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6829 results in Communications and signal processing

Page 109 of 342

  • 15 - More on Zeros

  • from Part II - Geometry and Statistics
  • Patrick Flandrin
  • Book:
    Explorations in Time-Frequency Analysis
    Published online:
    22 August 2018
    Print publication:
    06 September 2018, pp 139-167

  • Summary

    Thanks to its Bargmann representation, a Gaussian STFT can be factorized so as to be described by its zeros. This paves the way for a new approach that exploits the (usually ignored) zeros of the transform. Zeros can serve as centers for Voronoi cells whose statistics is investigated in terms of density, area, and shape. They can also be connected via a Delaunay triangulation, whose characterization in the noise-only situation permits, a contrario, to identify signals embedded in noise from “silent” points.

Explorations in Time-Frequency Analysis
  • Patrick Flandrin
  • Published online:
    22 August 2018
    Print publication:
    06 September 2018
  • An authoritative exposition of the methods at the heart of modern non-stationary signal processing from a recognised leader in the field. Offering a global view that favours interpretations and historical perspectives, it explores the basic concepts of time-frequency analysis, and examines the most recent results and developments in the field in the context of existing, lesser-known approaches. Several example waveform families from bioacoustics, mathematics and physics are examined in detail, with the methods for their analysis explained using a wealth of illustrative examples. Methods are discussed in terms of analysis, geometry and statistics. This is an excellent resource for anyone wanting to understand the 'why and how' of important methodological developments in time-frequency analysis, including academics and graduate students in signal processing and applied mathematics, as well as application-oriented scientists.

Essentials of Digital Signal Processing
  • B. P. Lathi, Roger A. Green
  • Published online:
    28 May 2018
    Print publication:
    28 April 2014
  • This textbook offers a fresh approach to digital signal processing (DSP) that combines heuristic reasoning and physical appreciation with sound mathematical methods to illuminate DSP concepts and practices. It uses metaphors, analogies and creative explanations, along with examples and exercises to provide deep and intuitive insights into DSP concepts. Practical DSP requires hybrid systems including both discrete- and continuous-time components. This book follows a holistic approach and presents discrete-time processing as a seamless continuation of continuous-time signals and systems, beginning with a review of continuous-time signals and systems, frequency response, and filtering. The synergistic combination of continuous-time and discrete-time perspectives leads to a deeper appreciation and understanding of DSP concepts and practices. For upper-level undergraduatesIllustrates concepts with 500 high-quality figures, more than 170 fully worked examples, and hundreds of end-of-chapter problems, more than 150 drill exercises, including complete and detailed solutionsSeamlessly integrates MATLAB throughout the text to enhance learning

Communication Theory
  • Charles M. Goldie, Richard G. E. Pinch
  • Published online:
    28 May 2018
    Print publication:
    07 November 1991
  • This book is an introduction, for mathematics students, to the theories of information and codes. They are usually treated separately but, as both address the problem of communication through noisy channels (albeit from different directions), the authors have been able to exploit the connection to give a reasonably self-contained treatment, relating the probabilistic and algebraic viewpoints. The style is discursive and, as befits the subject, plenty of examples and exercises are provided. Some examples and exercises are provided. Some examples of computer codes are given to provide concrete illustrations of abstract ideas.

Foundations of Signal Processing
  • Martin Vetterli, Jelena Kovačević, Vivek K Goyal
  • Published online:
    28 May 2018
    Print publication:
    04 September 2014
  • This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.

Introduction to Communication Systems
  • Upamanyu Madhow
  • Published online:
    28 May 2018
    Print publication:
    24 November 2014
  • Showcasing the essential principles behind modern communication systems, this accessible undergraduate textbook provides a solid introduction to the foundations of communication theory. Carefully selected topics introduce students to the most important and fundamental concepts, giving students a focused, in-depth understanding of core material, and preparing them for more advanced study. Abstract concepts are introduced to students 'just in time' and reinforced by nearly 200 end-of-chapter exercises, alongside numerous MATLAB code fragments, software problems and practical lab exercises, firmly linking the underlying theory to real-world problems, and providing additional hands-on experience. Finally, an accessible lecture-style organisation makes it easy for students to navigate to key passages, and quickly identify the most relevant material. Containing material suitable for a one- or two-semester course, and accompanied online by a password-protected solutions manual and supporting instructor resources, this is the perfect introductory textbook for undergraduate students studying electrical and computer engineering.

Stochastic Processes
  • Theory for Applications
  • Robert G. Gallager
  • Published online:
    28 May 2018
    Print publication:
    12 December 2013
  • This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.

Random Processes for Engineers
  • Bruce Hajek
  • Published online:
    11 May 2018
    Print publication:
    12 March 2015
  • This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include:Calculus of random processes in linear systemsKalman and Wiener filteringHidden Markov models for statistical inferenceThe estimation maximization (EM) algorithmAn introduction to martingales and concentration inequalities.Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).

  • Concluding Remarks

  • Bartłomiej Błaszczyszyn, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt, Martin Haenggi, University of Notre Dame, Indiana, Paul Keeler, Sayandev Mukherjee
  • Book:
    Stochastic Geometry Analysis of Cellular Networks
    Published online:
    26 March 2018
    Print publication:
    19 April 2018, pp 168-169

  • Summary

    Future wireless deployments will increasingly rely on HetNets to satisfy society's demands for high data rates coupled with high cell capacities. We argue that the design and deployment of such HetNets present many challenges, which, because of the much larger space of system deployment parameters relative to a single-tier network, cannot be feasibly addressed by the traditional approaches of measurement and simulation alone.

    We show that techniques and results from stochastic geometry can relieve system designers from the burden of having to perform exhaustive simulations of all feasible combinations of deployment parameters, because they yield analytical results for key performance metrics such as coverage probability, thereby permitting (a) a uniform comparison across architectures and (b) quick rejection of certain combinations of deployment parameters without needing to simulate their performance. These theoretical results are illustrated with examples of their application to transmission scenarios specified in the LTE standard.

    These analytical results for coverage probability have, until now, mostly been derived for independent Poisson deployments of base stations in tiers, a scenario for which there are tractable derivations of exact expressions. Although it is well known that real-world base station deployments do not behave like Poisson deployments, we show that the Poisson model is nonetheless fundamental to an analytical treatment of all deployments, for the following reasons: (a) the set of propagation losses to the typical location in an arbitrary network deployment converge asymptotically to that from a Poisson deployment of base stations and (b) long before this asymptotic limit is reached, the coverage results for a Poisson deployment can be employed to obtain very accurate approximations to the coverage results for various regular deployments. The present work is the first book-length treatment of these results.

    We also provide the first book-level exposition of exact results on coverage for certain non-Poisson deployment models that are analytically tractable. Such models include the Ginibre point process and determinantal point processes. We also discuss the challenges of understanding and evaluating the complex analytical expressions so obtained.

    For future work, in addition to stochastic geometry and point process theory covered in this book, other tools from probability may also be employed to analyze cellular networks.

  • 2 - The Role of Stochastic Geometry in HetNet Analysis

  • from Part I - Stochastic Geometry
  • Bartłomiej Błaszczyszyn, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt, Martin Haenggi, University of Notre Dame, Indiana, Paul Keeler, Sayandev Mukherjee
  • Book:
    Stochastic Geometry Analysis of Cellular Networks
    Published online:
    26 March 2018
    Print publication:
    19 April 2018, pp 13-17

  • Summary

    In Chapter 1, Section 1.8, we list several important and general analytical results for single-tier networks and multitier HetNets that were derived using results from stochastic geometry. Of course, the value of analytical results in yielding insights to help network design has long been recognized by the industry. Stochastic geometric approaches are only the latest, and by far the most successful, of a long line of analytical approaches that began almost immediately after the first “cellular” models for wireless communication were proposed. Before commencing a detailed study of stochastic geometry, it is useful to take a step back and examine competing analytical approaches to get a better idea of why stochastic geometric approaches achieved greater success. To do so, let us revisit the origins of the now-canonical hexagonal cell model.

    The Hexagonal Cellular Concept

    The earliest proposals for wireless coverage via hexagonal “cells” date back to 1947, even before the principles of information theory were published by Shannon in 1948. A more up-to-date overview of the cellular concept may be found in MacDonald's 1979 paper (MacDonald 1979), applied to what is now considered the “first-generation” or “1G” cellular standard, advanced mobile phone service. MacDonald's carefully reasoned rationale for the hexagonal cellular model bears reading even today:

  • He acknowledged that a practical cellular deployment would contain cells of different shapes and sizes (owing to topographic obstacles, restricted rights-ofway, etc.), but made the reasonable argument that systematization of the design and layout of a cellular system is greatly aided by modeling all cells of the system as having the same shape.

  • At the time MacDonald wrote his paper, cellular base stations transmitted using omnidirectional antennas. This in turn means that the boundary of the coverage region of a base station is circular. In other words, omnidirectional transmitting antennas at the base stations mean circular disk-shaped cells.

  • Unfortunately, circular disks do not tile (meaning, cover completely, without overlaps or gaps) the two-dimensional plane.

  • Three shapes that do tile the plane are equilateral triangles, squares, and (regular) hexagons.

  • For each of these three shapes, and with the base station located at the center of a cell with that shape, the farthest point within the cell is a vertex of that shape.

Page 109 of 342