Savitsky-Golay Filter Research Articles

Determination of gas discharge plasma potential by Langmuir probe using different methods

In a hollow cathode discharge in helium at reduced pressure, the profile of the plasma potential Up in the cathode-anode region was measured with a single Langmuir probe. A digital technique was used to control and analyze the experimental results. The probe current-voltage characteristic was generated by applying a voltage with a spectrum with an equal probability distribution in the measured voltage range. Three methods were compared: (1) differentiation of the probe current-voltage characteristic (IVC) by the Langmuir-Druyvesteyn (LD) method with the Savitsky-Golay (SG) filter; (2) definition of the position of the noise maximum in the experimental IVC; (3) determination of the voltage corresponding to the intersection of the asymptotes of different range of the IVC. Methods (2) and (3) were used both as alternatives to method (1) for measuring the potential Up and as additional ones when choosing free parameters of the SG filter for plasma diagnostics by method (1).

Automated tuning of denoising algorithms for noise removal in chromatograms

Different algorithms, such as the Savitzky-Golay filter and Whittaker smoother, have been proposed to improve the quality of experimental chromatograms. These approaches avoid excessive noise from hampering data analysis and as such allow an accurate detection and quantification of analytes. These algorithms require fine-tuning of their hyperparameters to regulate their roughness and flexibility. Traditionally, this fine-tuning is done manually until a signal is obtained that removes the noise while conserving valuable peak information. More objective and automated approaches are available, but these are usually method specific and/or require previous knowledge.In this work, the L-and V-curve, k-fold cross-validation, autocorrelation function and residual variance estimation approach are introduced as alternative automated and generally applicable parameter tuning methods. These methods do not require any previous information and are compatible with a multitude of denoising methods. Additionally, for k-fold cross-validation, autocorrelation function and residual variance estimation, a novel implementation based on median estimators is proposed to handle the specific shape of chromatograms, typically composed of alternating flat baselines and sharp peaks. These tuning methods are investigated in combination with four denoising methods; the Savitsky-Golay filter, Whittaker smoother, sparsity assisted signal smoother and baseline estimation and denoising using sparsity approach.It is demonstrated that the median estimators approach significantly improves the denoising and information conservation performance of relevant smoother-tuner combinations up to a factor 4 for simulated datasets and even up to a factor 10 for an experimental chromatogram. Moreover, the parameter tuning methods relying on residual variance estimation, k-fold cross-validation and autocorrelation function lead to similar small root-mean squared errors on the different simulated datasets and experimental chromatograms. The sparsity assisted signal smoother and baseline estimation and denoising using sparsity approach, which both rely on the use of sparsity, systematically outperform the two other methods and are hence most appropriate for chromatograms.

Frekans Alanı Öznitelik Çıkarımına Dayalı Makine Öğrenme Teknikleri ile Trapezius Yüzey EMG Sinyallerini Kullanarak Servikal Disk Fıtığı Hastalığının Tahmini

Cervical disk herniation (CDH) is a disease that affects the quality of life of many people due to the neck pain it causes. The aim of this study was to develop an automatic prediction system to aid in diagnosis by evaluating the change in the surface electrical activity of the trapezius muscle in SDH disease in order to find an answer to the question: 'Can the surface electromyogram (sEMG) recorded from the trapezius muscle be an effective indicator for the diagnosis of SDH disease?'. To this end, a dataset will be created using preprocessing and feature extraction methods from sEMG signals from CDH patients and healthy individuals. In the first step, the Savitsky-Golay filter is used to denoise the sEMG signals and the dominant frequency signals between 20 and 150 Hz are included in the study using the Butterworth filter design. Twenty PSD-based features in the frequency domain were then obtained from the signals to which we applied the Burg method. Eleven of the most significant features based on the information gain, gain ratio, and Gini values are selected to be submitted to the classifiers. 80% of all new feature areas are used for classification and the rest for prediction. The best classification accuracy of 91.6% was obtained with the Tree classifier using 10-fold cross-validation for classification. In addition, neural networks and CN2 rule inducer provided 87.5% classification accuracy for prediction using 20% of the remaining data that the classifiers had not seen before. The experimental results demonstrate that the trapezius muscle has different surface electrical activity in CDH patients and healthy subjects and that the frequency domain characteristics of this activity are important for disease prediction.

Analysis of Mouse Blood Serum in the Dynamics of U87 Glioblastoma by Terahertz Spectroscopy and Machine Learning

In this research, an experimental U87 glioblastoma small animal model was studied. The association between glioblastoma stages and the spectral patterns of mouse blood serum measured in the terahertz range was analyzed by terahertz time-domain spectroscopy (THz-TDS) and machine learning. The THz spectra preprocessing included (i) smoothing using the Savitsky–Golay filter, (ii) outlier removing using isolation forest (IF), and (iii) Z-score normalization. The sequential informative feature-selection approach was developed using a combination of principal component analysis (PCA) and a support vector machine (SVM) model. The predictive data model was created using SVM with a linear kernel. This model was tested using k-fold cross-validation. Achieved prediction accuracy, sensitivity, specificity were over 90%. Also, a relation was established between tumor size and the THz spectral profile of blood serum samples. Thereby, the possibility of detecting glioma stages using blood serum spectral patterns in the terahertz range was demonstrated.

Fabrication and evaluation of chitosan modified filter paper for chlorpyrifos detection in wheat by surface-enhanced Raman spectroscopy.

Chlorpyrifos is a commonly used organophosphorus pesticide in agriculture. However, its neurotoxicity poses a huge threat to human health. In the present study, a chitosan-modified filter paper-based surface enhanced Raman scattering active substrate (Ch/AgNPs/paper) was fabricated and used to detect trace amounts of chlorpyrifos in 120 treated wheat samples. Results showed that the Ch/AgNPs/paper substrate could be used to enhance the chlorpyrifos spectral fingerprint only up to a concentration of 0.000558 mg L-1 . Following Raman spectra acquisition, three pre-processing methods, including Savitzky-Golay (Savitsky-Golay filter with a second order polynomial) smoothing with first derivative and second derivative and normalization, were used to reduce baseline variation and increase resolutions of spectral peak features of the original spectra dataset. Then, prediction models based on partial least squares were established for detecting chlorpyrifos pesticide residue in wheat. The partial least squares model with normalization yielded optimal result, with a correlation coefficient of 0.9764, root mean square error of prediction of 1.22 mg L-1 in the prediction, and relative analysis deviation of 4.12. Five unknown samples were prepared to verify the accuracy of the prediction model. The predicted recoveries were calculated to be between 97.25% and 119.38% with an absolute t value of 0.598. The value of a t-test shows that the prediction model is accurate and reliable. The present study demonstrates that the proposed method can achieve rapid detection of chlorpyrifos in wheat. © 2022 Society of Chemical Industry.

Fiber Bragg grating sensor-based temperature monitoring of solar photovoltaic panels using machine learning algorithms

Fiber Bragg Grating (FBG) sensors are an emerging and prominent optical sensing technology of accurately measuring strain, depth, temperature, density, and several physical parameters. Due to high solar radiation, the increased solar panel temperature affects photovoltaic cell efficiency. Hence, monitoring the temperature of solar panels and providing proper cooling is essential to attain optimal electrical performance. FBG sensor is used to monitor the solar panel temperature in this research. The accuracy and stability of the peak search algorithms in the acquired experimental data are analyzed. Reisz fractional-order derivative and Savitsky-Golay filter are improved using a decision tree regressor to determine the peak and noisy spectrum with different signal-to-noise ratios. The algorithm surpassed the demerits of conventional peak algorithms used for the FBG spectrum. This work implements the fractional derivatives and a machine learning algorithm initially denoised. The number of epochs for linear regression is 15. The depth allowed for decision trees is 1000, and the number of estimators for the random forest is 150. A peak is detected with a decision tree regressor trained on clean and noiseless FBG data. Machine learning algorithms such as linear regression, random forest, and decision tree are compared. The decision tree regressor with hyperparameter tuning yields the best results with high accuracy of 99.83% compared to other conventional peak detection methods. The statistical tests and metaheuristic algorithms are also performed to assess the experimental outcome.

Forest cover trend analysis using MODIS time series and its climatic responses in the Mari El Republic of Russia

This study assesses whether MODIS NDVI satellite data time series can be used to detect changes in forest phenology over the different forest types of the Mari El Republic of Russia. Due to the severe climatic conditions, coniferous and deciduous forests of this region are especially vulnerable to climate change, which can lead to stresses from droughts and increase the frequency of wild fires in the long term. Time series analysis was applied to 16-day composite MODIS (MOD13Q1) (250 m) satellite data records (2000-2020) for the investigated territory, based on understanding that the NDVI trend vectors would enable detection of phenological changes in forest cover. There was also the determination of land cover/land use change for the area and examination of meteorological data for the investigated period. For the study, we utilized four phenological metrics: start of season (SOS), end of season (EOS), length of season (LOS), and Maximum vegetation index (MVI). The NDVI MODIS data series were smoothed in the TimeSAT software using the Savitsky-Golay filter. The results of the study show that over the 20-years period variations in phenological metrics do not have a significant impact on the productivity and growth of forest ecosystems in the Mari El Republic.

Saviztky–Golay Filtering for Solar Power Smoothing and Ramp Rate Reduction Based on Controlled Battery Energy Storage

Energy is present in every touch we make in our modern life. However, with the increase of energy-consuming devices, there is a burden to meet this demand with a clean power generation. Although solar and wind are considered as clean and renewable energy resources, many issues engender with their higher penetration into electricity grids. However, when renewable energy resources are integrated with battery energy storage systems (BESS), more smoothed and easily dispatchable power can be obtained. This paper investigates the smoothing quality of the solar photovoltaic power output with the help of BESS using a couple of approaches such as low pass filtering (LPF), moving average (MA) filtering, Gaussian filter (GF) and Saviztky-Golay (S-G) filter. Obviously, the smoothed dispatchable power has been achieved with all mentioned methods, however, the performance of moving average and low pass filters is not acceptable comparatively especially when longer window size and time constant are used, which consequently deteriorates the performance of storage system. In contrast, the paper introduces using the Savitsky-Golay filter to reduce battery ramp rate and battery charging and discharging power while smoothing the solar power fluctuations. The simulation results depict the performance of the proposed smoothing filter and compare its performance against MA, LPF and GF.

Software for analysis of vegetation indices dynamics

The article describes a software package designed for processing and analyzing of vegetation indices based on satellite data. A program is developed in the free-distributed environment Octave. The input data of the program are vegetation indices (MODIS NDVI and EVI). The data are pre-processed by removing the peak values using the Savitsky-Golay filter and a seasonal decomposition by a moving average. To exclude the influence of snow cover and the period without vegetation, data of the growing season are used in the calculation. The vegetation period is determined by phenological parameters of the beginning and end of the growth period. The program determines the phenological parameters by a double logistic function, an asymmetric Gaussian function, and a fourth-degree polynomial to approximate the original time series. After the preliminary processing, a linear trend of the series, its statistical significance, the minimum and maximum values, coefficients of variation, etc., are calculated. The correlation function between the vegetation indices and the time series set by the user is also implemented. The output data are exported in raster and text formats. In conclusion, an example of using the software for calculating the NDVI trends in the Uda River basin in Transbaikalia is given.

Determination of Flucloxacillin-sodium in Binary Mixture with Ampicillin-trihydrate Using Univariate and Multivariate Spectrophotometric Methods: A Comparative Study

Objectives: The aim of this study was to develop four simple and accurate spectrophotometric methods for determination of flucloxacillin-sodium in binary mixture with ampicillin-trihydrate without separation. Methods: One of them was a univariate constant center method and the other three methods were multivariate chemometric methods named; Savitsky-Golay filters, continuous wavelet transform of ratio spectra and wavelet transform of first derivative of the ratio spectra. Results: The proposed methods adopted for selective determination of flucloxacillin-sodium and obey Beer’s law in the range (2-20 µg mL-1). Conclusion: The proposed methods were simple, rapid, economic, accurate and precise; they were successfully applied for the determination of flucloxacillin-sodium in pure form and in pharmaceutical preparations.

Application of different analytical techniques for determination of velpatsvir and sofosbuvir in the pharmaceutical preparation

Three analytical methods have been developed and applied for determination of velapatasvir and sofosbuvir in their new FDA-approved pharmaceutical dosage form. Capillary electrophoresis has been introduced as a powerful separation analytical technique for the simultaneous analysis of the studied drugs within a shorter analytical run time. Separation has been carried out on fused silica capillary (50 cm × 75 µm internal diameter), background electrolyte solution consisted of borate buffer (40 mM, pH 10) and UV detection carried out at 225 nm. Also, two mathematical spectrophotometric methods have been applied for resolving the recorded overlapping UV spectra of velpatasvir and sofosbuvir. Direct zero-order spectrophotometric determination of velpatasvir was done at 339 nm where no significance absorbance or contribution from sofosbuvir was observed. Savitsky–Golay filters signal processing has been achieved to enable determination of sofosbuvir in its binary mixture with velpatasvir. The amplitude of the first derivative of the sofosbuvir spectra, calculated by Savitsky–Golay filters, at 251 nm enabled the determination of sofosbuvir without any contribution of velpatasvir. The described methods have been validated and applied for determination of the studied drugs in their pharmaceutical dosage form.

Different spectrophotometric methods applied for the analysis of simeprevir in the presence of its oxidative degradation product: Acomparative study

Five simple spectrophotometric methods were developed for the determination of simeprevir in the presence of its oxidative degradation product namely, ratio difference, mean centering, derivative ratio using the Savitsky-Golay filters, second derivative and continuous wavelet transform. These methods are linear in the range of 2.5–40μg/mL and validated according to the ICH guidelines. The obtained results of accuracy, repeatability and precision were found to be within the acceptable limits. The specificity of the proposed methods was tested using laboratory prepared mixtures and assessed by applying the standard addition technique. Furthermore, these methods were statistically comparable to RP-HPLC method and good results were obtained. So, they can be used for the routine analysis of simeprevir in quality-control laboratories.

Two dimensional mapping of iron release in marine sediments at submillimetre scale

Coastal and shelf sediments are considered as an important source of dissolved iron to the ocean. Here, we present a new numerical approach to estimate geochemical fluxes and production rates in an estuarine sediment at sub-millimetre resolution. This approach is based on application of Savitsky–Golay filter (SGF) procedure to two-dimensional concentration distributions of dissolved iron. We verified the procedure by applying it to artificial data of known production rates, and analysed the resulting uncertainty on production rates and fluxes across the water–sediment interface. This SGF procedure was applied to data from an intertidal mudflat that is densely inhabited by macrofauna (e.g. 630 ind m− 2 of Hediste diversicolor, I. Metais, pers.com.). Our analysis reveals an apparent recycling rate of 3780 ± 1399 μmol m− 2 d− 1 and a mean residence time of iron in the dissolved phase of 2.3 days. Visual identification of burrows permitted to calculate separately the diffusive flux across the sediment–water interface (104 ± 20 μmol m− 2 d− 1) and the bio-irrigational flux (410 ± 213 μmol m− 2 d− 1). Reactive iron particles will undergo on average 7.4 cycles of dissolution/precipitation before being released to the water column. These results show that estuarine sediments support intensive iron recycling that has probably a large impact on terrigeneous particles before being released into the ocean.

Zero order and signal processing spectrophotometric techniques applied for resolving interference of metronidazole with ciprofloxacin in their pharmaceutical dosage form

Four rapid, simple, accurate and precise spectrophotometric methods were used for the determination of ciprofloxacin in the presence of metronidazole as interference. The methods under study are area under the curve, simultaneous equation in addition to smart signal processing techniques of manipulating ratio spectra namely Savitsky–Golay filters and continuous wavelet transform. All the methods were validated according to the ICH guidelines where accuracy, precision and repeatability were found to be within the acceptable limits. The selectivity of the proposed methods was tested using laboratory prepared mixtures and assessed by applying the standard addition technique. So, they can therefore be used for the routine analysis of ciprofloxacin in quality-control laboratories.

Different approaches in manipulating ratio spectra applied for the analysis of Cefprozil in presence of its alkaline-induced degradation product: A comparative study

Four simple, accurate and precise stability-indicating spectrophotometric methods manipulating ratio spectra were developed and validated for simultaneous determination of Cefprozil (CZ) and its alkaline-induced degradation product (DCZ) without prior separation namely; ratio difference, mean centering, derivative ratio using Savitsky–Golay filter and continuous wavelet transform. The accuracy, precision and linearity ranges of the proposed methods were determined. The methods were validated and the specificity was assessed by analyzing synthetic mixtures containing the drug and its degradate. The four methods were applied for the determination of the cited drug in tablets and the obtained results were statistically compared with those of a reported method. The comparison showed that there are no significant differences between the proposed methods and the reported method regarding both accuracy and precision.

Simultaneous spectrophotometric determination of overlapping spectra of paracetamol and caffeine in laboratory prepared mixtures and pharmaceutical preparations using continuous wavelet and derivative transform

In the present paper, two spectrophotometric methods were used for the simultaneous analysis of paracetamol (PCT) and caffeine (CAF) in their laboratory prepared mixtures and pharmaceutical preparations. Simple spectrophotometric analysis of PCT and CAF is not possible due to their complete spectral overlap. The proposed methods are based on the application of continuous wavelet transform (CWT) and derivative transform (using Savitsky–Golay filters) on the ratio spectra to predict each of CAF and PCT. Several wavelet families were tested. Coif1 and Sym2 were found to give best results under optimum conditions. The transformed signals of ratio spectra were used to plot the calibration curves for both components. The predictability of the built calibrations was validated through their application on several synthetic mixtures of both drugs. The proposed methods were used for the prediction of CAF and PCT in pharmaceutical preparation. The obtained results were statistically compared to a reference HPLC method. No significant differences were found between the obtained results and those from the reference method. Being simple, rapid, cheap and sensitive, the proposed methods are recommended for the routine daily analysis of these two drugs in their mixtures in quality control laboratories.

Statistical and Computational Methods for Comparative Proteomic Profiling Using Liquid Chromatography-Tandem Mass Spectrometry

The combined method of LC-MS/MS is increasingly being used to explore differences in the proteomic composition of complex biological systems. The reliability and utility of such comparative protein expression profiling studies is critically dependent on an accurate and rigorous assessment of quantitative changes in the relative abundance of the myriad of proteins typically present in a biological sample such as blood or tissue. In this review, we provide an overview of key statistical and computational issues relevant to bottom-up shotgun global proteomic analysis, with an emphasis on methods that can be applied to improve the dependability of biological inferences drawn from large proteomic datasets. Focusing on a start-to-finish approach, we address the following topics: 1) low-level data processing steps, such as formation of a data matrix, filtering, and baseline subtraction to minimize noise, 2) mid-level processing steps, such as data normalization, alignment in time, peak detection, peak quantification, peak matching, and error models, to facilitate profile comparisons; and, 3) high-level processing steps such as sample classification and biomarker discovery, and related topics such as significance testing, multiple testing, and choice of feature space. We report on approaches that have recently been developed for these steps, discussing their merits and limitations, and propose areas deserving of further research.

Comments on the Use of Digital Filters

Abstract At the Microscopy and Microanalysis 2003 meeting, a member of the audience in one talk sharply criticized a speaker of a talk for his use of a Savitsky-Golay (S-G) digital filter for smoothing Electron Energy Loss Spectroscopy (EELS) data. The statement was made that the digital filter would decrease the resolution of the peak, i.e. widen the width, and that all digital filters do that, including the Top Hat filter. In support of this statement, he said to consider what would happen if the filter were applied to a Dirac delta function. I knew that his argument was not correct, but I didn't think of the reason until later. This interchange was on my mind because I was familiar with both of these filters due to implementing both the Top Hat and the Savitsky-Golay filters into my “Beerware” program, EELS-PLOT.

Highly accurate smoothing filter

An iterative filter for the smoothing of degraded line shapes with Gaussian noise, and a signal to noise ratio defined in a wide interval 20–∞ is presented. The smoothed line shape shows errors below 2% in its height and width parameters with regard to the true values used in the simulation. The filter reduces the Gaussian noise to less than a half. In the tests carried out with a PC computer, the new filter proved that the original line shape for a linewidth of 5–30 is better recovered than the Savitsky–Golay filter. The application of the procedure only involves the use of the linewidth parameter of the degraded peak which simplifies the smoothing process. The filter follows two basic operations: first, an oversmoothing is applied to the degraded line and second, an iterative enhancement on the oversmoothing spectrum is made. The resulting spectrum of these two operations is compared with the degraded line by a least squares fitting method. When the filter is used in a simplified version, it is useful not only to determine very overlapped lines in a degraded spectrum, but also to calculate the background in an experimental spectrum.

Analyses of small facets imaged with scanning-probe microscopy

Two tools for the analysis of facets as detected by scanning-probe microscopy (SPM) images are proposed. One tool is an adaptation of the radial-histogram transform proposed by D. Schleef et al. in Phys. Rev. B. 55, 2535 (1997). In this article the local slopes in the SPM image are in the present version determined by Savitsky–Golay filters with variable lengths [A. Savitsky and M. J. E. Golay, Anal. Chem. 36, 1627 (1964)]. These variable length filters turn out to be important to suppress the influence of noise obscuring the possibility to detect facets and to analyze corrugations with different length scales in SPM images, e.g., surface reconstructions. The other tool allows the direct quantitative determination of the orientation (with a standard deviation) of user-specified parts of facets. It makes use of a Savitsky–Golay filter as well. Both tools were applied to an artificially constructed SPM image and several experimental SFM images showing (ionic) MnO precipitates protruding out of a (metallic) Cu surface. It is shown that the Miller indices of the facets can be derived experimentally.