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Processing of Multidimensional Signals : Digital Signal Processing - Alexandre Smirnov

Processing of Multidimensional Signals

Digital Signal Processing

Hardcover Published: July 2009
ISBN: 9783540654490
Number Of Pages: 271

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In this book signals or images described by functions whose number of arguments varies from one to five are considered. This arguments can be time, spatial dimensions, or wavelength in a polychromatic signal. The book discusses the basics of mathematical models of signals, their transformations in technical pre-processing systems, and criteria of the systems quality. The models are used for the solution of practical tasks of system analysis, measurement and optimization, and signal restoration. Several examples are given.

Introductionp. 1
Signals as Physical Objects and Carriers of Informationp. 1
Black Box Paradigmp. 4
Multidimensional Signalsp. 6
Principal Chaptersp. 7
Analog, Discrete and Digital Signalsp. 13
Primary Analog Signal and Its Harmonic Spectrump. 13
Signal as Physical Objectp. 13
Properties of Function F(x, y, z,t)p. 14
Linear Signal Transformationsp. 19
Transformations of Signals and Transformations of Functionsp. 20
Spectrum of Primary Signalp. 20
Whittaker-Shannon Theoremp. 24
Signal Classificationp. 26
Images and Temporal Signalsp. 28
Adequate Mathematical Models of Signalsp. 28
Simplification for Mathematical Modelsp. 29
Rotationally Symmetric Imagesp. 33
Differences between Spatial and Temporal Signalsp. 34
Discrete and Digital Signalsp. 39
Discretizationp. 39
Spectrum of Discrete Signalp. 43
Digital Signalsp. 44
Signal Interpolation and Extrapolationp. 47
Additional Remark on Spatial and Temporal Signalsp. 49
Digital Signals in Computersp. 50
Signals Representationp. 50
Programmable Digital Signal Filtrationp. 51
Digital Imagesp. 54
Accuracy of Mathematical Models of Signalsp. 58
Spatio-Temporal Filtrationp. 63
Deterministic and Stochastic Component of Signal Transformationp. 63
Black Box Paradigmp. 63
Classification of Operators and Noises of Signal Transformationsp. 65
Signal Filtrationp. 68
Experimental Investigation of Filtersp. 68
Development of Mathematical Models of Filtrationp. 74
Linear Filtersp. 76
Operators of Space and Time Invariant Linear Filtrationp. 76
Difference between Spatial and Temporal Filtrationp. 79
Low-pass, By-pass and High-pass Filters 'p. 82
Linear Characteristic Correctionp. 84
Linear Space Variant Filtrationp. 85
Non-linear Filtersp. 86
Simplest Space and Time Invariant Non-linear Filtrationp. 86
Correction of Non-linear Characteristicsp. 90
General Non-linear Filtrationp. 91
Spatio-temporal Noisesp. 92
Statistical Characteristics of Noisep. 92
Additive and Multiplicative Noisep. 94
Linear and Non-linear Transformations of Additive Noisep. 96
Digital Filtrationp. 98
Temporal Non-Recursive and Recursive Digital Filtersp. 98
Spatial Digital Filtersp. 102
Program Realization of Digital Filtrationp. 105
Correction of Characteristics of Linear Digital Filtersp. 108
Non-linear Digital Filtrationp. 115
Signal Restorationp. 116
Formulation of Problemsp. 116
Restoration without Noisep. 116
Restoration by Regularized Pseudo-inverse Filtersp. 117
Noise in Signal Restoration Tasksp. 121
Accuracy of Mathematical Models of Signal Transformationsp. 122
Transformations of Errorsp. 122
Statistical Modeling and Estimation of Transformed Errorsp. 123
Discretization and Scanningp. 125
Signal Transmission and Signal Storagep. 125
Communication Channels and Multichannel Linesp. 125
Storage Media and Memoriesp. 127
System of Image Transmissionp. 129
Methods of Signal Writing and Readingp. 130
Discretization and Distortions of Discrete Signalsp. 134
Mathematical and Physical Discretizationp. 134
Filtration in Process of Signal Discretizationp. 135
Signal Distortions Caused by Discretization and Interpolationp. 138
Scanning for Reading and Writingp. 141
Types of Scanningp. 141
Ideal Scanning Elementsp. 143
Filtration in Scanning Processesp. 146
Scanning Systemsp. 147
Trajectories of Two-Dimensional Scanningp. 153
Limitations on Trajectories of Scanningp. 153
Spiral Rasterp. 156
Radial Rasterp. 157
Line Raster and Its Modificationsp. 159
Point Rasterp. 161
System of Alive Image Transmissionp. 163
Temporal and Spatial Distortions of Transmitted Imagesp. 163
System with Ideal and Non-ideal Videochannelp. 165
Usage of Comb Filters in Videochannelp. 167
Parallel Processing of Temporal Signalsp. 168
Imaging System Quality Assessmentp. 171
Philosophy of Quality Assessmentp. 171
Imaging Systemsp. 171
Criteria of Quality (Figures-of-Merit)p. 173
Quality of Imaging System as Opinion of Its Usersp. 174
Aim of Imagingp. 175
Standards of Qualityp. 177
Environment of Problem of Quality Assessmentp. 178
Measures of Qualityp. 179
Measures of Quality for Specialized Systemsp. 179
Measures of Quality Based on Paradigm of Ideal Imagingp. 181
Universal Measures of Qualityp. 183
Comparison of Measures of Qualityp. 185
Criteria of Qualityp. 185
Qualimetric Experimentp. 185
Averaging, Typization and Standardizationp. 187
Choice of Representative Group of Usersp. 188
Description of System Propertiesp. 189
Secondary Parametersp. 192
Optical Imaging System Optimizationp. 192
Mathematical Models of Optical Imaging Systemsp. 192
Wave and Geometrical Aberrationsp. 193
Criteria of Quality as Functions of Geometrical Aberrationsp. 197
Spatial Resolution and Resolving Powerp. 199
Spatial, Temporal and Spectral Resolutionp. 199
Dual Measures of Spatial Resolutionp. 200
Resolution of Imaging System with Noisep. 203
Rayleigh Criterionp. 205
Development of Spatial Resolution Criteriap. 207
Accuracy of System Optimizationp. 210
Modulated Signalsp. 213
Modulation and Demodulation of Signalsp. 213
Modulating Signals, Carriers and Modulated Signalsp. 213
Distortions of Modulated Signalsp. 216
Modulated Signal Classificationp. 218
Polychromatic Modulated Signalsp. 221
Light Generators and Light Receptorsp. 221
Polychromatic Imaging Systemsp. 224
Correction of Spectral Characteristicsp. 227
Chromatic Distortionsp. 228
Amplitude, Frequency, Phase and Polarization Modulationp. 229
Modulated Temporal Signalsp. 229
Radio Communicationp. 233
Doppler Effectp. 235
Polarization Modulationp. 235
Pulse Modulationp. 237
Discretization as Amplitude Pulse Modulationp. 237
Duration and Delay Modulation of Temporal Signalsp. 239
Pulse Modulation of Spatial Signalsp. 241
Pulse Modulation in Neural Networksp. 243
Concluding Remarksp. 243
On Fundamental Notions of Probability Theoryp. 253
On Applications of computers in Visual Artp. 257
Referencesp. 267
Indexp. 269
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540654490
ISBN-10: 3540654496
Series: Digital Signal Processing
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 271
Published: July 2009
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 1.75
Weight (kg): 1.29