Algorithms for Communications - Giovanni Cherubini

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Résumé :
Preface 3 Acknowledgments 3 1 Elements of signal theory 7 1.1 Continuous-time linear systems 7 1.2 Discrete-time linear systems 10 Discrete Fourier transform 13 The DFT operator 14 Circular and linear convolution via DFT 15 Convolution by the overlap-save method 17 IIR and FIR filters 19 1.3 Signal bandwidth 22 The sampling theorem 24 Heaviside conditions for the absence of signal distortion 26 1.4 Passband signals and systems 26 Complex representation 26 Relation between a signal and its complex representation 28 Baseband equivalent of a transformation 36 Envelope and instantaneous phase and frequency 37 1.5 Second-order analysis of random processes 38 1.5.1 Correlation 39 Properties of the autocorrelation function 40 1.5.2 Power spectral density 40 Spectral lines in the PSD 40 Cross power spectral density 42 Properties of the PSD 42 PSD through filtering 43 1.5.3 PSD of discrete-time random processes 43 Spectral lines in the PSD 44 PSD through filtering 45 Minimum-phase spectral factorization 46 1.5.4 PSD of passband processes 47 PSD of in-phase and quadrature components 47 Cyclostationary processes 50 1.6 The autocorrelation matrix 56 Properties 56 Eigenvalues 56 Other properties 57 Eigenvalue analysis for Hermitian matrices 58 1.7 Examples of random processes 60 1.8 Matched filter 66 White noise case 68 1.9 Ergodic random processes 69 1.9.1 Mean value estimators 71 Rectangular window 74 Exponential filter 74 General window 75 1.9.2 Correlation estimators 75 Unbiased estimate 76 Biased estimate 76 1.9.3 Power spectral density estimators 77 Periodogram or instantaneous spectrum 77 Welch periodogram 78 Blackman and Tukey correlogram 79 Windowing and window closing 79 1.10 Parametric models of random processes 82 ARMA 82 MA 84 AR 84 Spectral factorization of AR models 87 Whitening filter 87 Relation between ARMA, MA, and AR models 87 1.10.1 Autocorrelation of AR processes 89 1.10.2 Spectral estimation of an AR process 91 Some useful relations 92 AR model of sinusoidal processes 94 1.11 Guide to the bibliography 95 Bibliography 95 Appendixes 97 1.A Multirate systems 98 1.A.1 Fundamentals 98 1.A.2 Decimation 100 1.A.3 Interpolation 102 1.A.4 Decimator filter 104 1.A.5 Interpolator filter 105 1.A.6 Rate conversion 108 1.A.7 Time interpolation 109 Linear interpolation 110 Quadratic interpolation 112 1.A.8 The noble identities 112 1.A.9 The polyphase representation 113 Efficient implementations 114 1.B Generation of a complex Gaussian noise 121 1.C Pseudo-noise sequences 122 Maximal-length 122 CAZAC 124 Gold 125 2 The Wiener filter 129 2.1 The Wiener filter 129 Matrix formulation 130 Optimum filter design 132 The principle of orthogonality 134 Expression of the minimum mean-square error 135 Characterization of the cost function surface 136 The Wiener filter in the z-domain 137 2.2 Linear prediction 140 Forward linear predictor 141 Optimum predictor coefficients 141 Forward prediction error filter 142 Relation between linear prediction and AR models 143 First and second order solutions 144 2.3 The least squares method 145 Data windowing 146 Matrix formulation 146 Correlation matrix 147 Determination of the optimum filter coefficients 147 2.3.1 The principle of orthogonality 148 Minimum cost function 149 The normal equation using the data matrix 149 Geometric interpretation: the projection operator 150 2.3.2 Solutions to the LS problem 151 Singular value decomposition 152 Minimum norm solution 154 2.4 The estimation problem 155 Estimation of a random variable 155 MMSE estimation 155 Extension to multiple observations 157 Linear MMSE estimation of a random variable 158 Linear MMSE estimation of a random vector 158 2.4.1 The Cram?r-Rao lower bound 160 Extension to vector parameter 162 2.5 Examples of application 164 2.5.1 Identification of...

Biographie:
Preface 3 Acknowledgments 3 1 Elements of signal theory 7 1.1 Continuous-time linear systems 7 1.2 Discrete-time linear systems 10 Discrete Fourier transform 13 The DFT operator 14 Circular and linear convolution via DFT 15 Convolution by the overlap-save method 17 IIR and FIR filters 19 1.3 Signal bandwidth 22 The sampling theorem 24 Heaviside conditions for the absence of signal distortion 26 1.4 Passband signals and systems 26 Complex representation 26 Relation between a signal and its complex representation 28 Baseband equivalent of a transformation 36 Envelope and instantaneous phase and frequency 37 1.5 Second-order analysis of random processes 38 1.5.1 Correlation 39 Properties of the autocorrelation function 40 1.5.2 Power spectral density 40 Spectral lines in the PSD 40 Cross power spectral density 42 Properties of the PSD 42 PSD through filtering 43 1.5.3 PSD of discrete-time random processes 43 Spectral lines in the PSD 44 PSD through filtering 45 Minimum-phase spectral factorization 46 1.5.4 PSD of passband processes 47 PSD of in-phase and quadrature components 47 Cyclostationary processes 50 1.6 The autocorrelation matrix 56 Properties 56 Eigenvalues 56 Other properties 57 Eigenvalue analysis for Hermitian matrices 58 1.7 Examples of random processes 60 1.8 Matched filter 66 White noise case 68 1.9 Ergodic random processes 69 1.9.1 Mean value estimators 71 Rectangular window 74 Exponential filter 74 General window 75 1.9.2 Correlation estimators 75 Unbiased estimate 76 Biased estimate 76 1.9.3 Power spectral density estimators 77 Periodogram or instantaneous spectrum 77 Welch periodogram 78 Blackman and Tukey correlogram 79 Windowing and window closing 79 1.10 Parametric models of random processes 82 ARMA 82 MA 84 AR 84 Spectral factorization of AR models 87 Whitening filter 87 Relation between ARMA, MA, and AR models 87 1.10.1 Autocorrelation of AR processes 89 1.10.2 Spectral estimation of an AR process 91 Some useful relations 92 AR model of sinusoidal processes 94 1.11 Guide to the bibliography 95 Bibliography 95 Appendixes 97 1.A Multirate systems 98 1.A.1 Fundamentals 98 1.A.2 Decimation 100 1.A.3 Interpolation 102 1.A.4 Decimator filter 104 1.A.5 Interpolator filter 105 1.A.6 Rate conversion 108 1.A.7 Time interpolation 109 Linear interpolation 110 Quadratic interpolation 112 1.A.8 The noble identities 112 1.A.9 The polyphase representation 113 Efficient implementations 114 1.B Generation of a complex Gaussian noise 121 1.C Pseudo-noise sequences 122 Maximal-length 122 CAZAC 124 Gold 125 2 The Wiener filter 129 2.1 The Wiener filter 129 Matrix formulation 130 Optimum filter design 132 The principle of orthogonality 134 Expression of the minimum mean-square error 135 Characterization of the cost function surface 136 The Wiener filter in the z-domain 137 2.2 Linear prediction 140 Forward linear predictor 141 Optimum predictor coefficients 141 Forward prediction error filter 142 Relation between linear prediction and AR models 143 First and second order solutions 144 2.3 The least squares method 145 Data windowing 146 Matrix formulation 146 Correlation matrix 147 Determination of the optimum filter coefficients 147 2.3.1 The principle of orthogonality 148 Minimum cost function 149 The normal equation using the data matrix 149 Geometric interpretation: the projection operator 150 2.3.2 Solutions to the LS problem 151 Singular value decomposition 152 Minimum norm solution 154 2.4 The estimation problem 155 Estimation of a random variable 155 MMSE estimation 155 Extension to multiple observations 157 Linear MMSE estimation of a random variable 158 Linear MMSE estimation of a random vector 158 2.4.1 The Cram?r-Rao lower bound 160 Extension to vector parameter 162 2.5 Examples of application 164 2.5.1 Identification of...

Sommaire:
Preface 3 Acknowledgments 3 1 Elements of signal theory 7 1.1 Continuous-time linear systems 7 1.2 Discrete-time linear systems 10 Discrete Fourier transform 13 The DFT operator 14 Circular and linear convolution via DFT 15 Convolution by the overlap-save method 17 IIR and FIR filters 19 1.3 Signal bandwidth 22 The sampling theorem 24 Heaviside conditions for the absence of signal distortion 26 1.4 Passband signals and systems 26 Complex representation 26 Relation between a signal and its complex representation 28 Baseband equivalent of a transformation 36 Envelope and instantaneous phase and frequency 37 1.5 Second-order analysis of random processes 38 1.5.1 Correlation 39 Properties of the autocorrelation function 40 1.5.2 Power spectral density 40 Spectral lines in the PSD 40 Cross power spectral density 42 Properties of the PSD 42 PSD through filtering 43 1.5.3 PSD of discrete-time random processes 43 Spectral lines in the PSD 44 PSD through filtering 45 Minimum-phase spectral factorization 46 1.5.4 PSD of passband processes 47 PSD of in-phase and quadrature components 47 Cyclostationary processes 50 1.6 The autocorrelation matrix 56 Properties 56 Eigenvalues 56 Other properties 57 Eigenvalue analysis for Hermitian matrices 58 1.7 Examples of random processes 60 1.8 Matched filter 66 White noise case 68 1.9 Ergodic random processes 69 1.9.1 Mean value estimators 71 Rectangular window 74 Exponential filter 74 General window 75 1.9.2 Correlation estimators 75 Unbiased estimate 76 Biased estimate 76 1.9.3 Power spectral density estimators 77 Periodogram or instantaneous spectrum 77 Welch periodogram 78 Blackman and Tukey correlogram 79 Windowing and window closing 79 1.10 Parametric models of random processes 82 ARMA 82 MA 84 AR 84 Spectral factorization of AR models 87 Whitening filter 87 Relation between ARMA, MA, and AR models 87 1.10.1 Autocorrelation of AR processes 89 1.10.2 Spectral estimation of an AR process 91 Some useful relations 92 AR model of sinusoidal processes 94 1.11 Guide to the bibliography 95 Bibliography 95 Appendixes 97 1.A Multirate systems 98 1.A.1 Fundamentals 98 1.A.2 Decimation 100 1.A.3 Interpolation 102 1.A.4 Decimator filter 104 1.A.5 Interpolator filter 105 1.A.6 Rate conversion 108 1.A.7 Time interpolation 109 Linear interpolation 110 Quadratic interpolation 112 1.A.8 The noble identities 112 1.A.9 The polyphase representation 113 Efficient implementations 114 1.B Generation of a complex Gaussian noise 121 1.C Pseudo-noise sequences 122 Maximal-length 122 CAZAC 124 Gold 125 2 The Wiener filter 129 2.1 The Wiener filter 129 Matrix formulation 130 Optimum filter design 132 The principle of orthogonality 134 Expression of the minimum mean-square error 135 Characterization of the cost function surface 136 The Wiener filter in the z-domain 137 2.2 Linear prediction 140 Forward linear predictor 141 Optimum predictor coefficients 141 Forward prediction error filter 142 Relation between linear prediction and AR models 143 First and second order solutions 144 2.3 The least squares method 145 Data windowing 146 Matrix formulation 146 Correlation matrix 147 Determination of the optimum filter coefficients 147 2.3.1 The principle of orthogonality 148 Minimum cost function 149 The normal equation using the data matrix 149 Geometric interpretation: the projection operator 150 2.3.2 Solutions to the LS problem 151 Singular value decomposition 152 Minimum norm solution 154 2.4 The estimation problem 155 Estimation of a random variable 155 MMSE estimation 155 Extension to multiple observations 157 Linear MMSE estimation of a random variable 158 Linear MMSE estimation of a random vector 158 2.4.1 The Cram?r-Rao lower bound 160 Extension to vector parameter 162 2.5 Examples of application 164 2.5.1 Identification of...