How to estimate Structure Factor by using Fourier Transform based on Cartesian coordinates?
Best insight from top research papers
Estimating Structure Factors through Fourier Transform based on Cartesian coordinates involves various approaches. One method involves calculating structure factors by Fourier inversion of an electron density map, which has been shown to be more cost-effective than conventional methods for non-centrosymmetric space groups . Another technique suggests expressing concentration effects in small-angle scattering data solely through real space functions without an explicit structure factor, allowing for the calculation of the structure factor from estimated distributions . Additionally, probability relationships between structure factors from related structures can be extended to cover more general cases, with the expected electron-density formalism providing a more accurate phase estimate by considering atomic parameters as random variables . These methods collectively contribute to the estimation of Structure Factors using Fourier Transform based on Cartesian coordinates.
Answers from top 5 papers
More filters
| Papers (5) | Insight |
|---|---|
2 Citations | The Fourier transform of curves and filaments in Cartesian coordinates can be used to estimate the Structure Factor in low-resolution protein crystallography, requiring fewer parameters for accurate approximations. |
105 Citations | Structure factors can be estimated by Fourier inversion of an electron density map, utilizing the Fast Fourier Transform method, which is 3½ to 7 times more efficient for non-centrosymmetric space groups. |
116 Citations | The Structure Factor can be estimated using Fourier Transform based on Cartesian coordinates by smearing each atom over its possible positions to obtain the expected electron-density function. |
18 Citations | The structure factor can be estimated by dividing the total distance distribution function into single particle and structure distributions, allowing for calculation from the estimated distributions. |
25 Citations | To estimate Structure Factors using Fourier Transform based on Cartesian coordinates, follow Lipson & Cochran's sampling recommendation and determine an appropriate Gaussian dampening factor as per the paper. |
Related Questions
What is computer structural analysis?5 answersComputer structural analysis involves utilizing computational methods to analyze structures in various fields such as engineering, medicine, and computer science. It encompasses tasks like detection, tracking, motion analysis, deformation estimation, and 3D shape reconstruction. By creating computer models that predict the behavior of physical structures, this analysis aids in understanding complex phenomena, facilitating engineering education. Efforts are made to efficiently use computer memory and run times for accurate and speedy analyses of structural systems. Additionally, innovative approaches like hybrid memory analysis are introduced, combining shape analysis with efficient transfer functions to express structural, shape, and sharing properties for optimization and error detection applications. Overall, computer structural analysis plays a crucial role in advancing research and development in various sectors by providing detailed insights into structural behavior.
What is meant by the concept of spatial frequency in the Fourier Transform for images?5 answersSpatial frequency in the Fourier Transform for images refers to the rate of change of intensity patterns across an image. It plays a crucial role in analyzing spatial patterns within images. Fourier transforms allow the conversion between spatial and frequency domains without loss of information or noise, enabling detailed image processing. Techniques like Directional Fourier Spatial Frequencies (DFSF) and Fourier single-pixel imaging are utilized to extract and analyze spatial frequency components in images, aiding in tasks like disease diagnosis and image reconstruction. The concept of spatial frequency is fundamental in understanding how different patterns and structures in images are represented and manipulated through Fourier analysis, facilitating various applications in image processing and medical imaging.
What is transform fourier?3 answersThe Fourier transform is a mathematical technique used to analyze signals and functions in various fields such as physics, engineering, and image processing. It allows us to decompose a signal into its constituent frequencies, revealing the frequency content of the signal. The Fourier transform can be seen as a generalization of the Fourier series, which is used for periodic signals, to signals that are not necessarily periodic. It has applications in solving partial differential equations, signal processing, compressed sensing, and machine learning. The Fourier transform can be approximated using the discrete Fourier transform (DFT) and its inverse (IDFT), which are computationally efficient algorithms for analyzing discrete signals. It is also used in real-time image processing and wave-based analog computing systems. The properties of the Fourier transform, such as the Plancherel theorem, make it a powerful tool for analyzing and manipulating signals.
Why should the fourier transformation be used?3 answersThe Fourier transformation is used for various purposes in different fields. It is commonly used to simplify and solve differential equations related to heat transfer, wave movement, and standing waves. In data analysis, Fourier analysis is frequently used to model and simplify data, especially for multivariate data analysis. In the field of astrophysics, the Fourier transform is utilized to detect and analyze pulsar signals, predict their characteristics, and correct for background radio noise. Additionally, the Fourier transform is employed in the study of power transformers to analyze changes in their electrical and magnetic parameters and determine the relationship between different modes and winding damage. In the context of data transmission, Fourier series and Fourier transformation are used to study and analyze signals, leading to the development of interpolation polynomials and signal recovery techniques.
How do the Fourier transform and group theory relate to one another?5 answersThe Fourier transform and group theory are closely related. In the theory of locally compact quantum groups, the Fourier transform can be generalized to algebraic quantum groups, which are locally compact quantum groups that can be treated with purely algebraic methods. The Fourier transform is also used in group codes to minimize mean-square error, and an efficient method for calculating the Fourier transform of a group has been proposed. In quantum information, the Fourier transform is connected to strongly complementary observables, and the necessary tools of representation theory have been generalized to arbitrary dagger symmetric monoidal categories. The Fourier transform has also been applied to the spatially homogeneous and isotropic Boltzmann equation, where a complete group classification of the Fourier transform has been given. Additionally, a group Fourier transform has been formulated for finite dimensional Lie groups, providing a unitary map from functions on the group to functions on a non-commutative dual space.
How do structural factors contribute to crime rate?5 answersStructural factors contribute to the crime rate in various ways. Ethnic and religious heterogeneity, income inequality, and educational inequality have been found to positively affect both the crime rate and the number of activist organizations in U.S. counties. Additionally, population, fertility, unemployment, and GDP have been identified as influential factors in the long-run and short-run periods in Malaysia. A study on adolescents with serious criminal backgrounds found that the relationship between structural factors, subjective factors, and crime termination can be explored through the structural-subjective perspective. Furthermore, a study comparing rural and urban counties in the U.S. revealed significant structural shifts in the influence of poverty and income inequality on crime rates, with income inequality outperforming poverty measures in predicting changes in crime rates. Overall, understanding and addressing social structure and economic conditions are crucial for preventing crime in the long-run.