TWO‐DIMENSIONAL FILTERING AND THE SECOND DERIVATIVE METHOD

Geophysics ◽  
1966 ◽  
Vol 31 (3) ◽  
pp. 606-617 ◽  
Author(s):  
C. A. Meskó
Keyword(s):  
Second Derivative ◽  
Two Dimensional ◽  
Frequency Responses ◽  
Center Point ◽  
Average Accuracy ◽  
Two Dimensional Filtering ◽  
Derivative Formulas ◽  
Ring Method ◽  
Second Derivative Method ◽  
Accuracy Of Approximation

The data‐processing operations of second derivative formulas are equivalent to two‐dimensional digital filtering operations. Therefore any coefficient set can be described unambiguously by its two‐dimensional frequency response. The frequency responses can be represented by surfaces over the two‐dimensional frequency plane. We have simplified the representation by giving some curves intersected from these surfaces by a) planes, b) cylindrical surfaces perpendicular to the frequency plane. The coefficient sets given by Elkins (1951), Henderson and Zietz (1949), Rosenbach (1953), and the “center‐point‐and‐one‐ring” method are analysed. These formulas, in order of increasing “average” accuracy of approximation, are Henderson and Zietz, Rosenbach, “center‐point‐and‐one‐ring” method, Elkins. Henderson and Zietz’s formula and the “center‐point‐and‐one‐ring” method have depended significantly on direction, while Rosenbach’s formula is nearly nondirectional. Elkins’ formula lies between them.

Band Centers and Track Finding for Large Two-Dimensional Infrared Spectroscopic Arrays

2003 ◽  
Vol 57 (3) ◽  
pp. 323-330 ◽  
Author(s):  
Li Chen ◽  
Marc Garland
Keyword(s):  
Time Series ◽  
Spectral Data ◽  
Time Series Data ◽  
Series Data ◽  
Second Derivative ◽  
Two Dimensional ◽  
Peak Finding ◽  
Derivative Method ◽  
Computationally Intensive ◽  
Second Derivative Method

An efficient two-dimensional (2D) peak-finding algorithm is proposed to find peak maps that specify the peak centers of all bands in two-dimensional arrays of time-series infrared spectral data. The algorithm combines the second-derivative method with the intrinsic characteristics of 2D infrared reaction spectral data. Initially, the second-derivative method is used to detect all possible peak center positions, and then three criteria drawn from characteristics of 2D continuous spectral data are employed to filter peak positions. Four 2D peak maps are generated in a sequential order, with better and better approximations to the peak center positions being obtained in each. The 2D peak-finding algorithm has been successfully applied to both simulated spectra (to initially evaluate the algorithm) and then real 2D experimental spectra. The resulting peak maps exhibit very good estimates of the peak center positions. An ordering from the most significant to the least significant bands is obtained. The final peak maps can be used as starting parameters for various applications including the computationally intensive curve-fitting of time-series data.

Different Spectrophotometric and Chromatographic Methods for Determination of Mepivacaine and Its Toxic Impurity

2017 ◽  
Vol 100 (5) ◽  
pp. 1392-1399 ◽  
Author(s):  
Nada S Abdelwahab ◽  
Nehal F Fared ◽  
Mohamed Elagawany ◽  
Esraa H Abdelmomen
Keyword(s):  
Particle Size ◽  
Stationary Phase ◽  
Second Derivative ◽  
Spectrophotometric Measurement ◽  
Spectrophotometric Methods ◽  
Derivative Method ◽  
Tlc Plates ◽  
Second Derivative Method ◽  
Developing System

Abstract Stability-indicating spectrophotometric, TLC-densitometric, and ultra-performance LC (UPLC) methods were developed for the determination of mepivacaine HCl (MEP) in the presence of its toxic impurity, 2,6-dimethylanaline (DMA). Different spectrophotometric methods were developed for the determination of MEP and DMA. In a dual-wavelength method combined with direct spectrophotometric measurement, the absorbancedifference between 221.4 and 240 nm was used for MEPmeasurements, whereas the absorbance at 283 nm was used for measuring DMA in the binary mixture. In the second-derivative method, amplitudes at 272.2 and 232.6 nm were recorded and used for the determination of MEP and DMA, respectively. The developed TLC-densitometric method depended on chromatographic separation using silica gel 60 F254 TLC plates as a stationary phase and methanol–water–acetic acid (9 + 1 + 0.1, v/v/v) as a developing system, with UV scanning at 230 nm. The developed UPLC method depended on separation using a C18 column (250 × 4.6 mm id, 5 μm particle size) as a stationary phase and acetonitrile–water (40 + 60, v/v; pH 4 with phosphoric acid) as a mobilephase at a flow rate of 0.4 mL/min, with UV detection at 215 nm. The chromatographic run time was approximately 1 min. The proposed methods were validated with respect to International Conference on Harmonization guidelines regarding precision, accuracy, ruggedness, robustness, and specificity.

scholarly journals A method of two-dimensional filtering of modulated matrix data sequences

2019 ◽  
Vol 1205 ◽  
pp. 012016
Author(s):  
V G Getmanov ◽  
I I Astapov ◽  
N S Barbashina ◽  
A D Gvishiani ◽  
A N Dmitrieva ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Two Dimensional Filtering

Two-Dimensional Correlation Analysis, Fourier Self-Deconvolution, and Second-Derivative Studies on Assignments of the CH2 Stretching Bands for Cast Films of 2-Dodecyl-, 2-Pentadecyl-, and 2-Octadecyl-7,7,8,8-Tetracyanoquinodimethane

2000 ◽  
Vol 54 (5) ◽  
pp. 692-698 ◽  
Author(s):  
Hai-Shui Wang ◽  
Yukihiro Ozaki
Keyword(s):  
Infrared Spectra ◽  
Alkyl Chain ◽  
Second Derivative ◽  
Two Dimensional ◽  
Langmuir Blodgett ◽  
Cast Films ◽  
Band Region ◽  
Correlation Spectrum ◽  
Doublet Band ◽  
Different Origins

Infrared spectra have been measured for cast films of three kinds of 2-alkyl-7,7,8,8-tetracyanoquinodimethanes (C nTCNQ) prepared on KBr plates. Each infrared spectrum shows two components for the CH2 antisymmetric stretching band (2926 and 2918 cm−1), and the relative intensity of the two bands changes with the length of the alkyl chain. In contrast to the characteristic doublet band in the antisymmetric stretching band region, only one band seems to appear near 2850 cm−1 in the corresponding CH2 symmetric stretching band region. In order to reveal the number of the bands appearing in the CH2 antisymmetric and symmetric stretching regions and to explore the origins of these bands, Fourier self-deconvolution (FSD) and second-derivative methods have been applied to the infrared spectra of the cast films. The FSD analysis of the spectra for the three kinds of C nTCNQ derivatives measured at a 4 cm−1 resolution demonstrates that the CH2 symmetric stretching band also consists of two components (near 2853 and 2848 cm−1). The same conclusion has been obtained by the second derivative of the spectra measured at 1 cm−1 resolution. An asynchronous two-dimensional (2D) correlation spectrum created from time-dependent infrared spectra for a one-layer Langmuir–Blodgett (LB) film develops cross peaks at (2927 and 2916 cm−1) and (2854 and 2846 cm−1), suggesting that the bands at 2927 and 2916 cm−1 come from different species and those at 2854 and 2846 cm−1 also have different origins. The bands at 2918 and 2848 cm−1 may be due to the interdigitated part of the alkyl chain in the cast film, which has ordered ( trans-zigzag) form, while the bands near 2926 and 2853 cm−1 are probably ascribed to the noninterdigitated part of the alkyl chain, which has disordered form with several gauche conformations.

Usefulness of a Curve Fitting Method in the Analysis of Overlapping Overtones and Combinations of CH Stretching Modes

2002 ◽  
Vol 10 (1) ◽  
pp. 85-91 ◽  
Author(s):  
Yukiteru Katsumoto ◽  
Daisuke Adachi ◽  
Harumi Sato ◽  
Yukihiro Ozaki
Keyword(s):  
Curve Fitting ◽  
Second Derivative ◽  
Downward Shift ◽  
Fitting Method ◽  
Derivative Method ◽  
Structural Differences ◽  
Alcohol Mixtures ◽  
Curve Fitting Method ◽  
Second Derivative Method ◽  
Water Alcohol

This paper reports the usefulness of a curve fitting method in the analysis of NIR spectra. NIR spectra in the 7500–5500 cm−1 (1333–1818 nm) region were measured for water–methanol, water–ethanol and water–1-propanol mixtures with alcohol concentrations of 0–100 wt% at 25°C. The 6000–5600 cm−1 (1667–1786 nm) region, where the overtones and combinations of CH3 and CH2 stretching modes are expected to appear, shows significant band shifts with the increase in the alcohol content. To analyse the concentration-dependent spectral changes, a curve fitting method was utilised, and the results were compared with those obtained previously by a second derivative method. It was found that the first overtones of CH3 asymmetric and symmetric stretching modes of alcohols show a downward shift by about 15–30 cm−1 with the increase in the concentration of alcohols. The shifts are much larger for water–methanol mixtures than for water–ethanol and water–1-propanol mixtures. The first overtones and combinations of CH2 stretching modes of ethanol and 1-propanol also show a small downward shift. These shifts support our previous conclusion that there is an intermolecular “CH⃛O” interaction between the methyl group and water in the water–alcohol mixtures. The curve fitting method provided more feasible results for the band shifts than the second derivative method. It was revealed from the curve fitting method that the first overtone of the CH3 asymmetric stretching mode of water–methanol, water–ethanol and water–1-propanol mixtures shows different concentration-dependent plots. The first overtone of CH3 asymmetric stretching mode of water–methanol mixtures shifts more rapidly in the high methanol concentration range while that of water–1-propanol concentration shifts more markedly in the low 1-propanol concentration range. That of water–ethanol mixtures shows an intermediate trend. Based upon these differences structural differences among the three kinds of water–alcohol mixtures are discussed.

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