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Conjugate Duality and the Exponential Fourier Spectrum

  • Authors
  • Wray Britton

Part of the Lecture Notes in Statistics book series (LNS, volume 18)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Wray Britton
    Pages 1-16
  3. Wray Britton
    Pages 17-20
  4. Wray Britton
    Pages 26-27
  5. Wray Britton
    Pages 42-45
  6. Wray Britton
    Pages 50-58
  7. Wray Britton
    Pages 59-62
  8. Wray Britton
    Pages 63-90
  9. Wray Britton
    Pages 91-91
  10. Back Matter
    Pages 92-226

About this book

Introduction

For some fields such as econometrics (Shore, 1980), oil prospecting (Claerbout, 1976), speech recognition (Levinson and Lieberman, 1981), satellite monitoring (Lavergnat et al., 1980), epilepsy diagnosis (Gersch and Tharp, 1977), and plasma physics (Bloomfield, 1976), there is a need to obtain an estimate of the spectral density (when it exists) in order to gain at least a crude understanding of the frequency content of time series data. An outstanding tutorial on the classical problem of spectral density estimation is given by Kay and Marple (1981). For an excellent collection of fundamental papers dealing with modern spec­ tral density estimation as well as an extensive bibliography on other fields of application, see Childers (1978). To devise a high-performance sample spectral density estimator, one must develop a rational basis for its construction, provide a feasible algorithm, and demonstrate its performance with respect to prescribed criteria. An algorithm is certainly feasible if it can be implemented on a computer, possesses computational efficiency (as measured by compu­ tational complexity analysis), and exhibits numerical stability. An estimator shows high performance if it is insensitive to violations of its underlying assumptions (i.e., robust), consistently shows excellent frequency resolutipn under realistic sample sizes and signal-to-noise power ratios, possesses a demonstrable numerical rate of convergence to the true population spectral density, and/or enjoys demonstrable asymp­ totic statistical properties such as consistency and efficiency.

Keywords

Duality Dualität (Math.) Estimator Excel Harmonische Analyse Sequentialanalyse Stochastische Approximation

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5528-4
  • Copyright Information Springer-Verlag New York 1983
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90826-7
  • Online ISBN 978-1-4612-5528-4
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site