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Fundamentals Of Telecommunications 2021/2022
Programma di Fundamentals Of Telecommunications:
1 INTRODUCTION 7
1.1 TELECOMMUNICATION SYSTEMS AND SERVICES 9
1.2 Internet 12
1.3 Ideal transmission of a signal 12
1.3.1 Definition of signal in strict sense 12
1.3.2 Ideal transmission 12
2 SIGNALS IN TIME DOMAIN 15
2.1 GENERALITIES ON SIGNALS 17
2.1.1 Complex notation 17
2.1.2 Basic operations and faithful signals 18
2.2 Classification of signals 19
2.2.1 Time continuous and time discrete signals 19
2.2.2 Deterministic signals and random signals 19
2.3 TIME CONTINUOUS SIGNALS 21
2.3.1 Continuous signals 21
2.3.2 Signals with discontinuities 21
2.3.3 Signal duration 23
2.3.4 Factorization of time continous signals 26
2.3.5 Ideal Dirac pulse 28
2.3.6 Energy and power of time continuous signals 29
2.4 DISCRETE TIME SIGNALS 30
2.4.1 General case and sequences 30
2.4.2 Sequence lenght 32
2.4.3 Energy and power of sequences 33
2.5 AFFINITY BETWEEN SIGNALS 33
2.5.1 Affinity between energy signals 33
2.5.2 Affinity between power signals 39
2.5.3 Affinity between energy and power signals 40
2.5.4 Affinity between sequences 41
3 REPRESENTATION OF SIGNALS 43
3.1 REPRESENTATION OF SIGNALS IN TIME SERIES 45
3.1.1 Fourier series of periodic signals 45
3.1.2 Representation in series of orthogonal functions 46
3.1.3 Fourier series of signals with limited duration 48
3.1.4 Representation by means of samples interpolation 50
3.2 Representation in the space of signals 51
3.2.1 Gram-Schmidt Orthogonalization procedure 52
3.3 REPRESENTATION OF TIME CONTINUOUS SIGNALS IN THE FREQUENCY DOMAIN 53
3.3.1 Linear transformation of time continuous signals 53
3.3.2 Fourier transform and its properties 54
3.3.3 Demonstrations of some properties of thr Fourier transform56
3.3.4 Relevant examples of Fourier transforms 58
3.3.5 Affinity between energy signals represented in the frequency domain60
3.3.6 Energy spectra 61
3.3.7 Power spectra 62
3.3.8 Spectral extension of real signals 63
3.3.9 Discrete spectra of periodic signals 66
3.4 SAMPLING THEOREM 68
3.4.1 Sampling in the ferquency domain 68
3.4.2 Demonstration of the sampling theorem in the frequency domain68
3.4.3 Sampling in the time domain 69
3.5 COMPLEX REPRESENTATIONS OF TIME CONTINOUS SIGNALS 70
3.5.1 Representative complex signals 70
3.5.2 Real representations through the complex envelope 77
3.5.3 Representation of the complex envelope through samples 79
4 ELEMENTS ON SOURCE SIGNALS 81
4.1 ANALOG OR DIGITAL SIGNALS 83
4.2 ELEMENTS ON ANALOG SOURCE SIGNALS 83
4.2.1 Audio signals 83
4.2.2 Image signals 84
4.3 BASIC CONCEPTS ON DIGITAL SOURCE SIGNALS 87
4.3.1 Synchronous data flows and digital sequences 87
4.3.2 Source multilevel signals 88
4.3.3 Binary source signals 89
4.3.4 Synchronous and asynchronous signals 90
5 SIGNALS IN LINEAR BIPOLES AND QUADRUPOLES 91
5.1 LINEAR TRANSFORMATION BETWEEN TIME CONTINUOUS SIGNALS 93
5.1.1 Remarks on the electric nature of the signals 94
5.2 LTI TRANSFORMATIONS IN THE BIPOLES 97
5.2.1 Reflected response in the time and frequency domains 97
5.2.2 Relation between reflection coefficient and impedence 99
5.2.3 Further details on the reflection coefficient 99
5.3 LTI TRANSFORMATIONS IN THE QUADRUPOLES 100
5.3.1 Responses in the time and frequency domains 100
5.3.2 Diffusion parameters in LTI quadrupoles 101
5.3.3 Transfer in matching conditions 103
5.4 IDEAL QUADRUPOLE AND PERFECT QUADRUPOLES 106
5.4.1 Ideal quadrupole 106
5.4.2 Perfect quadrupoles 107
6 FUNDAMENTALS OF TRANSMISSION 111
6.1 IDEAL TRANSMISSION 113
6.1.1 Conditions for the ideal transport of the information 113
6.1.2 Perfect transmission systems 114
6.1.3 Perfect transmission means 116
6.1.4 Perfect linear channels 118
6.2 LINEAR PROCESSING OF TIME CONTINUOUS SIGNALS 120
6.2.1 Linear processing with no cut of the band 120
6.2.2 Examples of linear processing with no cut of the band 123
6.2.3 Elements on filters 125
6.2.4 Linear processing with cut of the band 127
6.3 PROCESSING OF STEP SIGNALS 129
6.3.1 Reversibility of the processing on step signals 129
6.3.2 Linear processing on step signals 132
6.3.3 Non linear processing of step signals 136
6.3.4 Return of the step waveform 137
6.3.5 Total processing with cut of the band 139
6.3.6 Total processing with reduction of the practical band 140
6.4 Multiplexing 140
6.5 SHORT INTRODUCTION TO THE ANALOGUE TO DIGITAL CONVERSION 141
6.6 SHORT INTRODUCTION TO THE CHANNEL CODING 143
6.6.1 Coding with redundancy on the binary flows 143
6.6.2 Encoding with modification of the cardinality 146
6.7 INTRODUCTION TO HARMONIC MODULATION 149
6.7.1 Introduction to the methods of harmonic modulation 149
6.7.2 Introduction on the modulation by product 149
6.7.3 Introduction on the harmonic angle modulation 151
7 ELEMENTS OF PROBABILITY, RANDOM VARIABLES AND STOCHASTIC PROCESSES 153
7.1 ELEMENTS OF PROBABILITY 155
7.1.1 Basic definitions 155
7.1.2 Axiomatic theory of the probability 155
7.1.3 Conditional probability 156
7.1.4 Total probability and Bayes’ Theorem 156
7.1.5 Independence between events 157
7.2 RANDOM VARIABLES 157
7.2.1 Distributions and density functions 157
7.2.2 Conditional distributions 158
7.2.3 Functions of random variable 159
7.2.4 Moments 160
7.2.5 Characteristic function and moment generating function of a random variable 160
7.2.6 Examples of distribution and density functions 161
7.2.7 Sequences 164
7.2.8 Transformations 164
7.2.9 Alternative Transformations 164
7.2.10 Independence 165
7.2.11 Mean, Variance And Covariance 166
7.2.12 Conditional Densities 166
7.2.13 Characteristic Function 166
7.2.14 Complex Random Variables 166
7.3 GENERALITIES ON THE STOCHASTIC PROCESSES 167
7.3.1 Generalities and definitions 167
7.3.2 Density and distribution probability functions of a stochastic process 167
7.3.3 Properties 168
7.3.4 Moments and related properties 168
7.3.5 Discrete time stochastic processes 169
7.3.6 Stationary processes 169
7.3.7 Cyclostationary processes 171
7.3.8 Ergodic processes 171
7.3.9 Spectral theory 172
7.3.10 Transformations of stochastic processes through systems 173
7.3.11 The Gaussian process 175
7.3.12 Random signals and their sources 175
7.3.13 Characterization of continuous processes 177
7.3.14 Stationary continuous processes 179
7.3.15 Cross correlation for stationary processes 181
7.3.16 Process sum and complex process 183
7.3.17 Real stationary dicrete processes 184
7.4 CYCLOSTATIONARY STOCHASTIC PROCESSES 185
7.4.1 First and second order cyclostationary processes 185
7.4.2 Processes represented by means of the complex envelope 186
7.4.3 Stationary process not in base band 188
7.5 PROCESSES REPRESENTED BY MEANS OF TIME SERIES 190
7.5.1 Real processes with random factors 190
7.5.2 Sampled processes in base band 192
7.5.3 Complex processes with random factors 194
7.5.4 Process sum of real processes with random factors 195
7.6 GAUSSIAN CONTINUOUS PROCESSES 196
7.6.1 Gaussian continuous processes: the noise 196
7.6.2 Stationary gaussian noise not in base band 198
7.6.3 White gaussian noise in the signal space 199
7.7 MARKOV PROCESSES 201
7.7.1 Properties of the Markov processes 201
7.7.2 Time discrete Markov process 201
7.7.3 Continuous time Markov processes 205
8 IMPERFECT TRANSMISSION 207
8.1 INTRODUCTION 209
8.2 IMPERFECT CONNECTION 209
8.2.1 Impairments in the electric connection 209
8.2.2 Additive unexpected effect in output 211
8.2.3 Imperfect transmission with linear time variant channel 213
8.2.4 Imperfect transmission with linear time invariant channel 214
8.2.5 Imperfect transmission with non linear channel 217
8.3 Imperfect transmission with independent disturbs 219
8.3.1 Independent (on the signal and among one another) disturbs 219
8.3.2 Reduction of the effects of independent disturbs 221
8.3.3 System additive gaussian noise 223
8.4 Spectral density and power analysis of a transmission system 223
8.4.1 Parameters of the single quadrupole and of the cascade (spectral density and power) 223
8.4.2 Power analysis of noisy quadrupoles 225
8.4.3 Sensitivity of the receiver 229
9 BASIC PRINCIPLES OF ANALOGUE MODULATION AND DEMODULATION 231
9.1 Modulation of harmonic signals 233
9.1.1 General schemes of transmitters for modulated harmonic signals233
9.2 Harmonic modulation with analogue modulating signal 235
9.2.1 Amplitude modulations family 235
9.2.2 Angle modulation: phase (PM) and frequency (FM) 237
9.3 Performance analysis of harmonic modulation systems with analogue signals 240
9.3.1 Performance of AM systems 240
9.3.2 Signal-noise ratio for PM and FM systems 241
9.4 Carrier synchronization and Phased Locked Loop 243
9.4.1 Carrier recovery track and hold 243
9.4.2 Phase detection and VCO 246
9.4.3 Linearised phase control loop and dynamic response 246
10 TRANSMISSION MEANS 250
10.1 INTRODUCTION TO THE TRANSMISSION MEANS 252
10.1.1 Metallic pairs 252
10.1.2 Optical fibers 253
10.1.3 Radio path 254
10.2 INTRODUZIONE AI MEZZI TRASMISSIVI REALI 255
10.3 MEZZI TRASMISSIVI METALLICI 256
10.3.1 Struttura delle coppie metalliche 256
10.3.2 Grandezze caratteristiche delle coppie metalliche 257
10.3.3 Comportamento delle coppie metalliche 261
10.3.4 Mezzi trasmissivi con coppie simmetriche 264
10.3.5 Mezzi trasmissivi con coppie coassiali 267
10.4 MEZZI TRASMISSIVI OTTICI 270
10.4.1 Struttura delle fibre ottiche 270
10.4.2 Grandezze caratteristiche delle fibre ottiche 271
10.4.3 Comportamento delle fibre ottiche a salto di indice 274
10.4.4 Mezzi trasmissivi con fibra ottica monomodo 278
10.5 MEZZI TRASMISSIVI REALI CON PORTANTE RADIO 279