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Signal Theory

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Signal theory provides a mathematical toolbox for modeling and analysis of physical systems. Stochastic processes are used to model more or less unknown signals. Signal theory has applications in communication engineering, signal processing, automatic control, medical engineering, and more. This book starts off by reviewing the needed background from probability theory and signals & systems. Then stochastic processes are introduced, both in discrete and continuous time, together with the impo...

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Signal theory provides a mathematical toolbox for modeling and analysis of physical systems. Stochastic processes are used to model more or less unknown signals. Signal theory has applications in communication engineering, signal processing, automatic control, medical engineering, and more. This book starts off by reviewing the needed background from probability theory and signals & systems. Then stochastic processes are introduced, both in discrete and continuous time, together with the important tools auto-correlation function and power-spectral density. Separate chapters focus on analyzing linear filters, sampling & reconstruction, some nonlinearities and modulation in terms of stochastic processes. The modulation chapter includes noise analyses of the considered modulation methods assuming that thermal noise dominates the picture. A separate chapter briefly covers multi-dimensional signals and systems as a preparation for image processing. A chapter on spectral estimation is included, which could be used as a basis for computer-based laborations. Problems are given at the end of each chapter. Hints and answers to most of those problems are provided in appendices. The book is suitable for an advanced course on engineering aspects of stochastic processes. It is written with an electrical engineering student in mind, but should be useful in other engineering disciplines as well. We do not dwell on the innermost details of stochastic processes. Instead we focus on the ability to deal with stochastic processes in situations that could very well be models of real-world problems. This book provides tools and understanding that can be used as a preparation for in-depth studies of subjects such as communication engineering, image and signal processing or analysis, and automatic control, just to mention a few. This book is intended for engineering students with a background in probability theory on one hand and signals and systems on the other hand. No prior knowledge of stochastic processes is assumed. Tables and formulas for Signal Theory

Stäng
    • Preface vii
    • Acronyms ix
    • 1
      1
      Introduction
        • 1.1
          1
          Signal Theory
        • 1.2
          2
          Outline
        • 1.3
          3
          Problems
    • 2
      5
      Deterministic Signals and Systems
        • 2.1
          5
          Signals
          • 2.1.1
            5
            Time-Continuous Signals
          • 2.1.2
            7
            Time-Discrete Signals
        • 2.2
          8
          Systems
        • 2.3
          12
          The Time Domain
          • 2.3.1
            12
            Time-Continuous Signals and Systems
          • 2.3.2
            17
            Time-Discrete Signals and Systems
        • 2.4
          19
          The Frequency Domain
          • 2.4.1
            19
            The Time-Continuous Fourier Transform
          • 2.4.2
            23
            The Time-Discrete Fourier Transform
        • 2.5
          27
          Representations of Some LTI Systems
          • 2.5.1
            27
            Linear Differential Equations
          • 2.5.2
            29
            Linear Difference Equations
        • 2.6
          32
          Filters and Filter Types
        • 2.7
          38
          Amplitude Modulation
        • 2.8
          39
          Principal Values
        • 2.9
          41
          Problems
    • 3
      47
      Stochastic Variables
        • 3.1
          47
          Events and Probability
        • 3.2
          50
          Stochastic Variables
        • 3.3
          51
          Probability Distributions and Densities
        • 3.4
          54
          Expectations
        • 3.5
          56
          Multi-Dimensional Stochastic Variables
        • 3.6
          60
          Conditional Distributions
        • 3.7
          63
          Gaussian variables
        • 3.8
          67
          Other Common Distributions
        • 3.9
          68
          Problems
    • 4
      73
      Stochastic Processes
        • 4.1
          73
          Basic Definitions
        • 4.2
          74
          Notation
        • 4.3
          76
          Predictability
        • 4.4
          78
          Ensembles and Averages
        • 4.5
          79
          Auto-Correlation
        • 4.6
          81
          Stationarity
        • 4.7
          85
          Signal Power
        • 4.8
          86
          Gaussian Processes
        • 4.9
          87
          Cross-Correlation and Cross-Spectrum
        • 4.10
          89
          Ergodicity
        • 4.11
          91
          White Noise
        • 4.12
          92
          Colored Noise
        • 4.13
          94
          Poisson Processes
        • 4.14
          96
          Problems
    • 5
      99
      Filtering Stochastic Processes
        • 5.1
          99
          Time-Continuous Filtering
          • 5.1.1
            100
            Ensemble averages
          • 5.1.2
            101
            Power Spectral Densities
          • 5.1.3
            103
            Gaussian Processes
          • 5.1.4
            104
            White Processes
        • 5.2
          105
          Time-Discrete Filtering
        • 5.3
          106
          The Non-Negativity of the PSD
        • 5.4
          108
          Prediction
        • 5.5
          110
          Cross-Correlation Revisited
        • 5.6
          112
          Problems
    • 6
      119
      Sampling and Reconstruction
        • 6.1
          120
          Sampling
          • 6.1.1
            121
            Deterministic input
          • 6.1.2
            124
            Stochastic input
        • 6.2
          125
          Pulse-Amplitude Modulation
          • 6.2.1
            125
            Deterministic input
          • 6.2.2
            125
            Stochastic input
        • 6.3
          127
          Reconstruction of Time-Continuous Signals
          • 6.3.1
            128
            Deterministic input
          • 6.3.2
            131
            Stochastic input
        • 6.4
          135
          Reconstruction of Time-Discrete Signals
          • 6.4.1
            136
            Deterministic input
          • 6.4.2
            137
            Stochastic input
        • 6.5
          138
          Problems
    • 7
      143
      Momentary Non-Linear Systems
        • 7.1
          143
          Examples of Non-Linear Systems
        • 7.2
          144
          Characterization of the System
        • 7.3
          146
          Characterization of the Input
        • 7.4
          146
          Gaussian Input
          • 7.4.1
            147
            Characteristic Functions
          • 7.4.2
            149
            Price’s Theorem
        • 7.5
          151
          Saturation
        • 7.6
          153
          Quantization
          • 7.6.1
            154
            Uniform Quantization of a Stochastic Variable
          • 7.6.2
            156
            The Quantization Error is Almost White
          • 7.6.3The Input and the Quantization Error are Almost Un-
        • 158
          correlated
          • 7.6.4
            159
            Distortion
          • 7.6.5
            160
            Impact of Saturation on the Quantization Distortion
          • 7.6.6
            162
            Non-Uniform Quantization
          • 7.6.7
            166
            A Note About Power Spectral Densities
        • 7.7
          166
          Problems
    • 8
      173
      Analog Modulation
        • 8.1
          174
          Amplitude Modulation
          • 8.1.1
            174
            Standard AM
          • 8.1.2
            176
            Suppressed Carrier Modulation
          • 8.1.3
            178
            Single Sideband Modulation
          • 8.1.4
            178
            Amplitude Modulation of Stochastic Processes
          • 8.1.5
            182
            Impact of Noise in AM Demodulation
        • 8.2
          185
          Angle Modulation
          • 8.2.1
            187
            Spectrum of Angle Modulation
          • 8.2.2
            188
            Phase Modulation
          • 8.2.3
            188
            Frequency Modulation
          • 8.2.4
            190
            Demodulation of PM and FM
          • 8.2.5
            192
            Broadband Angle Modulation of a Gaussian Process
          • 8.2.6
            196
            Narrowband Angle Modulation
          • 8.2.7
            197
            Impact of Noise in PM and FM Demodulation
          • 8.2.8
            199
            Pre-emphasized FM
        • 8.3
          202
          Problems
    • 9
      205
      Multi-Dimensional Processes
        • 9.1
          206
          Two-Dimensional Signals
          • 9.1.1
            206
            Deterministic Signals
          • 9.1.2
            207
            Stochastic Processes
        • 9.2
          208
          Two-Dimensional Systems
          • 9.2.1
            208
            Deterministic Input
          • 9.2.2
            210
            Probabilistic Input
        • 9.3
          211
          Spectral Description
          • 9.3.1
            211
            Two-Dimensional Fourier Transform
          • 9.3.2
            212
            Two-Dimensional Power Spectral Density
        • 9.4
          214
          Sampling and Reconstruction in Two Dimensions
          • 9.4.1
            214
            Deterministic Input
          • 9.4.2
            215
            Probabilistic Input
        • 9.5
          216
          Problems
    • 10
      219
      Spectral Estimation
        • 10.1
          219
          Estimation
        • 10.2
          221
          Estimating Auto-Correlation Functions
          • 10.2.1
            221
            Blackman-Tukey’s Estimate
          • 10.2.2
            222
            Bartlett’s Estimate
        • 10.3
          223
          Estimating Power Spectral Densities
          • 10.3.1
            223
            Periodograms
          • 10.3.2
            226
            Averaged Periodograms
          • 10.3.3
            226
            Smoothing
          • 10.3.4
            227
            Final Words on Estimation
    • 11
      229
      Extended Example: Reconstruction in CD Players
        • 11.1
          229
          Introduction
        • 11.2
          230
          Quantization at the Recording of the CD
        • 11.3
          232
          Reconstruction
          • 11.3.1
            233
            The First Generation: PAM
          • 11.3.2
            235
            The Second Generation: Oversampling
          • 11.3.3
            238
            The Third Generation: Noise Shaping
        • 11.4
          244
          Comments
    • 245
      A Hints to Problems
        • 245
          A2 Deterministic Signals and Systems
        • 247
          A3 Stochastic Variables
        • 248
          A4 Stochastic Processes
        • 249
          A5 Filtering Stochastic Processes
        • 251
          A6 Sampling and Reconstruction
        • 252
          A7 Momentary Non-Linear Systems
        • 253
          A8 Analog Modulation
        • 253
          A9 Multi-Dimensional Processes
    • 255
      B Answers to Problems
        • 255
          B2 Deterministic Signals and Systems
        • 259
          B3 Stochastic Variables
        • 261
          B4 Stochastic Processes
        • 262
          B5 Filtering Stochastic Processes
        • 264
          B6 Sampling and Reconstruction
        • 265
          B7 Momentary Non-Linear Systems
        • 267
          B8 Analog Modulation
        • 267
          B9 Multi-Dimensional Processes
Information

Författare:

Mikael Olofsson

Språk:

Engelska

ISBN:

9789144073538

Utgivningsår:

2011

Artikelnummer:

35676-01

Upplaga:

Första

Sidantal:

281

Köp- och leveransvillkor

Förlagskontakt

Jens Fredholm

Förläggare Teknik Teknik, matematik och statistik

046-31 21 58 E-post
Fritjof Janson

Förlagskoordinator Kurslitteratur och Kompetensutveckling

046-31 22 57 E-post
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