Fundamentals of signal theory, ed. 5

---

Title: Fundamentals of Signal Theory, ed. 5
Author: Jerzy Szabatin
ISBN: 978-83-206-1331-5
Publisher: WKL
Format: B5
Number of pages: 500 pages

---

About the book
The book discusses the mathematical foundations of signal theory. Methods of description and analytical representation (discrete and continuous) of deterministic and stochastic signals were presented, with particular emphasis on the latter. Frequency signal analysis is discussed. The issue of signal sampling was discussed in detail.
In addition, the general principles, classification and theoretical basis of different types of modulation as a fundamental operation in the field of signal transmission are discussed.
The book is addressed to the general electronics - especially to students of the relevant majors of higher education. It can be useful for postgraduate and doctoral students.

---

Table of Contents:
Przedmowa / 11
List of markings / 13

1. CHAPTER
The concept of a signal. Mathematical signal models
physical / 19

2. CHAPTER
Sygnały deterministyczne / 24
2.1. Deterministic model of the physical signal / 24
2.2 Parameters of real deterministic signals / 25
2.3 Examples of real deterministic signals / 31
2.3.1 Pulsed signals with limited energy / 31
2.3.2 Signals with infinite duration and limited
energy / 33
2.3.3 Non-periodic signals with limited average power / 35
2.3.4 Periodic signals / 37
2.3.5 Nearly periodic signals / 38
2.3.6 Distribution signals / 39
2.4 Complex signals / 48
2.5 Distribution of deterministic signals into components / 49
2.5.1 Real and imaginary component / 49
2.5.2 Fixed and variable component / 50
2.5.3. Even and odd components / 51
2.6. Determinant signal spaces / 52
2.6.1. Signals as elements of the function space / 52
2.6.2 Metric spaces / 53
2.6.3 Line spaces / 61
2.6.4 Standard linear spaces. spaces
Banacha / 63
2.6.5. Scalar product. Hilbert spaces / 67
2.7 Correlation analysis of deterministic signals / 72
2.7.1 Comparing deterministic signals / 72
2.7.2. Comparison of vectors in the space R ⁿ . Analogy
between vectors
and signals / 73
2.7.3. Signal correlation coefficients
deterministycznych / 77
2.7.4. Correlation functions of deterministic signals / 80
2.8 Splot / 91
2.8.1 Limits of the convolutional integral / 91
2.8.2 Convergence of the convolutional integral / 94
2.8.3 Properties of the weave / 94

3. CHAPTER
Analytical representation of signals
deterministycznych / 96
3.1 General remarks / 96
3.2. Discrete representations of deterministic signals / 97
3.2.1. Approximation of deterministic signals / 97
3.2.2 N-dimensional linear spaces. Space database / 98
3.2.3. Determination of signal representation in n-dimensional
unitary space. Bazy ortonormalne / l00
3.2.4 Determining the representation of the signal infinitely
dimensional unitary space. The problem of the best
aproksymacji / 102
3.2.5 Fourier series. Równia Parsevala / 108
3.2.6 Normalization of the orthogonal basis / 112
3.2.7 Examples of orthonormal sets complete / 113
3.3 Constant representations of deterministic signals / 131
3.3.1 The general concept. Integral transformations / 131
3.3.2 Fourier Transformation / 134
3.3.3 Hilbert transform. Analytical signal / 135
3.3.4 Hankel transformation. Kosinus and sine
Fourier transform / 138
3.3.5 Transformation of Mellin. Laplace transform / 140

4. CHAPTER
Stochastic signals / 142
4.1. Basic probabilistic concepts. Notation / 142
4.2 The concept of the stochastic process / 160
4.3 Classification of stochastic signals / 162
4.4. Description of stochastic signals / 165
4.4.1 The general concept describes / 165
4.4.2 Total n-dimensional density function
probabilities / 166
4.4.3 Average value. Autocorrelation function / 168
4.4.4 Two stochastic signals. Correlation functions
wzajemnej / 171
4.5 Differentiation and integration stochastyczne / 173
4.6. Stationary signals / 175
4.6.1. Stationary signals and stationary signals
on the n / 175 line
4.6.2 Stationary signals in a broader sense / 177
4.6.3 Physical interpretation of signal parameters
stacjonarnego / 179
4.6.4 Total Stationary Signals / 179
4.7. Signals ergodyczne / 181
4.8 Stochastic composite signals / 187
4.9 Normal signals / 190
4.10 Examples of stochastic signals / 196
4.10.1. Continuous signals with continuous time / 196
4.10.2 Discrete signals with continuous time / 206

4.10.2.1 Asynchronous signals / 206
4.10.2.2 Synchronous signals / 217

5. CHAPTER
Analytical representation of signals
stochastycznych / 224
5.1 General remarks / 224
5.2. Discrete representations of stochastic signals / 225
5.2.1 A complex Fourier series of periodic signal in the sense
średniokwadratowym / 225.
5.2.2. Complex Fourier series of non-period signal / 228
5.2.3 Developing Karhunen-Loève / 231
5.2.4 Szereg Kotielnikowa-Shannona / 241
5.3 Continuous representations of stochastic signals / 241
5.3.1. General concept / 241
5.3.2 Stochastic Fourier / 242 transformation
5.3.3 Stochastic Hilbert transformation. stochastic
analit analityczny / 244

6. CHAPTER
Frequency analysis of signals
deterministycznych / 245
6.1 General comments / 245
6.2 Fourier transform. Issues of F-transformability
and mutual unambiguity / 247
6.3 Fourier transform in the limit sense / 252
6.4. Signal spectrum / 253
6.5 Fourier / 256 transformation properties
6.5.1 Parity and oddness of signals and spectrum / 256
6.5.2 Theorems / 258
6.5.3. Description of signal parameters in the field
frequency / 264
6.5.4 Limits of the amplitude spectrum of the signal / 266
6.6 Examples of Fourier transform parisons / 269
6.6.1 Pairs of Fourier transform in the normal sense / 269
6.6.2. Fourier transform steam in the limit sense / 277
6.7 Fourier transform of periodic signal and its
compound with the complex Fourier series / 285
6.7.1. Spectrum signal spectrum and its representations
graphic / 285
6.7.2 Relationship between complex coefficients
Fourier series of periodic signal and transform
Fourier of the central segment of this signal / 289
6.7.3 Properties of a complex Fourier series / 290
6.7.4 Relations between complex and real
trigonometric Fourier series of signal
okresowego / 293
6.7.5 Convergence of the Fourier series. The Gibbs / 295 effect
6.8 The almost periodic signal spectrum / 298
6.9 Energy density spectrum and power density spectrum. spectrum
wzajemne / 300
6.10. Signal transition through the line system / 309
6.10.1 Relationships between input signal characteristics
and the output of the line system / 309
6.10.2. Linear system as a filter. Filters perfect / 313
6.10.3. Relationship between signal rise time
at the output of the low-pass filter and width
pass band filter / 317
6.11 The principle of uncertainty / 320
6.12 Analytical signal. The concept of vibration uogólniona / 323
6.13 Sampling theorem / 331
6.13.1 Basic version / 331
6.13.2 Discussion. Other variants of the sampling theorem / 338
6.13.3. Signal reproduction based on samples. sampling
perfect / 343
6.13.4 Numeric playback of the signal on the base
samples / 345

7. CHAPTER
Frequency analysis of stochastic signals / 347
7.1 General remarks / 347
7.2. Stochastic Fourier transform in the sense
border / 348
7.3 Frequency characteristics of signals
stochastycznych / 349
7.3.1 Power density spectrum / 349
7.3.2 Mutual power density spectra / 352
7.3.3. Examples of power density spectrum of signals
stochastycznych / 353
7.3.4 Ergodicity of the power density spectrum / 360
7.4 Transition of the stochastic signal by the linear system / 364
7.4.1 Relationships between input signal characteristics
and the output of the line system / 364
7.4.2 Theorem on superposition of power density spectrum / 367
7.5. Stochastic analytical signal. Drganie uogólnione / 368
7.6 Theorem on sampling stochastic signals / 374

8. CHAPTER
Modulation of signals / 379
8.1 General remarks / 379
8.2 Continuous modulation systems / 385
8.2.1 Classification of continuous modulation systems / 385
8.2.2 Amplitude modulation / 388
8.2.2.1 System AM -SC / 388
8.2.2.2 System AM / 396
8.2.2.3 SSB-SC / 403 system
8.2.2.4 SSB / 410 system
8.2.2.5 Analytical representation of the signal
jednowstęgowego / 410
8.2.2.6. The concept of the product of this modulation operator / 414
8.2.2.7 Comparison of amplitude modulation systems. System
VSB with partially suppressed sideband / 417
8.2.3 Angle modulation / 426
8.2.3.1 PM / 428 system
8.2.3.2 FM / 443 system
8.2.4 Resistance to interference of modulation systems
ciągłej / 450
8.3 Impulse modulation systems / 454
8.3.1 Classification of impulse modulation systems / 454
8.3.2 PAM system. Natural sampling and sampling
momentary / 456
8.3.3. PDM and PPM / 464 systems
8.3.4. PCM / 468 system
8.4 Frequency multiplexing and multiplication
czasowe / 479
List of literature / 487
Skorowidz / 489