Digital Signal Processing: Mathematical and Computational Methods, Software Development and Applications (Woodhead Publishing Series in Optical and Electronic Materials)

By Jonathan M. Blackledge

This ebook types the 1st a part of a whole MSc direction in a space that's primary to the continued revolution in details know-how and conversation structures. vastly exhaustive, authoritative and finished and bolstered with software program, this can be an advent to fashionable tools within the constructing box of electronic sign Processing (DSP). the focal point is at the layout of algorithms and the processing of electronic indications in parts of communications and regulate, supplying the reader with a accomplished advent to the underlying ideas and mathematical types.

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Four. five The Sampling Theorem . . . . . . . . . . . . . four. five. 1 Fourier rework of the brush functionality four. five. 2 facts of the Sampling Theorem. four. five. three Sine Interpolation four. 6 Fourier Filters . four. 6. 1 Lowpass Filters. four. 6. 2 Highpass Filters four. 6. three Bandpass Filters four. 6. four The Inverse filter out four. 7 The Kronecker Delta functionality and the DFT . four. eight Deriving Filters utilizing the DFT . . . . . . . four. nine Case examine: Scattering from Layered Media . four. nine. 1 advent to the Wave Equation .. four. nine. 2 Asymptotic Green's functionality resolution four. nine. three dialogue . four. 10 precis of significant effects four. eleven additional analyzing . four. 12 difficulties 102 104 one zero five 107 109 one hundred ten 111 111 different necessary Transforms five. 1 The Laplace rework five. 2 The Sine and Cosine Transforms five. 2. 1 The Sine rework five. 2. 2 The Cosine rework five. three The Walsh rework five. four The Cepstral rework . . . five. five The Hilbert remodel . . . . five. five. 1 Modulation and Demodulation five. five. 2 Quadrature Detection . . . . . . five. five. three The Analytic sign five. five. four Attributes of the Analytic sign five. five. five section Unwrapping . five. 6 Case research: FM Imaging by means of genuine 0 Conversion five. 6. 1 actual 0 Conversion . . . . . five. 6. 2 program to Seismic Imaging five. 7 STFT and The Gabor remodel . . . 114 114 123 123 124 a hundred twenty five 127 129 one hundred thirty 131 132 134 a hundred thirty five 136 136 138 139 86 87 87 88 89 89 ninety ninety ninety one ninety two ninety two ninety three ninety four ninety six ninety seven ninety seven ninety nine ninety nine a hundred a hundred one hundred and one CONTENTS five. eight five. nine five. 10 five. eleven five. 12 five. thirteen five. 14 five. 15 II 6 The Wigner and the Wigner-Ville Transforms . . . . . five. eight. 1 Origins of the Transforms for sign Processing five. eight. 2 homes of the Wigner-Ville remodel five. eight. three move time period Interference . five. eight. four Smoothing the Wigner-Ville Distribution five. eight. five The Discrete Wigner-Ville rework five. eight. 6 purposes . The Riemann-Liouville and the Wyle Transforms The z-Transform . . . . The Wavelet remodel . dialogue . precis of significant effects extra analyzing difficulties . Computational Linear Algebra Matrices and Matrix Algebra 6. 1 Matrices and Matrix Algebra 6. 1. 1 Addition of Matrices. 6. 1. 2 Subtraction of Matrices 6. 1. three Multiplication of a Matrix by way of a Scalar volume. 6. 1. four Multiplication of 2 Matrices . 6. 1. five additional leads to Matrix Multiplication. 6. 1. 6 The Unit Matrix . 6. 1. 7 The Transpose of a Matrix 6. 1. eight The Inverse Matrix . . 6. 1. nine Determinants 6. 1. 10 homes of Determinants 6. 2 structures of Linear Algebraic Equations 6. 2. 1 Formal tools of resolution. 6. 2. 2 assessment of adjA 6. 2. three Cramers Rule . 6. three Linear platforms . 6. three. 1 Inhomogeneous structures 6. three. 2 Homogeneous structures . 6. three. three Ill-conditioned platforms 6. three. four Under-determined structures 6. three. five Over-determined structures 6. four precis of significant effects 6. five extra interpreting 6. 6 difficulties . xvii 141 142 143 146 147 148 148 149 a hundred and fifty 152 154 154 157 158 161 162 163 163 163 164 164 a hundred sixty five 166 166 167 168 169 one hundred seventy 171 172 173 a hundred seventy five one hundred seventy five one hundred seventy five 176 177 177 178 a hundred and eighty one hundred eighty xviii CONTENTS 7 Direct tools of answer 7. 1 Gauss' process . 7. 1. 1 Generalization of the belief . 7. 1. 2 Conversion to Pseudo-Code 7. 1. three Pivots and Pivoting 7. 1. four Pivotal ideas . . 7. 2 Jordan's strategy 7. 2. 1 Matrix Inversion through Jordan's technique 7. 2. 2 Gauss' . v. Jordan's strategy . . 7. three LU Factorization 7.

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