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Upsampling01:22

Upsampling

262
Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
262
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

235
Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
235
Random Sampling Method01:09

Random Sampling Method

11.2K
Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
11.2K
Sampling Theorem01:15

Sampling Theorem

380
In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
380
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

101
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
101
Downsampling01:20

Downsampling

184
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
184

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相关实验视频

Updated: Jul 18, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

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用tensor超收缩与k点采样进行随机相近似的低缩放算法.

Chia-Nan Yeh1, Miguel A Morales1

  • 1Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States.

Journal of chemical theory and computation
|August 25, 2023
PubMed
概括
此摘要是机器生成的。

我们开发了一种新的,高效的算法,用于使用张量超收缩 (THC) 进行随机相近似 (RPA) 计算. 这种方法提供了用k点进行线性缩放和用系统大小进行立方缩放,以准确进行电子结构计算.

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相关实验视频

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科学领域:

  • 计算化学计算化学
  • 量子多体物理学 量子多体物理学
  • 电子结构理论 电子结构理论

背景情况:

  • 对电子排斥积分 (ERI) 的准确计算对于多体扰动理论至关重要.
  • 传统方法面临着显著的计算缩放挑战,随着系统大小的增加和k点采样.
  • 随机相近似 (RPA) 是电子结构的强大工具,但在计算上要求很高.

研究的目的:

  • 开发一个低缩放的算法用于RPA计算与k点采样.
  • 在张量超收缩 (THC) 电子排斥积分 (ERI) 框架内实现此算法.
  • 为大规模系统提供准确和高效的电子结构计算.

主要方法:

  • 采用了修订的互极分离密度拟合 (ISDF) 程序进行THC因子化.
  • 用于单粒子布洛赫轨道的动量依赖辅助基础.
  • 开发了一个公式,通过插入点的数量系统地控制准确性,避免预先优化.

主要成果:

  • 为RPA算法实现了对k点数进行线性缩放和对系统大小进行立方缩放.
  • 证明了ERI和RPA能量误差与THC辅助基的大小的快速趋同.
  • 该算法在没有对轨道稀疏性或局部性的假设的情况下运行.

结论:

  • 使用THC的低缩放RPA算法是一个强大的和有前途的方法,用于大规模的电子结构计算.
  • 这种方法为高阶多体扰动理论中的高效算法铺平了道路.
  • 对精度的系统控制和高效的缩放使其适用于复杂的系统.