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The Estimation and Tracking of Frequency

£41.99

Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: January 2013
  • availability: Available
  • format: Paperback
  • isbn: 9781107412859

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  • Many electronic and acoustic signals can be modelled as sums of sinusoids and noise. However, the amplitudes, phases and frequencies of the sinusoids are often unknown and must be estimated in order to characterise the periodicity or near-periodicity of a signal and consequently to identify its source. This book presents and analyses several practical techniques used for such estimation. The problem of tracking slow frequency changes over time of a very noisy sinusoid is also considered. Rigorous analyses are presented via asymptotic or large sample theory, together with physical insight. The book focuses on achieving extremely accurate estimates when the signal to noise ratio is low but the sample size is large. Each chapter begins with a detailed overview, and many applications are given. Matlab code for the estimation techniques is also included. The book will thus serve as an excellent introduction and reference for researchers analysing such signals.

    • Very detailed summary of the field (methods for measuring periodicity of signals)
    • Contains Matlab code for implementing the techniques discussed
    • Many applications treated
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    Reviews & endorsements

    'The authors show complete technical mastery of their subject and of the mathematical methods required … contains a considerable amount which is new, both conceptually and in a mathematical tightening-up of earlier work and gives a full and modern account of its subject … a full, clear and authoritative account which certainly advances the current stage of the subject. The text is to be firmly recommended to time series analysts, actual and aspiring, and to the more mathematically valiant of the engineers.' P. Whittle, Journal of Time Series Analysis

    '… the book is a valuable and detailed quality reference source…' A. T. Walden, Short Book Reviews

    'Quinn and Hannan's book … breaks new ground … This book fulfils a role … as a high-quality expository monograph.' Malcolm D. MacLeod, International Journal of Robust and Nonlinear Control

    '… I feel that this book will help all users who are graduates taking an advanced statistics or mathematics course in conjunction with communications systems.' Journal of the Royal Statistical Society

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    Product details

    • Date Published: January 2013
    • format: Paperback
    • isbn: 9781107412859
    • length: 280 pages
    • dimensions: 254 x 178 x 15 mm
    • weight: 0.49kg
    • availability: Available
  • Table of Contents

    Preface
    1. Introduction
    2. Statistical and probabilistic methods
    3. The estimation of a fixed frequency
    4. Techniques derived from ARMA modelling
    5. Estimation using Fourier coefficients
    6. Tracking frequency in low SNR conditions
    7. Other estimation techniques
    References
    Appendix. Matlab programs
    Author index
    Subject index.

  • Authors

    B. G. Quinn, University of Manchester

    E. J. Hannan

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