourier Transform of a Causal Function;247
7.11.1;6.11.1 Relationship Between Real and Imaginary Parts of the Fourier Transform of a Causal Function Using Hilbert Transform;248
7.11.2;6.11.2 Amplitude Spectrum |H(jw)| to a Minimum Phase Function H(s);249
7.12;6.12 More on Filters: Source and Load Impedances;249
7.12.1;6.12.1 Simple Low-Pass Filters;251
7.12.2;6.12.2 Simple High-Pass Filters;251
7.12.3;6.12.3 Simple Band-Pass Filters;253
7.12.4;6.12.4 Simple Band-Elimination or Band-Reject or Notch Filters;255
7.12.5;6.12.5 Maximum Power Transfer;258
7.12.6;6.12.6 A Simple Delay Line Circuit;259
7.13;6.13 Summary;259
7.14;Problems;260
8;Approximations and Filter Circuits;263
8.1;7.1 Introduction;263
8.2;7.2 Bode Plots;266
8.2.1;7.2.1 Gain and Phase Margins;272
8.3;7.3 Classical Analog Filter Functions;274
8.3.1;7.3.1 Amplitude-Based Design;274
8.3.2;7.3.2 Butterworth Approximations;275
8.3.3;7.3.3 Chebyshev (Tschebyscheff) Approximations;277
8.4;7.4 Phase-Based Design;282
8.4.1;7.4.1 Maximally Flat Delay Approximation;283
8.4.2;7.4.2 Group Delay of Bessel Functions;284
8.5;7.5 Frequency Transformations;286
8.5.1;7.5.1 Normalized Low-Pass to High-Pass Transformation;286
8.5.2;7.5.2 Normalized Low-Pass to Band-Pass Transformation;288
8.5.3;7.5.3 Normalized Low-Pass to Band-Elimination Transformation;288
8.5.4;7.5.4 Conversions of Specifications from Low-Pass, High-Pass, Band-Pass, and Band Elimination Filters to Normalized Low-Pass Filters;290
8.6;7.6 Multi-terminal Components;293
8.6.1;7.6.1 Two-Port Parameters;293
8.6.2;7.6.2 Circuit Analysis Involving Multi-terminal Components and Networks;297
8.6.3;7.6.3 Controlled Sources;298
8.7;7.7 Active Filter Circuits;299
8.7.1;7.7.1 Operational Amplifiers, an Introduction;299
8.7.2;7.7.2 Inverting Operational Amplifier Circuits;300
8.7.3;7.7.3 Non-inverting Operational Amplifier Circuits;302
8.7.4;7.7.4 Simple Second-Order Low-Pass and All-Pass Circuits;304
8.8;7.8 Gain Constant Adjustment;305
8.9;7.9 Scaling;307
8.9.1;7.9.1 Amplitude (or Magnitude) Scaling, RLC Circuits;307
8.9.2;7.9.2 Frequency Scaling, RLC Circuits;308
8.9.3;7.9.3 Amplitude and Frequency Scaling in Active Filters;308
8.9.4;7.9.4 Delay Scaling;310
8.10;7.10 RC-CR Transformations: Low-Pass to High-Pass Circuits;312
8.11;7.11 Band-Pass, Band-Elimination and Biquad Filters;314
8.12;7.12 Sensitivities;318
8.13;7.13 Summary;321
8.14;Problems;321
9;Discrete-Time Signals and Their Fourier Transforms;330
9.1;8.1 Introduction;330
9.2;8.2 Sampling of a Signal;331
9.2.1;8.2.1 Ideal Sampling;331
9.2.2;8.2.2 Uniform Low-Pass Sampling or the Nyquist Low-Pass Sampling Theorem;333
9.2.3;8.2.3 Interpolation Formula and the Generalized Fourier Series;336
9.2.4;8.2.4 Problems Associated with Sampling Below the Nyquist Rate;338
9.2.5;8.2.5 Flat Top Sampling;341
9.2.6;8.2.6 Uniform Band-Pass Sampling Theorem;343
9.2.7;8.2.7 Equivalent continuous-time and discrete-time systems;344
9.3;8.3 Basic Discrete-Time (DT) Signals;344
9.3.1;8.3.1 Operations on a Discrete Signal;346
9.3.2;8.3.2 Discrete-Time Convolution and Correlation;348
9.3.3;8.3.3 Finite duration, right-sided, left-sided, two-sided, and causal sequences;349
9.3.4;8.3.4 Discrete-Time Energy and Power Signals;349
9.4;8.4 Discrete-Time Fourier Series;351
9.4.1;8.4.1 Periodic Convolution of Two Sequences with the Same Period;353
9.4.2;8.4.2 Parseval’s Identity;353
9.5;8.5 Discrete-Time Fourier Transforms;354
9.5.1;8.5.1 Discrete-Time Fourier Transforms (DTFTs);354
9.5.2;8.5.2 Discrete-Time Fourier Transforms of Real Signals with Symmetries;355
9.6;8.6 Properties of the Discrete-Time Fourier Transforms;358
9.6.1;8.6.1 Periodic Nature of the Discrete-Time Fourier Transform;358
9.6.2;8.6.2 Superposition or Linearity;359
9.6.3;8.6.3 Time Shift or Delay;360
9.6.4;8.6.4 Modulation or Frequency Shifting;360
9.6.5;8.6.5 Time Scaling;360
9.6.6;8.6.6 Differentiation in Frequency;361
9.6.7;8.6.7 Differencing;361
9.6.8;8.6.8 Summation or Accumulation;363
9.6.9;8.6.9 Convolution;363
9.6.10;8.6.10 Multiplication in Time;364
9.6.11;8.6.11 Parseval’s Identities;365
9.6.12;8.6.12 Central Ordinate Theorems;365
9.6.13;8.6.13 Simple Digital Encryption;365
9.7;8.7 Tables of Discrete-Time Fourier Transform (DTFT) Properties and Pairs;366
9.8;8.8 Discrete-Time Fourier-transforms from Samples of the Continuous-Time Fourier-Transforms;367
9.9;8.9 Discrete Fourier Transforms (DFTs);369
9.9.1;8.9.1 Matrix Representations of the DFT and the IDFT;371
9.9.2;8.9.2 Requirements for Direct Computation of the DFT;372
9.10;8.10 Discrete Fourier Transform Properties;373
9.10.1;8.10.1 DFTs and IDFTs of Real Sequences;373
9.10.2;8.10.2 Linearity;373
9.10.3;8.10.3 Duality;374
9.10.4;8.10.4 Time Shift;374
9.10.5;8.10.5 Frequency Shift;375
9.10.6;8.10.6 Even Sequences;375
9.10.7;8.10.7 Odd Sequences;375
9.10.8;8.10.8 Discrete-Time Convolution Theorem;376
9.10.9;8.10.9 Discrete-Frequency Convolution Theorem;377
9.10.10;8.10.10 Discrete-Time Correlation Theorem;378
9.10.11;8.10.11 Parseval’s Identity or Theorem;378
9.10.12;8.10.12 Zero Padding;378
9.10.13;8.10.13 Signal Interpolation;379
9.10.14;8.10.14 Decimation;381
9.11;8.11 Summary;381
9.12;Problems;381
10;Discrete Data Systems;385
10.1;9.1 Introduction;385
10.2;9.2 Computation of Discrete Fourier Transforms (DFTs);386
10.2.1;9.2.1 Symbolic Diagrams in Discrete-Time Representations;386
10.2.2;9.2.2 Fast Fourier Transforms (FFTs);387
10.3;9.3 DFT (FFT) Applications;390
10.3.1;9.3.1 Hidden Periodicity in a Signal;390
10.3.2;9.3.2 Convolution of Time-Limited Sequences;392
10.3.3;9.3.3 Correlation of Discrete Signals;395
10.3.4;9.3.4 Discrete Deconvolution;396
10.4;9.4 z-Transforms;398
10.4.1;9.4.1 Region of Convergence (ROC);399
10.4.2;9.4.2 z-Transform and the Discrete-Time Fourier Transform (DTFT);402
10.5;9.5 Properties of the z-Transform;402
10.5.1;9.5.1 Linearity;402
10.5.2;9.5.2 Time-Shifted Sequences;403
10.5.3;9.5.3 Time Reversal;403
10.5.4;9.5.4 Multiplication by an Exponential;403
10.5.5;9.5.5 Multiplication by n;404
10.5.6;9.5.6 Difference and Accumulation;404
10.5.7;9.5.7 Convolution Theorem and the z-Transform;404
10.5.8;9.5.8 Correlation Theorem and the z-Transform;405
10.5.9;9.5.9 Initial Value Theorem in the Discrete Domain;406
10.5.10;9.5.10 Final Value Theorem in the Discrete Domain;406
10.6;9.6 Tables of z-Transform Properties and Pairs;407
10.7;9.7 Inverse z-Transforms;408
10.7.1;9.7.1 Inversion Formula;408
10.7.2;9.7.2 Use of Transform Tables (Partial Fraction Expansion Method);409
10.7.3;9.7.3 Inverse z-Transforms by Power Series Expansion;412
10.8;9.8 The Unilateral or the One-Sided z-Transform;413
10.8.1;9.8.1 Time-Shifting Property;413
10.9;9.9 Discrete-Data Systems;415
10.9.1;9.9.1 Discrete-Time Transfer Functions;418
10.9.2;9.9.2 Schur-Cohn Stability Test;419
10.9.3;9.9.3 Bilinear Transformations;419
10.10;9.10 Designs by the Time and Frequency Domain Criteria;421
10.10.1;9.10.1 Impulse Invariance Method by Using the Time Domain Criterion;423
10.10.2;9.10.2 Bilinear Transformation Method by Using the Frequency Domain Criterion;425
10.11;9.11 Finite Impulse Response (FIR) Filter Design;428
10.11.1;9.11.1 Low-Pass FIR Filter Design;429
10.11.2;9.11.2 High-Pass, Band-Pass, and Band-Elimination FIR Filter Designs;431
10.11.3;9.11.3 Windows in Fourier Design;434
10.12;9.12 Digital Filter Realizations;437
10.12.1;9.12.1 Cascade Form of Realization;440
10.12.2;9.12.2 Parallel Form of Realization;440
10.12.3;9.12.3 All-Pass Filter Realization;441
10.12.4;9.12.4 Digital Filter Transposed Structures;441
10.12.5;9.12.5 FIR Filter Realizations;441
10.13;9.13 Summary;442
10.14;Problems;443
11;Analog Modulation;446
11.1;10.1 Introduction;446
11.2;10.2 Limiters and Mixers;448
11.2.1;10.2.1 Mixers;449
11.3;10.3 Linear Modulation;449
11.3.1;10.3.1 Double-Sideband (DSB) Modulation;449
11.3.2;10.3.2 Demodulation of DSB Signals;450
11.4;10.4 Frequency Multipliers and Dividers;452
11.5;10.5 Amplitude Modulation (AM);454
11.5.1;10.5.1 Percentage Modulation;455
11.5.2;10.5.2 Bandwidth Requirements;455
11.5.3;10.5.3 Power and Efficiency of an Amplitude Modulated Signal;456
11.5.4;10.5.4 Average Power Contained in an AM Signal;457
11.6;10.6 Generation of AM Signals;458
11.6.1;10.6.1 Square-Law Modulators;458
11.6.2;10.6.2 Switching Modulators;458
11.6.3;10.6.3 Balanced Modulators;459
11.7;10.7 Demodulation of AM Signals;460
11.7.1;10.7.1 Rectifier Detector;460
11.7.2;10.7.2 Coherent or a Synchronous Detector;460
11.7.3;10.7.3 Square-Law Detector;461
11.7.4;10.7.4 Envelope Detector;461
11.8;10.8 Asymmetric Sideband Signals;463
11.8.1;10.8.1 Single-Sideband Signals;463
11.8.2;10.8.2 Vestigial Sideband Modulated Signals;464
11.8.3;10.8.3 Demodulation of SSB and VSB Signals;465
11.8.4;10.8.4 Non-coherent Demodulation of SSB;466
11.8.5;10.8.5 Phase-Shift Modulators and Demodulators;466
11.9;10.9 Frequency Translation and Mixing;467
11.10;10.10 Superheterodyne AM Receiver;470
11.11;10.11 Angle Modulation;472
11.12;Chap10Sec31;473
11.12.1;10.12.1 Narrowband (NB) Angle Modulation;475
11.12.2;10.12.2 Generation of Angle Modulated Signals;476
11.13;10.12 Spectrum of an Angle Modulated Signal;477
11.13.1;10.12.1 Properties of Bessel Functions;478
11.13.2;10.12.2 Power Content in an Angle Modulated Signal;480
11.14;10.13 Demodulation of Angle Modulated Signals;482
11.14.1;10.13.1 Frequency Discriminators;482
11.14.2;10.13.2 Delay Lines as Differentiators;484
11.15;10.14 FM Receivers;485
11.15.1;10.14.1 Distortions;485
11.15.2;10.14.2 Pre-emphasis and De-emphasis;486
11.15.3;10.14.3 Distortions Caused by Multipath Effect;487
11.16;10.15 Frequency-Division Multiplexing (FDM);488
11.16.1;10.15.1 Quadrature Amplitude Modulation (QAM) or Quadrature Multiplexing (QM);489
11.16.2;10.15.2 FM Stereo Multiplexing and the FM Radio;490
11.17;10.16 Pulse Modulations;491
11.17.1;10.16.1 Pulse Amplitude Modulation (PAM);492
11.17.2;10.16.2 Problems with Pulse Modulations;492
11.17.3;10.16.3 Time-Division Multiplexing (TDM);494
11.18;10.17 Pulse Code Modulation (PCM);495
11.18.1;10.17.1 Quantization Process;495
11.18.2;10.17.2 More on Coding;497
11.18.3;10.17.3 Tradeoffs Between Channel Bandwidth and Signal-to-Quantization Noise Ratio;498
11.18.4;10.17.4 Digital Carrier Modulation;499
11.19;10.18 Summary;501
11.20;Problems;501
12;Appendix A: Matrix Algebra;505
12.1;A1 Matrix Notations;505
12.2;A.2 Elements of Matrix Algebra;506
12.2.1;A.2.1 Vector Norms;507
12.3;A.3 Solutions of Matrix Equations;508
12.3.1;A.3.1 Determinants;508
12.3.2;A.3.2 Cramer’s Rule;509
12.3.3;A.3.3 Rank of a Matrix;510
12.4;A.4 Inverses of Matrices and Their Use in Determining the Solutions of a Set of Equations;511
12.5;A.5 Eigenvalues and Eigenvectors;512
12.6;A.6 Singular Value Decomposition (SVD);516
12.7;A.7 Generalized Inverses of Matrices;517
12.8;A.8 Over- and Underdetermined System of Equations;518
12.8.1;A. 8.1 Least-Squares Solutions of Overdetermined System of Equations (m>n);518
12.8.2;A.8.2 Least-Squares Solution of Underdetermined System of Equations (