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Performance Evaluation of Gibbs Sampling for Bayesian Extracting Sinusoids

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Computational Problems in Engineering

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 307))

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Abstract

This chapter involves problems of estimating parameters of sinusoids from white noisy data by using Gibbs sampling (GS) in a Bayesian inferential framework which allows us to incorporate prior knowledge about the nature of sinusoidal data into the model. Modifications of its algorithm is tested on data generated from synthetic signals and its performance is compared with conventional estimators such as Maximum Likelihood (ML) and Discrete Fourier Transform (DFT) under a variety of signal to noise ratio (SNR) conditions and different lengths of data sampling (N), regarding to Cramér–Rao lower bound (CRLB) that is a limit on the best possible performance achievable by an unbiased estimator given a dataset. All simulation results show its effectiveness in frequency and amplitude estimation of noisy sinusoids.

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Acknowledgements

This work has been supported by the Research Fund of Istanbul University with project numbers are UDP-33672 and YADOP-19681.

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, Istanbul University, Istanbul, Turkey

    M. Cevri

  2. Faculty of Science and Letters, Department of Mathematics, Marmara University, Istanbul, Turkey

    D. Üstündag

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  1. M. Cevri
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  2. D. Üstündag
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Correspondence to M. Cevri .

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Editors and Affiliations

  1. Technical University of Sofia, Sofia, Bulgaria

    Nikos Mastorakis

  2. Technical University of Sofia, Sofia, Bulgaria

    Valeri Mladenov

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Cevri, M., Üstündag, D. (2014). Performance Evaluation of Gibbs Sampling for Bayesian Extracting Sinusoids. In: Mastorakis, N., Mladenov, V. (eds) Computational Problems in Engineering. Lecture Notes in Electrical Engineering, vol 307. Springer, Cham. https://doi.org/10.1007/978-3-319-03967-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-03967-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03966-4

  • Online ISBN: 978-3-319-03967-1

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