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# 数学代写|Matlab代考|ENGR1035 Spectrum of the Chesapeake Bay

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Matlab ENGR1035是由数学家和计算机程序员Cleve Moler发明的。MATLAB的想法是基于他1960年代的博士论文。Moler成为新墨西哥大学的一名数学教授，并开始为他的学生开发MATLAB作为一种爱好。他在1967年与他曾经的论文导师George Forsythe开发了MATLAB的最初线性代数编程。随后在1971年开发了线性方程的Fortran 代码。

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## 数学代写|Matlab代考|数学代写|Matlab代考|Spectrum of the Chesapeake Bay

For our final example, we perform a Fourier analysis of hourly sea-level measurements taken at the mouth of the Chesapeake Bay during the 2000 days from 9 April 1985 to 29 June 1990. Figure 5.7.4 shows 200 days of this record, starting from 1 July 1985. As this figure shows, the measurements contain a wide range of oscillations. In particular, note the large peak near day 90 that corresponds to the passage of Hurricane Gloria during the early hours of 27 September 1985 .

Utilizing the entire 2000 days, we plotted the amplitude of the Fourier coefficients as a function of period in Figure 5.7.5. We see a general rise of the amplitude as the period increases. Especially noteworthy are the sharp peaks near periods of 12 and 24 hours. The largest peak is at $12.417$ hours and corresponds to the semidiurnal tide. Thus, our Fourier analysis shows that the dominant oscillations at the mouth of the Chesapeake Bay are the tides. A similar situation occurs in Baltimore harbor. Furthermore, with this spectral information we could predict high and low tides very accurately.

Although the tides are of great interest to some, they are a nuisance to others because they mask other physical processes that might be occurring. For that reason we would like to remove them from the tidal gauge history and see what is left. One way would be to zero out the Fourier coefficients corresponding to the tidal components and then plot the resulting Fourier series. Another method is to replace each hourly report with an average of hourly reports that occurred 24 hours ahead of and behind a particular report. We construct this average in such a manner that waves with periods of the tides sum to zero. ${ }^{24}$ Such a filter is a popular method for eliminating unwanted waves from a record. Filters play an important role in the analysis of data. We plotted the filtered sea level data in Figure 5.7.6. Note that summertime ( $0-50$ days) produces little variation in the sea level compared to wintertime (100-150 days) when intense coastal storms occur.

## 数学代写|Matlab代考|Design Your Own Snow Tire, Part II

In Part I of this project you examined the spectrum of a simple model for a snow tire and you found the effect of tread thickness and spacing on the spectrum of the noise produced as the treads struck the pavement. Clearly, if you were to introduce a more complex and perhaps more realistic model, the calculations would become very cumbersome. But now, capitalizing on the work of the previous project, you can use the fast Fourier transform to compute the spectrum once you decide on a tread pattern. That is the object of this project.

Step 1: For $-\pi<t<\pi$ and assuming that this pattern repeats with a period of $2 \pi$, devise a function $f(t)$, where it equals 1 when the tread is striking the roadway and 0 when it is not.

Step 2: Use the code that you developed in the previous project to find the amplitude of the Fourier coefficients as a function of the harmonic. Test out your code by recovering the results from Example 5.1.3.

Step 3: Our tire pattern of two thin treads is not very realistic. Modify your code so that it now has 4 thick treads separated by thin gaps. Compare the spectrum when the gaps are uniformly spaced and one where they are randomly spaced.

# Matlab代写

## 数学代写|Matlab代考|Design Your Own Snow Tire, Part II

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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。