Search results for "Fourier transform"
showing 10 items of 1138 documents
Biorthogonal Wavelet Transforms Originating from Discrete and Discrete-Time Splines
2018
This chapter describes how to generate families of biorthogonal wavelet transforms in spaces of periodic signals using prediction p-filters originating from discrete-time and discrete splines. The transforms are generated by the lifting scheme (Sweldens (Wavelet applications in signal and image processing III, vol 2569, 1995, [7]), Sweldens (Appl Comput Harmon Anal 3:186–200, 1996, [8]), Sweldens (SIAM J Math Anal 29:511–546, 1997, [9]), see also Sect. 7.1 of this volume). The discrete-time wavelets related to those transforms are (anti)symmetric, well localized in time domain and have flat spectra. These families comprise wavelets with any number of local discrete vanishing moments (LDVMs)…
FOURIER TRANSFORMS, FRACTIONAL DERIVATIVES, AND A LITTLE BIT OF QUANTUM MECHANICS
2020
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set, $\Sc'(\mathbb R)$, the set of tempered distributions, provided they satisfy some mild conditions. We discuss some examples, and we show how our definition can be used in a quantum mechanical context.
Determination of sugars in depilatory formulations: a green analytical method employing infrared detection and partial least squares regression.
2011
A green analytical method was developed for the analysis of sugar-based depilatories. Three independent partial least squares (PLS) regression models were built for the direct determination of glucose, fructose and maltose without any sample pretreatment based on their attenuated total reflectance - Fourier transform infrared (ATR-FTIR) spectra. The models showed adequate prediction capabilities with root-mean-square-errors of prediction ranging from 7.04 to 12.55 mg sugar g(-1) sample. As a reference procedure, gradient liquid chromatography with on-line infrared detection, employing background correction based on cubic smoothing splines, was used. The analysis revealed changes in the suga…
Quality control Fourier transform infrared determination of diazepam in pharmaceuticals
2007
A quality control procedure has been developed for the determination of diazepam in pharmaceuticals using Fourier transform infrared (FTIR) spectroscopy. The method involves the off-line extraction of diazepam with chloroform by sonication and direct determination in the extracts through peak area measurement in the interval between 1672 and 1682 cm(-1) using a baseline correction defined between 1850 and 1524 cm(-1). For standardization it was used an external calibration line established from standard solutions of diazepam in chloroform. The method provides a limit of detection of 0.04 mg per tablet (n=5), a relative standard deviation (R.S.D.) of 0.5% for 5 independent measurements of a …
ATR-FTIR spectroscopy as a quality control system for monitoring the storage of blood products
2021
Blood screening is a fundamental part of disease diagnosis and monitoring health. Attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy offers an innovative solution to streamlining the process, especially for multianalyte detection in aqueous samples. However, samples always undergo a storage phase before they are processed for testing and blood transfusion. In this study, we investigated the effect of standard storage procedures on the macromolecular composition of whole blood, and plasma collected in blood tubes for diagnostic purposes and initial screening of blood products. Periphery blood samples were collected from 10 volunteers and then stored for 14 days a…
Comparison of two partial least squares infrared spectrometric methods for the quality control of pediculosis lotions.
2006
Two vibrational spectroscopy procedures have been developed and compared for the direct and simultaneous determination of piperonyl butoxide and tetramethrin, the active ingredients of alcoholic capillary lotions, for hair pediculosis diseases. Nine lotions, purchased from the Spanish market, were analyzed using both, attenuated total reflectance (ATR) and transmission FT-IR measurements, and based on the use of partial least squares (PLS) multivariate calibration. A reduced set of 15 matched standards (11 for calibration and 4 for validation) was employed using both measurement modes. The spectral wave number ranges between 1757 and 1712 cm(-1) was selected to determine tetramethrin by bot…
Feature selection strategies for quality screening of diesel samples by infrared spectrometry and linear discriminant analysis.
2012
Abstract A rapid approach has been developed for the characterization of diesel quality, based on attenuated total reflectance – Fourier transform infrared (ATR-FTIR) spectrometry, which could be useful for diagnosing the sample quality condition. As a supervised technique, linear discriminant analysis (LDA) was employed to process the spectrometric data. The role of variable selection methods was also evaluated. Successive projection algorithm (SPA) and genetic algorithm (GA) feature selection techniques were applied prior to the discriminative procedure. It was aimed to compare the effect of feature selection procedures on classification capability of IR spectrometry for the diesel sample…
Difficulties of density functional theory in predicting the torsional potential of 2,2?-bithiophene
1998
The internal rotation of 2,2′-bithiophene was investigated within the density functional theory (DFT) approach. Fully optimized DFT torsional potentials are compared with Moller–Plesset (MP2) results which predict a fourfold potential with s-cis- and s-trans-gauche minima. DFT calculations fail in describing the energetics of the internal rotation because they favor planar vs. perpendicular conformers. Gradient-corrected functionals provide torsional potentials where the gauche minima have almost vanished and the s-ciss-trans interconversion barriers are twice as high as the barriers obtained at the MP2 level. The use of local functionals augments the shortcomings of the DFT approach. The g…
Self-broadening coefficients and improved line intensities for the ν7 band of ethylene near 10.5μm, and impact on ethylene retrievals from Jungfraujo…
2014
Relying on high-resolution Fourier transform infrared (FTIR) spectra, the present work involved extensive measurements of individual line intensities and self-broadening coefficients for the ν7 band of 12C2H4. The measured self-broadening coefficients exhibit a dependence on both J and Ka. Compared to the corresponding information available in the latest edition of the HITRAN spectroscopic database, the measured line intensities were found to be higher by about 10% for high J lines in the P branch and lower by about 5% for high J lines of the R branch, varying between these two limits roughly linearly with the line positions. The impact of the presently measured line intensities on retrieva…
Evidence for a critical dose above which damage to carbonate ester bonds in PADC appear after gamma ray and ultra soft X-ray exposures
2020
Abstract It has been confirmed that the density of carbonate ester in poly(allyl diglycol carbonate) (PADC), which is a well-known polymeric nuclear track detector CR-39, begins decreasing above a critical dose of about 60 kGy during exposures to Co-60 gamma rays and Ultra Soft X-rays (USX: Kα (Al) with energy 1.49 keV). After exposure to Co-60 gamma rays at 77 K and room temperature (RT), a significant difference in Electron Spin Resonance (ESR) spectra has been observed at both sides of a critical dose of 60 kGy, where is a threshold for the degradation of carbonate ester in PADC. Namely, the types of free radicals in PADC are different from each other below and above this critical dose. …