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  • Conference proceedings
  • © 2000

Noise, Oscillators and Algebraic Randomness

From Noise in Communication Systems to Number Theory

Editors:

  • The book is an original attempt to connect the noise in experimental physics (electronic oscillators, receivers...) to arithmetic
  • Several forms of noise are covered: classical and quantum noise, phase noise, 1/f noise
  • Concrete applications of analytical number theory are also provided
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics (LNP, volume 550)

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Table of contents (22 papers)

  1. Front Matter

    Pages I-VIII
  2. Introduction

    • Michel Planat
    Pages 1-5
  3. Mathemagics

    • Pierre Cartier
    Pages 6-67
  4. Thermal and Quantum Noise in Active Systems

    • Jean-Michel Courty, Francesca Grassia, Serge Reynaud
    Pages 71-83
  5. Dipole at ν = 1

    • V. Pasquier
    Pages 84-106
  6. 1/f Fluctuations in Cosmic Ray Extensive Air Showers

    • E. Faleiro, J.M.G. GĂ³mez
    Pages 125-136
  7. Stochastic Resonance and the Benefit of Noise in Nonlinear Systems

    • François Chapeau-Blondeau
    Pages 137-155
  8. Time is Money

    • Marcel Ausloos, Nicolas Vandewalle, Kristinka Ivanova
    Pages 156-171
  9. Phase Noise Metrology

    • Enrico Rubiola, Vincent Giordano
    Pages 189-215
  10. Geometry and Dynamics of Numbers Under Finite Resolution

    • Jacky Cresson, Jean-Nicolas DĂ©nariĂ©
    Pages 305-323
  11. Diophantine Conditions and Real or Complex Brjuno Functions

    • Pierre Moussa, Stefano Marmi
    Pages 324-342
  12. Algebraic and Analytic Randomness

    • Jean-Paul Allouche
    Pages 345-356
  13. Algebraic Dynamics and Transcendental Numbers

    • Michel Waldschmidt
    Pages 372-378

About this book

Noise is ubiquitous in nature and in man-made systems. Noise in oscillators perturbs high-technology devices such as time standards or digital communication systems. The understanding of its algebraic structure is thus of vital importance. The book addresses both the measurement methods and the understanding of quantum, 1/f and phase noise in systems such as electronic amplifiers, oscillators and receivers, trapped ions, cosmic ray showers and in commercial applications. A strong link between 1/f noise and number theory is emphasized. The twenty papers in the book are comprehensive versions of talks presented at a school in Chapelle des Bois (Jura, France) held from April 6 to 10, 1999, by engineers, physisicts and mathematicians.

Editors and Affiliations

  • Laboratoire de Physique et Merologie, des Oscillateurs du CNRS, Besançon Cedex, France

    Michel Planat

Bibliographic Information

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access