Subspace fitting approaches for frequency estimation using real-valued data

Mahata, Kaushik

doi:10.1109/tsp.2005.851129

Cited by 19 publications

(10 citation statements)

References 15 publications

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“…In particular, the digital signal can be represented according to: (10) in which I 0 satisfies the constraint 2 0 I 0 =  + n2 for an unknown integer n, and ∆ is much smaller than   . From equation (10) it follows that: (11) and, in the hypothesis that the frequency error  is small:…”

Section: Analysis Of the Effects Of A Frequency Errormentioning

confidence: 99%

Least square procedures to improve the results of the three-parameter sine fitting algorithm

et al. 2015

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The paper presents two approaches to improve the three parameter sine fitting algorithm and attain accurate estimates of the parameters of a sinusoidal signal corrupted by noise. As the four parameter sine fitting algorithm, which is usually adopted to improve the estimates of the three parameter algorithm, in theory, the proposed ones can be inserted into iterative schemes and repeated until a target precision is gained. Anyway, the use of the proposed algorithms is particularly suggested for those applications in which the results must be gained in very short times, which are in contrast to long iterative procedures. In these cases, when a single run of the algorithms has to offer the required improvement, the proposed ones are valid alternatives with respect to the four parameter algorithm, sharing with it almost comparable accuracy.

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Section: Analysis Of the Effects Of A Frequency Errormentioning

confidence: 99%

Least square procedures to improve the results of the three-parameter sine fitting algorithm

et al. 2015

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“…To obtain frequencies of sinusoids, there are numerous methods proposed in the literature. Among these methods, one famous solution branch is based on subspace properties such as multiple signal classification (MUSIC) [15][16][17][18][19], estimation of signal parameters via rotational invariance techniques (ESPRIT) [20][21][22], and other eigendecomposition-based methods [23,24]. Although the MUSIC method provides good estimation, it requires pseudospectral peaks searching procedure, which is computationally intensive and time consuming.…”

Section: Introductionmentioning

confidence: 99%

Novel subspace method for frequencies estimation of two sinusoids with applications to vital signals

Chen

Lin

2017

IET signal process.

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This study proposes a novel subspace method to estimate frequencies of two sinusoids embedded in noise. The estimation process is basically composed of three main steps. Two principal eigenvectors of the autocorrelation matrix for the received vector are first found. Then, the authors use the elements of these eigenvectors to form a set of linear and non-linear equations to solve an ambiguous matrix linked two signal subspaces which contain the information of frequencies. With the product of the matrix formed from these two eigenvectors and the solved ambiguous matrix, they can finally find the frequencies. In addition, they also combine an interleaving technique with the proposed method to improve the estimation performance for two close sinusoidal frequencies. Simulation results for synthetic data and practical vital signals are used to demonstrate the performance of the proposed method. The demonstrated results show that the proposed method is feasible for frequencies estimation of two sinusoids, and it can be applied to the case of very close sinusoidal frequencies.

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“…Interestingly, the problem of taking the nature of real signals into account has been addressed in the frequency estimation literature, i.e., for the case where sinusoids are not constrained to being integer multiples of a fundamental frequency. Some examples of adaptations of well-known estimators to this problem are for maximum likelihood methods [21], [22], subspace methods [23], [24], Capon's method [25], and the linear prediction [26] method.…”

Section: Introductionmentioning

confidence: 99%

Accurate Estimation of Low Fundamental Frequencies From Real-Valued Measurements

Christensen

2013

IEEE Trans. Audio Speech Lang. Process.

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In this paper, the difficult problem of estimating low fundamental frequencies from real-valued measurements is addressed. The methods commonly employed do not take the phenomena encountered in this scenario into account and thus fail to deliver accurate estimates. The reason for this is that they employ asymptotic approximations that are violated when the harmonics are not well-separated in frequency, something that happens when the observed signal is real-valued and the fundamental frequency is low. To mitigate this, we analyze the problem and present some exact fundamental frequency estimators that are aimed at solving this problem. These estimators are based on the principles of nonlinear least-squares, harmonic fitting, optimal filtering, subspace orthogonality, and shift-invariance, and they all reduce to already published methods for a high number of observations. In experiments, the methods are compared and the increased accuracy obtained by avoiding asymptotic approximations is demonstrated.

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Subspace fitting approaches for frequency estimation using real-valued data

Cited by 19 publications

References 15 publications

Least square procedures to improve the results of the three-parameter sine fitting algorithm

Least square procedures to improve the results of the three-parameter sine fitting algorithm

Novel subspace method for frequencies estimation of two sinusoids with applications to vital signals

Accurate Estimation of Low Fundamental Frequencies From Real-Valued Measurements

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