DFT Interpolation Algorithm for Kaiser–Bessel and Dolph–Chebyshev Windows

Duda, Krzysztof

doi:10.1109/tim.2010.2046594

Cited by 74 publications

(77 citation statements)

References 12 publications

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“…For the case of arbitrary windows, only a few methods have been presented. The state of the art for arbitrary windows is represented by the estimators of Duda [14] and Candan [15].…”

Section: Introductionmentioning

confidence: 99%

“…In [14], Duda builds on previous magnitude spectrum interpolators [16,17] derived for the Rife-incent Class I windows in order to build a first coarse estimator, whose error is compensated by an optimized polynomial remapping of the coarse estimated value to obtain a finer estimate, with the accuracy of the method controlled through the polynomial order of the remapping. In [15], Candan proposes a method derived from his previous work on the rectangular window case [18], itself building on a previous complex spectrum interpolator [19], where a corrected interpolator is derived from the Taylor expansion of the signal's Discrete-Time Fourier Transform (DTFT) around the sinusoid frequency location.…”

Section: Introductionmentioning

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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“…For the case of arbitrary windows, only a few methods have been presented. The state of the art for arbitrary windows is represented by the estimators of Duda [14] and Candan [15].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Werner

Germain

2016

Applied Sciences

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“…In (Agrež, 2002) multipoint IpDFT was introduced with the feature of reducing long range leakage and thus reducing systematic estimation errors. IpDFT algorithm for the signal analyzed with arbitrary, even non cosine window was given in (Duda, 2011a).…”

Section: Interpolated Dft Algorithmsmentioning

confidence: 99%

Interpolation Algorithms of DFT for Parameters Estimation of Sinusoidal and Damped Sinusoidal Signals

Duda¹

2012

Fourier Transform - Signal Processing

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“…The estimators were further improved and extended for decaying sinusoids or exponentials [7][8][9]. The Kasier-Bessel and Dolph-Chebyshev windows are known for superior performance in multitone detection [10]. Frequency estimation of the weighted real tones [11].…”

Section: Introductionmentioning

confidence: 99%

A Novel Frequency Estimation of Sinusoid by iterative interpolation DFT algorithm

Huang¹,

Suo²,

Shi³

2016

Proceedings of the 2016 4th International Conference on Machinery, Materials and Computing Technology

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Abstract. The frequency estimation of sinusoidal signal based on discrete fourier transform (DFT) is investigated, which performance is caused to decline due to the error of interpolation direction when the signal frequency is close to quantized frequency of DFT. To solve this problem, a new algorithm without weighting window is proposed. Firstly, a coarse frequency estimation in DFT spectrum is acquired, then a high-accuracy frequency near the coarse frequency by iterative interpolation is estimated. The simulation results show that errors caused by a mistaken location of the spectral line can be significantly reduced and the algorithm is simple and has good performance in mean square error and accuracy.

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DFT Interpolation Algorithm for Kaiser–Bessel and Dolph–Chebyshev Windows

Cited by 74 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

Interpolation Algorithms of DFT for Parameters Estimation of Sinusoidal and Damped Sinusoidal Signals

A Novel Frequency Estimation of Sinusoid by iterative interpolation DFT algorithm

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