### 统计代写|化学计量学作业代写chemometrics代考|Dealing with Noise

statistics-lab™ 为您的留学生涯保驾护航 在代写化学计量学chemometrics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写化学计量学chemometrics代写方面经验极为丰富，各种代写化学计量学chemometrics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|化学计量学作业代写chemometrics代考|Dealing with Noise

Physico-chemical data always contain noise, where the term “noise” is usually reserved for small, fast, random fluctuations of the response. The first aim of any scientific experiment is to generate data of the highest quality, and much effort is

usually put into decreasing noise levels. The simplest experimental way is to perform $n$ repeated measurements, and average the individual spectra, leading to a noise reduction with a factor $\sqrt{n}$. In NMR spectroscopy, for example, a relatively insensitive analytical method, signal averaging is routine practice, where one has to strike a balance between measurement time and data quality.

As an example, we consider the prostate data, where each sample has been measured in duplicate. The replicate measurements of the prostate data cover consecutive rows in the data matrix. Averaging can be done using the following steps.

Also in the averaged data the noise is appreciable; reducing the noise level while taking care not to destroy the data structure would make subsequent analysis much easier.

The simplest approach is to apply a running mean, i.e., to replace every single value by the average of the $k$ points around it. The value of $k$, the so-called window size, needs to be optimized; large values lead to a high degree of smoothing, but also to peak distortion, and low values of $k$ can only make small changes to the signal. Very often $k$ is chosen on the basis of visual inspection, either of the smoothed signal itself or of the residuals. Running means can be easily calculated using the function embed, providing a matrix containing successive chunks of the original data vector as rows; using the function rowMeans one then can obtain the desired running means.

## 统计代写|化学计量学作业代写chemometrics代考|Baseline Removal

In some forms of spectroscopy one can encounter a baseline, or “background signal” that is far away from the zero level. Since this influences measures like peak height and peak area, it is of utmost importance to correct for such phenomena.

Infrared spectroscopy, for instance, can lead to scatter effects-the surface of the sample influences the measurement. As a result, one often observes spectral offsets: two spectra of the same material may show a constant difference over the whole wavelength range. This may be easily removed by taking first derivatives (i.e., looking at the differences between intensities at sequential wavelengths, rather than the intensities themselves). Take a look at the gasoline data:
$>$ nir.diff $<-t(a p p l y{g a s o l i n e \$ N I R, 1$, diff)$)$• matplot (wavelengths$[-1]+1$, t(nir.diff),$\mathrm{xlab}=$“Wavelength$(\mathrm{nm}\rangle^{*}, y 1 a b=” 1 / \mathrm{R}$(1st deriv.)”, type$=” n$“)$>a b l i n e(h=0$, col = “gray”$)$matines (wavelengths$[-1]+1, t$(nir.diff), lty = 1) Note that the number of variables decreases by one. The result is shown in Fig. 3.5. Comparison with the original data (Fig. 2.1) shows more detailed structure; the price is an increase in noise. A better way to obtain first-derivative spectra is given by the Savitsky-Golay filter (here using the sgolayfilt function from the signal package), which is not only a smoother but can also be used to calculate derivatives: nir.deriv <- apply(gasoline\$NIR, 1, sgolayfilt, m = 1)
In this particular case, the differences between the two methods are very small. Also second derivatives are used in practice-the need to control noise levels is even bigger in that case.

Another way to remove scatter effects in infrared spectroscopy is Multiplicative Scatter Correction (MSC, Geladi et al. 1985; Nis et al. 1990). One effectively models

the signal of a query spectrum as a linear function of the reference spectrum:
$$y_{q}=a+b y_{r}$$

## 统计代写|化学计量学作业代写chemometrics代考|Aligning Peaks—Warping

Many analytical data suffer from small shifts in peak positions. In NMR spectroscopy, for example, the position of peaks may be influenced by the $\mathrm{pH}$. What complicates matters is that in NMR, these shifts are by no means uniform over the data; rather, only very few peaks shift whereas the majority will remain at their original locations.

The peaks may even move in different directions. In mass spectrometry, the shift is more uniform over the $m / z$ axis and is more easy to account for-if one aims to analyse the data in matrix form, binning is required, and in many cases a suitable choice of bins will already remove most if not all of the effects of shifts. Moreover, peak shifts are usually small, and may be easily corrected for by the use of standards.
The biggest shifts, however, are encountered in chromatographic applications, especially in liquid chromatography. Two different chromatographic columns almost never give identical elution profiles, up to the extent that peaks may even swap posi-tions. The situation is worse than in gas chromatography, since retention mechanisms are more complex in the liquid phase than in the gas phase. In all forms of column chromatography, column age is an important factor: a column that has been used for some time almost certainly will show different chromatograms than when freshly installed.

## 统计代写|化学计量学作业代写chemometrics代考|Baseline Removal

>nir.diff $<-t(apply{gasoline$ NIR, 1,d一世FF))$• matplot（波长[−1]+1, t(nir.diff), Xl一种b=“波长(n米⟩∗,是1一种b=”1/R（一阶导数）”， 输入=”n “) >一种bl一世n和(H=0, col = “灰色”) 日光（波长[−1]+1,吨(nir.diff), lty = 1) 注意变量的数量减一。结果如图 3.5 所示。与原始数据（图 2.1）的比较显示了更详细的结构；代价是噪音的增加。Savitsky-Golay 滤波器（这里使用信号包中的 sgolayfilt 函数）给出了获得一阶导数光谱的更好方法，它不仅更平滑，还可以用于计算导数： nir.deriv <- apply (gasoline$ NIR, 1, sgolayfilt, m = 1)

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。