Phase correction of discrete Fourier transform coefficients to reduce frequency estimation bias of single tone complex sinusoid

Liao, Jan‐Ray; Chen, Chun‐Ming

doi:10.1016/j.sigpro.2013.05.021

Cited by 37 publications

(30 citation statements)

References 22 publications

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“…A typical engineering solution is to refine this coarse estimate by a fine search over ±0.5 bins around this peak [2,14,15,18,27,28]. Approaches to refining the coarse estimate can be divided into iterative approaches and direct approaches [27].…”

Section: Estimating Sinusoidal Parameters From 3 Bins Of Spectrummentioning

confidence: 99%

“…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.…”

Section: Estimating Sinusoidal Parameters From 3 Bins Of Spectrummentioning

confidence: 99%

“…Abe and Smith report correction functions for the LQIFFT [30] and Werner proposes magnitude and bin correction functions for the XQIFFT [20]. As we are focused solely on direct methods, a discussion of the particular form or performance of XQIFFT correction functions is outside the scope of this article since correction functions are considered to be iterative methods [27]. …”

Section: Correction Functionsmentioning

confidence: 99%

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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%

Section: Estimating Sinusoidal Parameters From 3 Bins Of Spectrummentioning

confidence: 99%

Section: Correction Functionsmentioning

confidence: 99%

See 1 more Smart Citation

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

Werner

Germain

2016

Applied Sciences

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“…These effects will lead to significant errors in spectral analysis such as parameter estimation [2,3]. In order to obtain accurate estimates of signal parameters, a lot of solutions were proposed [4][5][6][7][8][9][10][11][12][13][14]. The interpolation discrete Fourier transform (IpDFT) algorithm is one of the most popular algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, simple analytical solutions can be obtained when the maximum sidelobe decay windows (MSDW, also known as Rife-Vincent class I windows) are adopted [11]. However, the algorithms mentioned above are all established on a very important assumption that the leakage coming from the image component plays a minor role and could be ignored [11][12][13]. In fact, if signals contain a small number of cycles, the negative frequency component usually will exercise great influences on the estimators [15].…”

Section: Introductionmentioning

confidence: 99%

Generalization of interpolation DFT algorithms and frequency estimators with high image component interference rejection

Luo

Hou

Ouyang

et al. 2016

EURASIP J. Adv. Signal Process.

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This paper focuses on the problem of frequency estimation of noise-contaminated sinusoidal. A basic tool to solve this problem is the interpolated discrete Fourier transform (DFT) algorithms, in which the influences of the spectral leakage from negative frequency are often neglected, resulting in significant errors in estimation when the signals contained small cycles. In this paper, analytic expressions of the interference due to the image component are derived and its influences on the traditional two-point interpolated DFT algorithms are analyzed. Based on the achieved expressions, the interpolated DFT algorithms are generalized and a novel frequency estimator with high image component interference rejection is proposed. Simulation results show that the frequency errors returned by the new algorithm are very small even though only one or two cycles are obtained. Comparative studies indicate that the new algorithm also has a good performance in the noise condition. With the advantages of high precision and strong robustness against additive noise, the proposed algorithm is a good choice for frequency estimation when the negative frequency interference is the dominant error source.

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Efficient Parameter Estimation

2022

Joint Communications and Sensing

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Phase correction of discrete Fourier transform coefficients to reduce frequency estimation bias of single tone complex sinusoid

Cited by 37 publications

References 22 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

Generalization of interpolation DFT algorithms and frequency estimators with high image component interference rejection

Efficient Parameter Estimation

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