Iterative frequency estimation by interpolation on Fourier coefficients

Aboutanios, Elias; Mulgrew, Bernie

doi:10.1109/tsp.2005.843719

Cited by 388 publications

(273 citation statements)

References 12 publications

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“…Approaches to refining the coarse estimate can be divided into iterative approaches and direct approaches [27]. Iterative approaches (e.g., [29]) involve multiple rounds of function evaluations or a series of DTFT evaluations that narrow in on the solution. Direct methods form the estimate (K,X ) using a single function evaluation on…”

Section: Estimating Sinusoidal Parameters From 3 Bins Of Spectrummentioning

confidence: 99%

Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

Werner

Germain

2016

Applied Sciences

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Abstract:The magnitude of the Discrete Fourier Transform (DFT) of a discrete-time signal has a limited frequency definition. Quadratic interpolation over the three DFT samples surrounding magnitude peaks improves the estimation of parameters (frequency and amplitude) of resolved sinusoids beyond that limit. Interpolating on a rescaled magnitude spectrum using a logarithmic scale has been shown to improve those estimates. In this article, we show how to heuristically tune a power scaling parameter to outperform linear and logarithmic scaling at an equivalent computational cost. Although this power scaling factor is computed heuristically rather than analytically, it is shown to depend in a structured way on window parameters. Invariance properties of this family of estimators are studied and the existence of a bias due to noise is shown. Comparing to two state-of-the-art estimators, we show that an optimized power scaling has a lower systematic bias and lower mean-squared-error in noisy conditions for ten out of twelve common windowing functions.

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Section: Estimating Sinusoidal Parameters From 3 Bins Of Spectrummentioning

confidence: 99%

Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

Werner

Germain

2016

Applied Sciences

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“…The ACT derived in the previous section yields a pure exponential, simplifying the signal model and permitting the use of any pure tone frequency estimators, such as those of [5], [6] for the power system frequency estimation. This, however, requires that the amplitudes of the individual phases are known.…”

Section: A Practical Frequency Estimation Algorithmmentioning

confidence: 99%

“…The optimal transformation is then given by the traditional CT of (5). Under this assumption, we apply the CT and proceed, using the FIID algorithm, to obtain an estimate,f , of the system frequency.…”

Section: A Practical Frequency Estimation Algorithmmentioning

confidence: 99%

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An adaptive Clarke transform based estimator for the frequency of balanced and unbalanced three-phase power systems

Aboutanios

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-In this paper we examine the general problem of estimating the frequency of a balanced or unbalanced three-phase power system. The Clarke transform is commonly employed to transform the three real voltages to in-phase and quadrature components that are combined to form a complex exponential, the frequency of which can then be estimated. The imbalance between the voltages in an unbalanced system results in significant performance degradation. We address this problem by generalising the Clarke transformation to the case where the voltages are not equal. We then propose a new simple yet accurate algorithm for the estimation of the frequency. We simulate the algorithm and show that it achieves the performance that is obtained in the balanced case, practically sitting on the Cramér-Rao Bound.

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“…The literature [4] explains the interpolation iterative algorithm based on Fourier coefficient. Through preliminarily estimating the position of spectral peak in FFT operation, and then using iterative calculation to calculate the FFT coefficients front and rear the peak position, this algorithm can improve measurement precision as a result.…”

Section: Common Interpolation Algorithmmentioning

confidence: 99%

Design and implementation of an airborne improved radio frequency measuring instrument based on FPGA

Wei¹

2015

Advances in Intelligent Systems Research

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According to short wave radio signal of a certain active airborne frequency measurement instrument part device still adopts pure hardware building mode and acquisition data scattered, leading to large volume, monitoring performance is limited, the real-time problem, low accuracy and can not upgrade the system corresponding to the complex environment. A new algorithm is proposed based on the FPGA parallel processing advantages. The algorithm is in the FFT frequency estimation based on serial iterative algorithm modified for parallel computing, and the feasibility of the algorithm is verified by simulation. Hardware part, the system integrates the CPU and FPGA into a chip, greatly reduces the equipment size and development time and uses high speed 14 bit A/D 125MHz data acquisition to improve the precision of frequency measurement. Many experiments show that each module design is reasonable, the system runs stably, Compared with the original instrument of frequency measurement accuracy is improved more than 1 times, the system response time is reduced to 0.1s~0.2s, and provide effective data for real-time monitoring and fault detection of radio frequency radio signal. The measuring instrument has been successfully applied to the corresponding forces equipment examination.

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Iterative frequency estimation by interpolation on Fourier coefficients

Cited by 388 publications

References 12 publications

Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

An adaptive Clarke transform based estimator for the frequency of balanced and unbalanced three-phase power systems

Design and implementation of an airborne improved radio frequency measuring instrument based on FPGA

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