High-Resolution Frequency Analysis by the Use of Derivatives of the Fourier Transform: Application to Fluorescence Quantum Beats

1999 ◽  
Vol 72 (6) ◽  
pp. 1225-1231
Author(s):  
Hirohiko Kono ◽  
Isao Kawata ◽  
Nobuhiro Ohta
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Frequency Analysis ◽  
Quantum Beats ◽  
The Fourier Transform ◽  
Derivatives Of

scholarly journals Time series forecasting using amplitude-frequency analysis of STL components

2021 ◽  
Vol 2094 (3) ◽  
pp. 032019
Author(s):  
D G Chkalova
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Frequency Analysis ◽  
Software Implementation ◽  
Phase Operator ◽  
Economic Time Series ◽  
Economic Time ◽  
Harmonic Components ◽  
The Fourier Transform ◽  
Forecast Quality

Abstract The problem of economic time series analysis and forecasting using amplitude-frequency analysis of STL decomposition is considered. An amplitude-phase operator was chosen as an apparatus for extraction the series harmonic components, the advantages of which (compared to the Fourier transform) are: calculations speed, result accuracy, simplicity and interpretability of software implementation. The forecast quality was carried out using the MAPE metric. Significantly higher prediction quality was achieved compared to Facebook Prophet forecasting package.

The Pseudo-Atom Approximation in Direct Phase Determination of Protein Structures.

1997 ◽  
Vol 3 (S2) ◽  
pp. 1025-1026
Author(s):  
Douglas L. Dorset
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Protein Structures ◽  
Direct Methods ◽  
Direct Solution ◽  
Phase Problem ◽  
Electron Crystallography ◽  
Phase Determination ◽  
The Fourier Transform

In principle, the availability of high-resolution micrographs in electron crystallography is a direct solution of the phase problem that has been used to great advantage for the study of proteins. However, as the resolution of the determination increases, the Fourier transform of the micrograph becomes a less accurate phase source. Hence, alternative direct methods for phase determination have been evaluated, if only to extend the resolution of most reliable lower resolution phases to the limit of the electron diffraction pattern. The first demonstration of its feasibility was published in a study of bacteriorhodopsin extending 15 Å image phases to beyond 3 Å by maximum entropy and likelihood procedures i. Later studies demonstrated that convolutional methods also can be effective.In protein crystallography, there is always an interest in carrying out a true ab initio determinations, if only because of the challenge to traditional direct methods that become statistically less reliable as the number of atoms in the unit cell increases.

Fast rigid-body refinement for molecular-replacement techniques

1992 ◽  
Vol 25 (2) ◽  
pp. 281-284 ◽  
Author(s):  
E. E. Castellano ◽  
G. Oliva ◽  
J. Navaza
Keyword(s):  
Fourier Transform ◽  
Rigid Body ◽  
Least Squares ◽  
Fourier Coefficients ◽  
Molecular Replacement ◽  
Present Formulation ◽  
Judicious Choice ◽  
The Fourier Transform ◽  
Derivatives Of ◽  
Patterson Search

A method for the least-squares rigid-body refinement of a general electron density model is described. The present formulation is different from a previously reported one in the computation of the derivatives of the calculated Fourier coefficients, which are derived analytically here. This, together with a judicious choice of the Fourier transform search arrays, makes the procedure extremely fast and sufficiently accurate. Although originally designed simply to optimize the values of the positional parameters obtained by Patterson search techniques, the method proved to be extremely efficient as an aid for evaluation of the correctness of potential molecular-replacement solutions.

The absorption spectrum of C2H2 around ν1 + ν3: energy standards in the 1.5 μm region and vibrational clustering

1994 ◽  
Vol 72 (11-12) ◽  
pp. 1241-1250 ◽  
Author(s):  
Q. Kou ◽  
G. Guelachvili ◽  
M. Abbouti Temsamani ◽  
M. Herman
Keyword(s):  
Absorption Spectrum ◽  
Fourier Transform ◽  
High Resolution ◽  
Rotational Analysis ◽  
Vibrational Assignment ◽  
Calibration Standards ◽  
Vibrational Levels ◽  
Vibrational Transitions ◽  
The Fourier Transform ◽  
Anharmonic Couplings

We have recorded the Fourier transform absorption spectrum of acetylene, C2H2, at high resolution, around 6500 cm−1. The positions of the strongest rovibrational lines are measured with respect to the rovibrational lines in 3-0 of CO. They provide secondary calibration standards in that range with an accuracy of 3 × 10−4 cm−1. The rotational analysis of the data gives evidence of five vibrational levels of [Formula: see text] symmetry, in addition to the bright combination level (1010000). This is demonstrated to strictly fit the predicted anharmonic resonance pattern in that region, which permits the vibrational assignment of those extra transitions. Study of the relative intensities of the reported vibrational transitions suggests the need to include new quartic anharmonic couplings. This is supported by the rovibrational analysis of the cold bands around 8500 cm−1, involving the (1110000) bright level, which is also presented.

scholarly journals A Note on the Generalized Relativistic Diffusion Equation

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1009
Author(s):  
Luisa Beghin ◽  
Roberto Garra
Keyword(s):  
Fourier Transform ◽  
Fundamental Solution ◽  
Diffusion Equation ◽  
Fractional Derivatives ◽  
Stable Process ◽  
Caputo Fractional Derivatives ◽  
The Fourier Transform ◽  
Derivatives Of

We study here a generalization of the time-fractional relativistic diffusion equation based on the application of Caputo fractional derivatives of a function with respect to another function. We find the Fourier transform of the fundamental solution and discuss the probabilistic meaning of the results obtained in relation to the time-scaled fractional relativistic stable process. We briefly consider also the application of fractional derivatives of a function with respect to another function in order to generalize fractional Riesz-Bessel equations, suggesting their stochastic meaning.

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