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相关概念视频

Linear Approximation in Frequency Domain01:26

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
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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.
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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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基于前向后向线性预测的光谱分辨率增强中的参数估计 总最小平方方法

Yusheng Qin1,2, Xin Han1, Xiangxian Li1

  • 1Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, China.

Applied spectroscopy
|July 14, 2023
PubMed
概括

一种新方法通过使用自回归 (AR) 建模来推断米歇尔森干扰信号来提高福里埃变换红外光谱仪 (FTIR) 的分辨率. 前向后向线性预测总最小平方 (FB-TLS) 方法有效地抑制噪声和虚假峰值.

关键词:
线性预测 线性预测在 TLS 中使用 TLS.这是一个干扰信号干扰信号.解决方案的增强解决方案的增强频谱分辨率的使用总的最小平方数.

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科学领域:

  • 频谱学是一种光谱学.
  • 分析化学 分析化学
  • 物理化学 物理化学

背景情况:

  • 福里埃变换红外光谱法 (FTIR) 依赖于米歇尔森干扰仪.
  • 改善FTIR中的光谱分辨率对于详细分析至关重要.
  • 使用自回归 (AR) 模型的线性预测方法对于信号外推是常见的.

研究的目的:

  • 为AR模型参数估计引入和评估前向后向线性预测总最小平方 (FB-TLS) 方法.
  • 通过推断迈克尔森干扰信号来增强FTIR的光谱分辨率.
  • 为了将FB-TLS方法与现有的技术比较,如Burg和最小平方.

主要方法:

  • 为迈克尔森干扰信号建立一个自回归 (AR) 模型.
  • 使用拟议的FB-TLS方法估计AR模型参数.
  • 模拟各种信号噪声比率和模型订单以评估性能.

主要成果:

  • 该FB-TLS方法有效地抑制噪声,并避免在光谱分辨率增强中出现虚假峰值.
  • 模拟表明,在某些条件下,FB-TLS的表现优于伯格和最小平方方法.
  • 在NH3光谱上的实验验证表明,成功地将分辨率从2厘米−1提高到1厘米−1,预测误差低 (0.21%).

结论:

  • 该FB-TLS方法是一种强大的和有效的技术,用于增强FTIR光谱分辨率.
  • 这种方法在光谱细节和精度方面提供了显著的改进.
  • 该FB-TLS方法具有先进的光谱分析和应用的前景.