Advances in Shannon s Sampling Theory

The book will interest graduate students and professionals in electrical engineering, communications, and applied mathematics.

Author: AhmedI. Zayed

Publisher: Routledge

ISBN: 9781351468190

Category: Mathematics

Page: 334

View: 479

Download →

Advances in Shannon's Sampling Theory provides an up-to-date discussion of sampling theory, emphasizing the interaction between sampling theory and other branches of mathematical analysis, including the theory of boundary-value problems, frames, wavelets, multiresolution analysis, special functions, and functional analysis. The author not only traces the history and development of the theory, but also presents original research and results that have never before appeared in book form. Recent techniques covered include the Feichtinger-Gröchenig sampling theory; frames, wavelets, multiresolution analysis and sampling; boundary-value problems and sampling theorems; and special functions and sampling theorems. The book will interest graduate students and professionals in electrical engineering, communications, and applied mathematics.
Posted in:

Advanced Topics in Shannon Sampling and Interpolation Theory

Advanced Topics in Shannon Sampling and Interpolation Theory is the second volume of a textbook on signal analysis solely devoted to the topic of sampling and restoration of continuous time signals and images.

Author: Robert J.II Marks

Publisher: Springer Science & Business Media

ISBN: 9781461397571

Category: Technology & Engineering

Page: 360

View: 187

Download →

Advanced Topics in Shannon Sampling and Interpolation Theory is the second volume of a textbook on signal analysis solely devoted to the topic of sampling and restoration of continuous time signals and images. Sampling and reconstruction are fundamental problems in any field that deals with real-time signals or images, including communication engineering, image processing, seismology, speech recognition, and digital signal processing. This second volume includes contributions from leading researchers in the field on such topics as Gabor's signal expansion, sampling in optical image formation, linear prediction theory, polar and spiral sampling theory, interpolation from nonuniform samples, an extension of Papoulis's generalized sampling expansion to higher dimensions, and applications of sampling theory to optics and to time-frequency representations. The exhaustive bibliography on Shannon sampling theory will make this an invaluable research tool as well as an excellent text for students planning further research in the field.
Posted in:

Sampling Theory and Applications

The chapters of this volume are based on talks given at the eleventh international Sampling Theory and Applications conference held in 2015 at American University in Washington, D.C. The papers highlight state-of-the-art advances and trends ...

Author: Stephen D. Casey

Publisher: Springer Nature

ISBN: 9783030362911

Category: Mathematics

Page: 197

View: 466

Download →

The chapters of this volume are based on talks given at the eleventh international Sampling Theory and Applications conference held in 2015 at American University in Washington, D.C. The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing. Chapters have been written by prominent mathematicians, applied scientists, and engineers with an expertise in sampling theory. Claude Shannon’s 100th birthday is also celebrated, including an introductory essay that highlights Shannon’s profound influence on the field. The topics covered include both theory and applications, such as: • Compressed sensing• Non-uniform and wave sampling• A-to-D conversion• Finite rate of innovation• Time-frequency analysis• Operator theory• Mobile sampling issues Sampling: Theory and Applications is ideal for mathematicians, engineers, and applied scientists working in sampling theory or related areas.
Posted in:

Sampling Theory a Renaissance

Today, research themes such as Compressed Sensing and Frame Theory re-energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing.

Author: Götz E. Pfander

Publisher: Birkhäuser

ISBN: 9783319197494

Category: Mathematics

Page: 532

View: 554

Download →

Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem, a central pillar of Sampling Theory. The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary, novel mathematical theories. Today, research themes such as Compressed Sensing and Frame Theory re-energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing. It touches upon trendsetting areas such as Compressed Sensing, Finite Frames, Parametric Partial Differential Equations, Quantization, Finite Rate of Innovation, System Theory, as well as sampling in Geometry and Algebraic Topology.
Posted in:

Advanced Topics in Shannon Sampling and Interpolation Theory

Advanced Topics in Shannon Sampling and Interpolation Theory is the second volume of a textbook on signal analysis solely devoted to the topic of sampling and restoration of continuous time signals and images.

Author: Robert J.II Marks

Publisher: Springer

ISBN: 0387979069

Category: Technology & Engineering

Page: 360

View: 840

Download →

Advanced Topics in Shannon Sampling and Interpolation Theory is the second volume of a textbook on signal analysis solely devoted to the topic of sampling and restoration of continuous time signals and images. Sampling and reconstruction are fundamental problems in any field that deals with real-time signals or images, including communication engineering, image processing, seismology, speech recognition, and digital signal processing. This second volume includes contributions from leading researchers in the field on such topics as Gabor's signal expansion, sampling in optical image formation, linear prediction theory, polar and spiral sampling theory, interpolation from nonuniform samples, an extension of Papoulis's generalized sampling expansion to higher dimensions, and applications of sampling theory to optics and to time-frequency representations. The exhaustive bibliography on Shannon sampling theory will make this an invaluable research tool as well as an excellent text for students planning further research in the field.
Posted in:

Nonuniform Sampling

Our understanding of nature is often through nonuniform observations in space or time. In space, one normally observes the important features of an object, such as edges. The less important features are interpolated.

Author: Farokh Marvasti

Publisher: Springer Science & Business Media

ISBN: 9781461512295

Category: Technology & Engineering

Page: 924

View: 762

Download →

Our understanding of nature is often through nonuniform observations in space or time. In space, one normally observes the important features of an object, such as edges. The less important features are interpolated. History is a collection of important events that are nonuniformly spaced in time. Historians infer between events (interpolation) and politicians and stock market analysts forecast the future from past and present events (extrapolation). The 20 chapters of Nonuniform Sampling: Theory and Practice contain contributions by leading researchers in nonuniform and Shannon sampling, zero crossing, and interpolation theory. Its practical applications include NMR, seismology, speech and image coding, modulation and coding, optimal content, array processing, and digital filter design. It has a tutorial outlook for practising engineers and advanced students in science, engineering, and mathematics. It is also a useful reference for scientists and engineers working in the areas of medical imaging, geophysics, astronomy, biomedical engineering, computer graphics, digital filter design, speech and video processing, and phased array radar.
Posted in:

Sampling Theory in Fourier and Signal Analysis Advanced Topics

Thus ( 1 ) € Bf , and the application of Shannon's sampling theorem completes the proof , noting that f ( -k ) = 0 for k e N. Observing that , by sin Az = f ...

Author: J. R. Higgins

Publisher: Oxford University Press

ISBN: 0198534965

Category: Mathematics

Page: 296

View: 690

Download →

Volume 1 in this series laid the mathematical foundations of sampling theory; Volume 2 surveys the many applications of the theory both within mathematics and in other areas of science. Topics range over a wide variety of areas, and each application is given a modern treatment.
Posted in:

Broadcasting and Optical Communication Technology

A.I. Zayed, Advances in Shannon's Sampling Theory, Boca Raton, Fla. ... An in-depth study of the sample theorem and its numerous variations is provided in ...

Author: Richard C. Dorf

Publisher: CRC Press

ISBN: 9781420003116

Category: Technology & Engineering

Page: 424

View: 701

Download →

In two editions spanning more than a decade, The Electrical Engineering Handbook stands as the definitive reference to the multidisciplinary field of electrical engineering. Our knowledge continues to grow, and so does the Handbook. For the third edition, it has been expanded into a set of six books carefully focused on a specialized area or field of study. Broadcasting and Optical Communication Technology represents a concise yet definitive collection of key concepts, models, and equations in the fields of broadcasting and optical communication, thoughtfully gathered for convenient access. Addressing the challenges involved in modern communications networks, Broadcasting and Optical Communication Technology explores communications, information theory, and devices, covering all the basic information needed for a thorough understanding of these areas. It also examines the emerging areas of adaptive estimation and optical communication, including lightwave technology, long-distance fiber optic communications, and photonic networks. Articles include defining terms, references, and sources of further information. Encompassing the work of the world's foremost experts in their respective specialties, Broadcasting and Optical Communication Technology presents the latest developments, the broadest scope of coverage, and new material on mobile communications. It offers fast, convenient access to specialists in need of detailed reference on the job.
Posted in:

Generalizing Sampling Theory for Time varying Nyquist Rates Using Self adjoint Extensions of Symmetric Operators with Deficiency Indices 1 1 in Hilbert Spaces

To this end, following work by A. Kempf, the sampling points at a Nyquist rate are identified as the eigenvalues of self-adjoint extensions of a simple symmetric operator with deficiency indices (1,1).

Author: Yufang Hao

Publisher:

ISBN: OCLC:827771557

Category:

Page: 139

View: 656

Download →

Sampling theory studies the equivalence between continuous and discrete representations of information. This equivalence is ubiquitously used in communication engineering and signal processing. For example, it allows engineers to store continuous signals as discrete data on digital media. The classical sampling theorem, also known as the theorem of Whittaker-Shannon-Kotel'nikov, enables one to perfectly and stably reconstruct continuous signals with a constant bandwidth from their discrete samples at a constant Nyquist rate. The Nyquist rate depends on the bandwidth of the signals, namely, the frequency upper bound. Intuitively, a signal's 'information density' and 'effective bandwidth' should vary in time. Adjusting the sampling rate accordingly should improve the sampling efficiency and information storage. While this old idea has been pursued in numerous publications, fundamental problems have remained: How can a reliable concept of time-varying bandwidth been defined? How can samples taken at a time-varying Nyquist rate lead to perfect and stable reconstruction of the continuous signals? This thesis develops a new non-Fourier generalized sampling theory which takes samples only as often as necessary at a time-varying Nyquist rate and maintains the ability to perfectly reconstruct the signals. The resulting Nyquist rate is the critical sampling rate below which there is insufficient information to reconstruct the signal and above which there is redundancy in the stored samples. It is also optimal for the stability of reconstruction. To this end, following work by A. Kempf, the sampling points at a Nyquist rate are identified as the eigenvalues of self-adjoint extensions of a simple symmetric operator with deficiency indices (1,1). The thesis then develops and in a sense completes this theory. In particular, the thesis introduces and studies filtering, and yields key results on the stability and optimality of this new method. While these new results should greatly help in making time-variable sampling methods applicable in practice, the thesis also presents a range of new purely mathematical results. For example, the thesis presents new results that show how to explicitly calculate the eigenvalues of the complete set of self-adjoint extensions of such a symmetric operator in the Hilbert space. This result is of interest in the field of functional analysis where it advances von Neumann's theory of self-adjoint extensions.
Posted in:

Advances in Imaging and Electron Physics

I. Starting Point Sampling theory deals with the reconstruction of ... most famous result in this direction is the Whittaker–Shannon–Kotel'nikov formula, ...

Author: Peter W. Hawkes

Publisher: Elsevier

ISBN: 0080490050

Category: Technology & Engineering

Page: 400

View: 509

Download →

Advances in Imaging and Electron Physics merges two long-running serials--Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.
Posted in:

Progress in Physics vol 3 2013

The Nyquist-Shannon Sampling Theorem is fundamental to the field of information theory, and is well known in digital signal processing and remote sensing ...

Author: Dmitri Rabounski

Publisher: Infinite Study

ISBN:

Category:

Page: 198

View: 233

Download →

The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics
Posted in:

Advances in Mathematics Research

This book presents research from leading scholars throughout the world.

Author: Gabriel Oyibo

Publisher: Nova Publishers

ISBN: 1590332237

Category: Mathematics

Page: 244

View: 609

Download →

This book presents research from leading scholars throughout the world. Contents: Preface; Reduction Theory of Von Neumann Algebras in Real Case; Some Recent Results and Problems for Set-Valued Mappings; On (p, s)-Regularity of the Inversion Problem for the Sturm-Liouville Equation; Spaces of Functions Holomorphic in Convex Bounded Domains of C and Smooth Up to the Boundary; Weak Bilevel Programming Problems: Existence of Solutions; A Remark about the Shannon's Sampling Theorem; Quantum Integral Equations with Kernels of Quantum White Noise in Space and Time; On the Dependence Structure of a System of Components with a Multivariate Shot-Noise Hazard Rate Process; Global Exponential Stability and Periodic Solutions of Cellular Neural Networks (CNN's) with Delays; Some Remarks on the Charged Top; On a Transport Operator Arising in Growing Cell Populations Spectral Analysis; On Viscoelastic Fluids in Elongation; Fuzzy relational Model for Knowledge Processing and Decision Making; Index
Posted in:

Non uniform Sampling

This thesis is dedicated to the exploration of the ways to break through the Shannon-Nyquist sampling rate by applying non-uniform sampling techniques.

Author: Chenchi Luo

Publisher:

ISBN: OCLC:844687197

Category: Algorithms

Page:

View: 389

Download →

Modern signal processing applications emerging in telecommunication and instrumentation industries have placed an increasing demand for ADCs with higher speed and resolution. The most fundamental challenge in such a progress lies at the heart of the classic signal processing: the Shannon-Nyquist sampling theorem which stated that when sampled uniformly, there is no way to increase the upper frequency in the signal spectrum and still unambiguously represent the signal except by raising the sampling rate. This thesis is dedicated to the exploration of the ways to break through the Shannon-Nyquist sampling rate by applying non-uniform sampling techniques. Time interleaving is probably the most intuitive way to parallel the uniform sampling process in order to achieve a higher sampling rate. Unfortunately, the channel mismatches in the TIADC system make the system an instance of a recurrent non-uniform sampling system whose non-uniformities are detrimental to the performance of the system and need to be calibrated. Accordingly, this thesis proposed a flexible and efficient architecture to compensate for the channel mismatches in the TIADC system. As a key building block in the calibration architecture, the design of the Farrow structured adjustable fractional delay filter has been investigated in detail. A new modified Farrow structure is proposed to design the adjustable FD filters that are optimized for a given range of bandwidth and fractional delays. The application of the Farrow structure is not limited to the design of adjustable fractional delay filters. It can also be used to implement adjustable lowpass, highpass and bandpass filters as well as adjustable multirate filters. This thesis further extends the Farrow structure to the design of filters with adjustable polynomial phase responses.\r : \r : Inspired by the theory of compressive sensing, another contribution of this thesis is to use randomization as a means to overcome the limit of the Nyquist rate. This thesis investigates the impact of random sampling intervals or jitters on the power spectrum of the sampled signal. It shows that the aliases of the original signal can be well shaped by choosing an appropriate probability distribution of the sampling intervals or jitters such that aliases can be viewed as a source of noise in the signal power spectrum. A new theoretical framework has been established to associate the probability mass function of the random sampling intervals or jitters with the aliasing shaping effect. Based on the theoretical framework, this thesis proposes three random sampling architectures, i.e., SAR ADC, ramp ADC and level crossing ADC, that can be easily implemented based on the corresponding standard ADC architectures. Detailed models and simulations are established to verify the effectiveness of the proposed architectures. A new reconstruction algorithm called the successive sine matching pursuit has also been proposed to recover a class of spectrally sparse signals from a sparse set of non-uniform samples onto a denser uniform time grid so that classic signal processing techniques can be applied afterwards.
Posted in:

Advances in Instrumentation Vol 26

This limitation is caused by the aliasing effect that sampling has on the signal . ... by the Shannon Sampling Theorem ( 1 ) which says that if the sampling ...

Author:

Publisher:

ISBN: 0876641575

Category:

Page:

View: 196

Download →

Posted in:

Simulation of Communication Systems

Modeling, Methodology and Techniques Michel C. Jeruchim, Philip Balaban, K. Sam Shanmugan ... A. I. Zayed, Advances in Shannon's Sampling Theory, CRC Press, ...

Author: Michel C. Jeruchim

Publisher: Springer Science & Business Media

ISBN: 9780306462672

Category: Technology & Engineering

Page: 907

View: 170

Download →

Since the first edition of this book was published seven years ago, the field of modeling and simulation of communication systems has grown and matured in many ways, and the use of simulation as a day-to-day tool is now even more common practice. With the current interest in digital mobile communications, a primary area of application of modeling and simulation is now in wireless systems of a different flavor from the `traditional' ones. This second edition represents a substantial revision of the first, partly to accommodate the new applications that have arisen. New chapters include material on modeling and simulation of nonlinear systems, with a complementary section on related measurement techniques, channel modeling and three new case studies; a consolidated set of problems is provided at the end of the book.
Posted in:

Multiresolution Multirate Signal Processing

A. I. Zayed, Advances in Shannon's Sampling Theory, CRC Press, 1993. A. K. Louis, P. Maass, and A. Rieder, Wavelets: Theory and applications, John Wiley, ...

Author: Gadre

Publisher: McGraw-Hill Education

ISBN: 9789352601455

Category:

Page:

View: 268

Download →

N/A
Posted in:

Sampling Theory

A comprehensive guide to sampling for engineers, covering the fundamental mathematical underpinnings together with practical engineering principles and applications.

Author: Yonina C. Eldar

Publisher: Cambridge University Press

ISBN: 9781107003392

Category: Computers

Page: 836

View: 905

Download →

A comprehensive guide to sampling for engineers, covering the fundamental mathematical underpinnings together with practical engineering principles and applications.
Posted in:

Advances in Imaging and Electron Physics

Figure 1 Diagram showing the sampling process of a continuous functionf with a ... WNKS sampling theorem states as follows (original quote from Shannon ...

Author:

Publisher: Academic Press

ISBN: 9780323850971

Category: Technology & Engineering

Page: 340

View: 824

Download →

Advances in Imaging and Electron Physics, Volume 219, merges two long-running serials, Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science, digital image processing, electromagnetic wave propagation, electron microscopy and the computing methods used in all these domains. Contains contributions from leading authorities on the subject matter Informs and updates on the latest developments in the field of imaging and electron physics Provides practitioners interested in microscopy, optics, image processing, mathematical morphology, electromagnetic fields, electrons and ion emission with a valuable resource Features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing
Posted in:

Spherical Sampling

This book presents, in a consistent and unified overview, results and developments in the field of today ́s spherical sampling, particularly arising in mathematical geosciences.

Author: Willi Freeden

Publisher: Birkhäuser

ISBN: 9783319714585

Category: Mathematics

Page: 596

View: 926

Download →

This book presents, in a consistent and unified overview, results and developments in the field of today ́s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.
Posted in: