Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Browse subjects
  3. Engineering
  4. Communications and signal processing
  5. Content listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

6385 results in Communications and signal processing

Page 90 of 320

  • 6 - From Time and Frequency to Time-Frequency

  • from Part I - Basics and Constraints
  • Patrick Flandrin
  • Book:
    Explorations in Time-Frequency Analysis
    Published online:
    22 August 2018
    Print publication:
    06 September 2018, pp 40-49

  • Summary

    The simplest and most intuitive time-frequency transforms are the Short-Time Fourier Transform (STFT) and the associated spectrogram (squared STFT), which are in close connection with the Gabor transform when using a Gaussian window. Given a 1D signal, its STFT is a 2D function whose redundancy is controlled by a reproducing kernel. This kernel can be equivalently seen as an ambiguity function, i.e., a 2D time-frequency correlation function that is constrained by uncertainty. Building upon the classical duality which exists between “correlation functions” and “energy distributions,” we end up with the Wigner distribution as a central tool for time-frequency signal analysis. The Wigner distribution happens however to be a member of larger classes (such as Cohen's) to which the spectrogram belongs too.

  • 8 - On Stationarity

  • from Part I - Basics and Constraints
  • Patrick Flandrin
  • Book:
    Explorations in Time-Frequency Analysis
    Published online:
    22 August 2018
    Print publication:
    06 September 2018, pp 56-66

  • Summary

    Stationarity is a central concept in time-frequency analysis, but its formal definition in terms of global time-shift invariance is demanding, callingfor a more operational viewpoint that better matches intuition and common practice. A concept of relative stationarity is proposed, which not only makes the observation time-scale enter the picture but also permits to test for stationarity.

  • 11 - A Digression on the Hilbert–Huang Transform

  • 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 98-105

  • Summary

    Rather than considering the disentanglement of multicomponent nonstationary signals as a time-frequency post-processing, a possibility is to first decompose the observation into modes that are amenable to some further demodulations. In this spirit, this chapter reviews a technique that has recently gained popularity, namely “Empirical Mode Decomposition” and the associated “Hilbert-Huang Transform.” The rationale of those data-driven methods is presented, as well as their actual implementation, with a brief discussion of pros and cons with respect to more conventional time-frequency analysis.

  • 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.

  • 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 90 of 320