Table Of ContentC.H.EacicaKOB
PaflHOTexHmecKne uerni
h cnrHajibi
«Bbicmaa niKOJia» MocKBa
Signals
Circuits
and
S.I.Baskakov
Translated from the Russian
by
Boris V. Kuznetsov
Mir Publishers Moscow
First published 1986
Revised from the 1983 Russian edition
TO THE READER
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Mir Publishers
Ha amAuucKOM H3UK.e
tainted in the Union of Soviet Socialist Republics
8ff3flaTejibCTB0 «Bbicmast niKOJia», 1983
English translation, Mir Publishers, 1986
Contents
Preface 9
Introduction 12
Part One. Signals 15
Chapter 1 Elements of the General Theory of Signals 15
1.1 Classification of Signals 15
1.2 Dynamic Representation of Signals 20
1.3 Geometric Methods in Signal Theory 25
1.4 The Theory of Orthogonal Signals 30
Summary 38
Review Questions 39
Problems 40
Advanced Problems 41
Chapter 2 Spectral Representations of Signals 42
2.1 Periodic Signals and Fourier Series 42
2.2 Spectral Analysis of Nonperiodic Signals.
The Fourier Transform 49
2.3 Basic Properties of the Fourier Transform 57
2.4 Spectra of Nonintegrable Signals 62
2.5 The Laplace Transform 67
2.6 Basic Properties of the Laplace Transform 71
Summary 74
Review Questions 75
Problems 75
Advanced Problems 77
Chapter 3 Power Spectra of Signals. Principleso f Correla
tion Analysis 78
3.1 Cross-Spectral Density. Power Spectrum 78
3.2 Correlation Analysis of Signals 84
3.3 The Autocorrelation Function of Discrete Signals 91
3.4 The Cross-Correlation Function of Two Signals 96
Summary 100
Review Questions 100
Problems 101
Advanced Problems 102
Chapter 4 Modulated Signals 103
4.1 Amplitude-Modulated Signals 103
4.2 Angle Modulation 112
4.3 Pulsed FM Signals 122
Summary 129
Review Questions 129
6 Contents
Problems 130
Advanced Problems 131
Chapter 5 Band-Limited Signals 133
5.1 Some Mathematical Models and Properties of
Band-Limited Signals 133
5.2 The Kotelnikov Theorem 137
5.3 Narrowband Signals 143
5.4 The Analytic Signal and the Hilbert Transform 149
Summary 158
Review Questions 159
Problems 160
Advanced Problems 161
Chapter 6 An Outline of the Theory of Random Signals 162
6.1 Random Variables and Their Characteristics 162
6.2 Statistical Characteristics of Two and More Ran
dom Variables 170
6.3 Random Processes 177
Summary 185
Review Questions 186
Problems 187
Advanced Problems 187
Chapter 7 The Correlation Theoryo f Random Processes 189
7.1 The Spectral Representation of Stationary Random
Processes 189
7.2 Differentiation and Integration of Random Pro
cesses 196
7.3 Narrowband Random Processes 203
Summary 215
Review Questions 216
Problems 217
Advanced Problems 218
Part Two. Circuits 219
Chapter 8 Response of Linear Stationary Systems to De
terministic Signals 219
8.1 Physical Systems and Their Mathematical Models 219
8.2 The Impulse, Step and Frequency Responses of
Linear Stationary Systems 222
8.3 Linear Dynamic Systems 230
8.4 Spectral (Frequency-Domain) Analysis 239
8.5 The Operational Method 248
Summary 255
Contents
Review Questions 256
Problems 256
Advanced Problems 258
Chapter 9 Response of Frequency-Selective Systems to De
terministic Signals 259
9.1 Models of Frequency-Selective Circuits 259
9.2 Response of Frequency-Selective Circuits to Broad
band Excitations 268
9.3 Response of Frequency-Selective Circuits to Nar
rowband Excitations 274
Summary 286
Review Questions 287
Problems 288
Advanced Problems 289
Chapter 10 Response of Linear Stationary Networks to
Random Signals 290
10.1 Spectral Analysis of the Response of Linear
Stationary Circuits to Random Signals 290
10.2 Sources of Fluctuation Noise in Circuit Com
ponents 300
Summary 309
Review Questions 310
Problems 310
Advanced Problems 311
Chapter 11 Signal Transformations in Nonlinear Circuits 313
11.1 Lag-Free (Zero-Memory) Nonlinear Transforma
tions 313
11.2 The Spectral Composition of the Current in a
Zero-Memory Nonlinear Element Driven by a
Harmonic Excitation 318
11.3 Nonlinear Tuned Amplifiers and Frequency Mul
tipliers 323
11.4 Lag-Free (Zero-Memory) Nonlinear Transforma
tions of a Sum of Harmonic Signals 326
11.5 Amplitude Modulation. Detection of AM Signals 330
11.6 Response of Lag-Free (Zero-Memory) Nonlinear
Circuits to Stationary Random Signals 337
Summary 342
Review Questions 343
Problems 343
Advanced Problems 344
Contents
Chapter 12 Signal Transformations in Linear Parametric
Circuits 345
12.1 Response of Resistive Parametric Circuits 345
12.2 Energy and Power Relations in Reactive Para
metric Elements 352
12.3 Principles of Parametric Amplification 358
12.4 Nonstationary Dynamic Systems 366
12.5 Response of Parametric Systems with Random
Characteristics to Harmonic Signals 372
Summary 376
Review Questions 377
Problems 378
Advanced Problems 378
Chapter 13 A Basic Theory of Linear Circuit Synthesis 380
13.1 Analytical Properties of the Driving-Point Impe
dance of a Passive Linear One-Port 380
13.2 Synthesis of Passive One-Ports 385
13.3 Frequency Characteristics of Two-Ports 391
13.4 Low-Pass Filters 395
13.5 Implementation of Filters 401
Summary 406
Review Questions 407
Problems 407
Advanced Problems 408
Chapter 14 Active Networks withF eedback.S elf-Excited
Oscillatory Systems 409
14.1 The Transfer Function of a Linear Feedback
System 409
14.2 Stability of Feedback Networks 415
14.3 Active RC Filters 420
14.4 Self-Excited Harmonic Oscillators. The Small-
Signal Condition 426
14.5 Self-Excited Harmonic Oscillators. The Large-
Signal Condition 435
Summary 443
Review Questions 444
Problems 445
Advanced Problems 447
Chapter 15 Discrete Signals. Principles of Digital Filtering 448
15.1 Discrete Pulse Sequences 448
15.2 Digitization of Periodic Signals 453
15.3 The Theory of the z-Transform 458
15.4 Digital Filters 462
Contents
15.5 Implementation of Digital Filtering Algorithms 468
15.6 Synthesis of Linear Digital Filters 411
Summary 434
Review Questions 484
Problems 455
Advanced Problems 486
Chapter 16 Optimum Linear Signal Filtering 487
16.1 Optimum Linear Filtering of Known Signals 487
16.2 Implementation of Matched Filters 493
16.3 Optimum Filtering of Random Signals 501
Summary 5P4
Review Questions 504
Problems 505
Advanced Problems 505
Appendices jpg
Bibliography 510
Index 512
Preface
The present book is a course on signals and circuits as it is
taught in the USSR. This subject figures prominently among the
fundamental disciplines essential to the expertise of communication
engineers. Keeping pace with overall progress in science and
technology and reflecting the current trends in component design
and theory, this course combines and sets forth in a systematic way
the most important principles in the field of communications.
In his work on the text, the author has been guided by the idea
that material should be specifically tailored to the teaching practice
at college. This approach has governed the selection of material and
the degree of detail in its presentation: its pages contain what, as
the author believes, the student can fully assimilate during the time
allotted. Specific circuit types, their study and comparative
analysis-all this belongs to the specialized subjects in
communication engineering.
This text includes a wide variety of material and a wealth of
concepts and techniques which will come the student’s way for the
first time. Ample space is devoted to mathematical tools of study.
To link theory closer to practice, the chapters contain a great
number of examples and problems giving the student deeper
insight into the techniques of engineering analysis.
Subject-matter and structure. The book is in two parts. Part One,
Signals, introduces the reader to the methods currently used to
describe and study the properties of signals. Among other things, it
covers the classification of signals, the fundamental principle of the
geometric treatment of the signal space, the spectral and correlation
analysis of deterministic signals, the theory of modulated signals,
and the discrete presentation of band-limited continuous signals.
The methods used to analyse and measure the characteristics of
random signals are discussed in detail.
Part Two, Circuits, gives a systematic exposition of the principles
underlying the analysis and determination of the response of linear
and nonlinear circuits to both deterministic and random signals.
Special emphasis is placed on the role of narrowband frequency-
selective networks. Techniques are discussed that are used to
synthesize linear two-terminal (one-port) and four-terminal
(two-port) networks having a predetermined frequency response,
and consideration is given to the passage of signals through linear
parametric circuits. In the pages devoted to nonlinear lag-free
(zero-memory) circuits, the reader will learn about the most
important forms of signal transformations, such as modulation,
detection, multiplication, and frequency conversion. Material is
included on the theory of harmonic self-excited oscillators and the
more recent trends that have come into being only recently in the
wake of advances in microelectronics. These include active filters
for analog signals and, as a most promising technique, digital signal
