Savitzky–Golay smoothing and differentiation filter for even number data

Luo, Jianwen; Kong, Ying; Bai, Jing

doi:10.1016/j.sigpro.2005.02.002

Cited by 283 publications

(110 citation statements)

References 5 publications

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“…Although there are several methods for estimatingẊ from X [25,36], this topic is beyond the scope of the present study and is not presented here. We assume that this calculation is done in some way, andẊ are given.…”

Section: Reconstruction Of Continuous-time Pdssmentioning

confidence: 99%

Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

Kera

Hasegawa

2016

Nonlinear Dyn

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Reconstruction of nonlinear dynamical systems from noisy time series data has attracted much attention in recent years, and it has broad applications in many fields, especially in theoretical biology. Here, we propose a reconstruction algorithm based on the noise-tolerant algebraic approach that can infer underlying continuous-time polynomial dynamical systems from the observed time series data. The advantages of our approach are that it can handle nonlinearity, and it can be applied to noisy systems. Our approach reduces the range of monomials to be considered without any a priori knowledge as many other studies does. We apply the proposed method to two oscillatory systems (the FitzHugh-Nagumo and the Oregonator) subject to noise, where the conventional fitting methods based on L 1 and L 2 regularizations often fail. Our numerical experiments show that the proposed method accurately reconstructs the continuous-time polynomial dynamical systems. We also apply the method to a chaotic system and show the effectiveness of our approach.

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Section: Reconstruction Of Continuous-time Pdssmentioning

confidence: 99%

Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

Kera

Hasegawa

2016

Nonlinear Dyn

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“…The soil samples in Schafertal site were measured in the same laboratory conditions since the weather did not allow ASD field measurements. PPTs of the spectral data included three types: (1) A second-order transformation of the polynomial Savitzky-Golay smoothing [20,46] was performed to minimize variance between samples caused by grinding and the optical setup. This transformation was found to be an optimal spectral pretreatment in similar studies [19,47,48].…”

Section: Field and Laboratory Spectral Measurementsmentioning

confidence: 99%

Mapping the Spectral Soil Quality Index (SSQI) Using Airborne Imaging Spectroscopy

et al. 2015

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Soil quality (SQ) assessment has numerous applications for managing sustainable soil function. Airborne imaging spectroscopy (IS) is an advanced tool for studying natural and artificial materials, in general, and soil properties, in particular. The primary goal of this research was to prove and demonstrate the ability of IS to evaluate soil properties and quality across anthropogenically induced land-use changes. This aim was fulfilled by developing and implementing a spectral soil quality index (SSQI) using IS obtained by a laboratory and field spectrometer (point scale) as well as by airborne hyperspectral imaging (local scale), in two experimental sites located in Israel and Germany. In this regard, 13 soil physical, biological, and chemical properties and their derived soil quality index (SQI) were measured. Several mathematical/statistical procedures, consisting of a series of operations, including a principal component analysis OPEN ACCESSRemote Sens. 2015, 7 15749(PCA), a partial least squares-regression (PLS-R), and a partial least squares-discriminate analysis (PLS-DA), were used. Correlations between the laboratory spectral values and the calculated SQI coefficient of determination (R 2 ) and ratio of performance to deviation (RPD) were R 2 = 0.84; RPD = 2.43 and R 2 = 0.78; RPD = 2.10 in the Israeli and the German study sites, respectively. The PLS-DA model that was used to develop the SSQI showed high classification accuracy in both sites (from laboratory, field, and imaging spectroscopy). The correlations between the SSQI and the SQI were R 2 = 0.71 and R 2 = 0.7, in the Israeli and the German study sites, respectively. It is concluded that soil quality can be effectively monitored using the spectral-spatial information provided by the IS technology. IS-based classification of soils can provide the basis for a spatially explicit and quantitative approach for monitoring SQ and function at a local scale.

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“…Besides, many filters of trend extraction such as GLAS weighted moving average filters, Henderson weighted moving average filters are represented in [24]. There are also many smoothers, such as the Savitzky-Golay (SG) filter [25,26], Hodrick-Prescott smoothers [27], Loess smoother [28] and smoothing B-spline [29] to be adopted to achieve trend extraction.…”

Section: Transient Cpamentioning

confidence: 99%

Minimum-Information-Entropy-Based Control Performance Assessment

Meng

Fang

Liu

2013

Entropy

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Abstract:Generally, the controller design should be performed to narrow the shape of the probability density function of the tracking error. A small information entropy value corresponds to a narrow distribution function, which means that the uncertainty of the related random variable is small. In this paper, information entropy is introduced in the field of control performance assessment (CPA). For the unknown time delay case, the minimum information entropy (MIE) benchmark is presented, and a MIE-based performance index is defined. For the known time delay case, a tight upper bound of MIE is derived and adopted as a performance benchmark to assess the stochastic control performance. Based on these, the control performance assessment procedures are developed for both the steady and the transient processes. Simulation tests and an industrial case study of a main steam pressure system of a 1,000MW power unit are utilized to verify the effectiveness of the proposed procedures.

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Savitzky–Golay smoothing and differentiation filter for even number data

Cited by 283 publications

References 5 publications

Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

Mapping the Spectral Soil Quality Index (SSQI) Using Airborne Imaging Spectroscopy

Minimum-Information-Entropy-Based Control Performance Assessment

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