Estimating parameters in noisy low frequency exponentially damped sinusoids and exponentials

Barry G. Quinn

doi:10.1109/ICASSP.2016.7472488

Estimating parameters in noisy low frequency exponentially damped sinusoids and exponentials

Barry G. Quinn^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

6 Citations (Scopus)

Abstract

There has been much recent interest in damped sinusoidal models, probably as a result of their relevance to magnetic resonance imaging. In [1], a model which allowed the sinusoid to decay to 0 was examined, and a Fourier coefficient estimation procedure was proposed. [2] noted that in order for any asymptotic theory to be available, the decay should not be allowed to complete, and examined the asymptotic behavior of a Fourier coefficient procedure based on this assumption, for which the asymptotic behavior ofnonlinear least squares estimators had already been derived in [3]. In this paper, we consider the problem of estimating the frequency and damping factor when the frequency is so low that only a finite number of periods appear in the data. Additionally, we consider a Fourier technique for estimating the damping factor in a noisy real exponential.

Original language	English
Title of host publication	2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
Place of Publication	Piscataway, NJ
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	4298-4302
Number of pages	5
Volume	2016-May
ISBN (Electronic)	9781479999880
DOIs	https://doi.org/10.1109/ICASSP.2016.7472488
Publication status	Published - 18 May 2016
Event	41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China Duration: 20 Mar 2016 → 25 Mar 2016

Other

Other	41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Country/Territory	China
City	Shanghai
Period	20/03/16 → 25/03/16

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10.1109/ICASSP.2016.7472488

Cite this

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title = "Estimating parameters in noisy low frequency exponentially damped sinusoids and exponentials",

abstract = "There has been much recent interest in damped sinusoidal models, probably as a result of their relevance to magnetic resonance imaging. In [1], a model which allowed the sinusoid to decay to 0 was examined, and a Fourier coefficient estimation procedure was proposed. [2] noted that in order for any asymptotic theory to be available, the decay should not be allowed to complete, and examined the asymptotic behavior of a Fourier coefficient procedure based on this assumption, for which the asymptotic behavior ofnonlinear least squares estimators had already been derived in [3]. In this paper, we consider the problem of estimating the frequency and damping factor when the frequency is so low that only a finite number of periods appear in the data. Additionally, we consider a Fourier technique for estimating the damping factor in a noisy real exponential.",

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Quinn, BG 2016, Estimating parameters in noisy low frequency exponentially damped sinusoids and exponentials. in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings. vol. 2016-May, 7472488, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 4298-4302, 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016, Shanghai, China, 20/03/16. https://doi.org/10.1109/ICASSP.2016.7472488

Estimating parameters in noisy low frequency exponentially damped sinusoids and exponentials. / Quinn, Barry G.
2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings. Vol. 2016-May Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2016. p. 4298-4302 7472488.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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Estimating parameters in noisy low frequency exponentially damped sinusoids and exponentials

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