Fractional-order derivative spectroscopy for resolving simulated overlapped Lorenztian peaks

Li, Yuan-lu; Tang, Huiqiang; Chen, Hai-xiu

doi:10.1016/j.chemolab.2011.01.013

Cited by 20 publications

(17 citation statements)

References 20 publications

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“…One of the well-known drawbacks of the semidifferentiation procedure is increase in the current noise upon its application [2,42,72]. Although this effect might complicate deconvolution of overlapped semiderivative signals leading to higher errors, the presence of current noise should have the same impact for all the equations discussed above, i.e.…”

Section: Parametermentioning

confidence: 99%

“…The main disadvantages of the semi-derivative analysis are related to an increase in current noise due to application of differentiation, requirements of subtraction of background currents and formation of artificial semi-derivative signals when the sign of the current does not change when the potential scan is reversed [42,72].…”

Section: Introductionmentioning

confidence: 99%

“…An extensive description of the theory of semidifferentiation and semi-integration can be found elsewhere [11,14,51,[53][54][55][56][57][58][59][60]; here, we focus only on practical aspects of its application in analysis of voltammetric data for systems with reactions under conditions of semi-infinite linear diffusion and when oxidised and reduced species are soluble in the electrolyte phase. It should be stressed that most of the modern electrochemical software offer a possibility of data transformation using both abovementioned methods making their application easily accessible.…”

Section: Introductionmentioning

confidence: 99%

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Semi-differential analysis of irreversible voltammetric peaks

Grdeń

2016

J Solid State Electrochem

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Voltammetric peaks obtained by simulation of electrochemical reactions under conditions of linear semi-infinite diffusion with an irreversible electron transfer process are analysed using a semi-differentiation procedure. Obtained semi-derivative peaks, separated or overlapped, are fitted with appropriate mathematical functions. The functions used for data fitting include a function describing symmetrical peaks, proposed by several authors for fitting irreversible semiderivative peaks, and two alternative functions that express asymmetric shape of the irreversible semi-derivative signals. When applied to the overlapped irreversible semi-derivative peaks, the latter two functions allow calculating certain electrochemical parameters with a better accuracy as compared with the function derived for the symmetrical peaks.

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Section: Parametermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semi-differential analysis of irreversible voltammetric peaks

Grdeń

2016

J Solid State Electrochem

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“…In the proposed method, the operational matrices were used to compute the NIOD of a signal through expanding the signals by the Haar wavelets and constructing Haar wavelet operational matrix of the NIOD [7]. Advantage of the proposed method is that the NIOD of a signal can be easily obtained by matrix-vector multiplication.…”

Section: Introduction On-integer Order Differentiation (Niod) Is a Gementioning

confidence: 99%

“…After the first application of the signal semi-differentiation, an entirely new perspective has been outlined in analytical science. Such as the fractional derivative was proposed to determine the overlapping band spectral parameters [4], the fractional order differentiation was used to improve signal resolution by Mocak et al [5], the 2.5 order derivative combined with Fourier least square fitting was designed to process noised overlapped peaks [6], the fractional order derivative spectroscopy was used to resolve the overlapped Lorentzian peaks [7], the fractional order differentiation was widely used to detect the edges and enhance the texture of images [8]- [14]. In these applications, an important task is to implement the NIOD.…”

Section: Introduction On-integer Order Differentiation (Niod) Is a Gementioning

confidence: 99%

Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement

Pan

Meng

et al. 2015

Measurement Science Review

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Non-integer order differentiation is changing application of traditional differentiation because it can achieve a continuous interpolation of the integer order differentiation. However, implementation of the non-integer order differentiation is much more complex than that of integer order differentiation. For this purpose, a Haar wavelet-based implementation method of non-integer order differentiation is proposed. The basic idea of the proposed method is to use the operational matrix to compute the noninteger order differentiation of a signal through expanding the signal by the Haar wavelets and constructing Haar wavelet operational matrix of the non-integer order differentiation. The effectiveness of the proposed method was verified by comparison of theoretical results and those obtained by another non-integer order differential filtering method. Finally, non-integer order differentiation was applied to enhance signal.

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Correction of overlapping peaks of Pb and As spectrum based on a chaotic particle swarm optimization–Gaussian mixture statistical model

Zhang

Zhao

et al. 2020

Journal of Chemometrics

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Energy‐dispersive X‐ray fluorescence spectroscopy has been effectively applied to detect heavy metals in soil because of its fast detection speed, low cost, and high accuracy. However, overlapping peaks appear in the detection of some heavy metals, such as Pb and As, resulting in significant errors in the detection. Therefore, it is impossible to accurately predict the content of heavy metals in soil. To solve this problem, a Gaussian mixture statistical model (GMSM) is applied based on physical characteristics randomly formed by X‐rays combined with statistical ideas. Subsequently, when estimating the parameters of the GMSM, performing particle swarm optimization (PSO) causes the parameters to fall into the local optima easily. Chaos theory is introduced to the PSO algorithm to promote its weight update strategy, and the chaotic PSO (CPSO) with an anti‐premature mechanism is proposed to achieve global convergence. When using CPSO‐GMSM to analyze the overlapping peaks, the relative error compared with the actual single metal sample is less than 0.0693, and the error compared with the actual characteristic peak position is less than 0.0133. The overlapping peaks are corrected effectively, providing a foundation for the accurate quantitative analysis of heavy metals in soil.

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Fractional-order derivative spectroscopy for resolving simulated overlapped Lorenztian peaks

Cited by 20 publications

References 20 publications

Semi-differential analysis of irreversible voltammetric peaks

Semi-differential analysis of irreversible voltammetric peaks

Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement

Correction of overlapping peaks of Pb and As spectrum based on a chaotic particle swarm optimization–Gaussian mixture statistical model

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