Against the long-range spectral leakage of the cosine window family

Chen, Kui Fu; Jiang, Jing Tao; Crowsen, Stephen

doi:10.1016/j.cpc.2008.12.019

Cited by 33 publications

(18 citation statements)

References 42 publications

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“…However, there are two drawbacks in the classic version: the spectral leakage effect (SLE) caused by the lack of periodicity and the picket fence effect (PFE) due to the frequency sampling [1]. These effects will lead to significant errors in spectral analysis such as parameter estimation [2,3].…”

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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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.

View full text Add to dashboard Cite

show abstract

“…Linear approximation of the spectrum allows for linearizing relationships to determine component frequencies and this feature of the LIDFT method differs it from other methods of signal estimation [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method

Borkowski¹

2011

Metrology and Measurement Systems

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This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.

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“…Nonparametric spectrum interpolation methods make it possible to zoom in on the frequency domain but do not decrease the errors caused by long-range spectral leakage (i.e., by sidelobes of spectrum lines of neighbor components in the spectrum), which are defined by the frequency characteristic of the data window applied [47]. Similarly, the long-range spectral leakage is neglected in all noniterative interpolated DFT methods, except the DFT linear interpolation method (LIDFT) [33][34][35]45] and the multipoint weighted interpolated DFT (MWIDFT) method [36,38,43]. However, the MWIDFT method is defined only for some classes of cosine-family data windows, i.e., for the class I of Rife-Vincent windows [21], also called the maximum sidelobe decay windows [38,41,43].…”

Section: Introduction: Spectral Analysis and The Unit Circle Approximmentioning

confidence: 99%

“…Similarly, the long-range spectral leakage is neglected in all noniterative interpolated DFT methods, except the DFT linear interpolation method (LIDFT) [33][34][35]45] and the multipoint weighted interpolated DFT (MWIDFT) method [36,38,43]. However, the MWIDFT method is defined only for some classes of cosine-family data windows, i.e., for the class I of Rife-Vincent windows [21], also called the maximum sidelobe decay windows [38,41,43]. Some of the interpolated DFT methods are applied only for the rectangular data window, for which errors caused by long-range spectral leakage are the highest [28][29][30], and some of these interpolations are proposed only for others specific data windows [21, 23-27, 39, 44, 46].…”

Section: Introduction: Spectral Analysis and The Unit Circle Approximmentioning

confidence: 99%

Minimization of Maximum Errors in Universal Approximation of the Unit Circle by a Polygon

Borkowski¹

2011

Metrology and Measurement Systems

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This paper presents a universal approximation of the unit circle by a polygon that can be used in signal processing algorithms. Optimal choice of the values of three parameters of this approximation allows one to obtain a high accuracy of approximation. The approximation described in the paper has a universal character and can be used in many signal processing algorithms, such as DFT, that use the mathematical form of the unit circle. One of the applications of the described approximation is the DFT linear interpolation method (LIDFT). Applying the results of the presented paper to improve the LIDFT method allows one to significantly decrease the errors in estimating the amplitudes and frequencies of multifrequency signal components. The paper presents the derived formulas, an analysis of the approximation accuracy and the region of best values for the approximation parameters.

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Against the long-range spectral leakage of the cosine window family

Cited by 33 publications

References 42 publications

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

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

Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method

Minimization of Maximum Errors in Universal Approximation of the Unit Circle by a Polygon

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