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# 统计代写|贝叶斯分析代考Bayesian Analysis代写|ERTH695 Unit of Measurement of Frequency

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## 统计代写|贝叶斯分析代考Bayesian Analysis代写|Unit of Measurement of Frequency

The international measurement of frequency is hertz $(\mathrm{Hz})$, which is one cycle per second and is equivalent to $2 \pi$ radians per second. Note a frequency of $f$ cycles per second is equivalent to $\omega$ radians per second, that is to say,
$$\omega=2 \pi f \Leftrightarrow f=\omega / 2 \pi$$
Now consider a time series of length $n{Y(t), t=1,2, \ldots, n}$, where $n$, is even; thus, consider fitting a regression model with $Y(t)$ as the response and $n-1$ predictor variables: $\cos (2 \pi t / n), \sin (2 \pi t / n), \cos (4 \pi t / n), \sin (4 \pi t / n), \ldots$, $\cos (2(n / 2-1) \pi t / n), \sin (2(n / 2-1) \pi t / n), \cos (\pi t)$.

## 统计代写|贝叶斯分析代考Bayesian Analysis代写|The Spectrum

A plot of $A_r^2, r=1,2, .$. versus $r$ is the Fourier line spectrum, and the raw periodogram in $\mathrm{R}$ is obtained by joining the tips of the spikes in the Fourier line spectrum, which produces a continuous plot, where the scaling is done so that the area equals the variance. The periodogram distributes the variance over frequency, which according to Cowperwait and Metcalfe ${ }^{2, ~ p p . ~}{ }^{175-177}$ has several disadvantages. The first is that the chosen frequencies are arbitrary, while the second is that the periodogram does not become smoother as the number of observations increases but includes more spikes packed loser together. To counteract this, the remedy is to smooth the periodogram by computing the moving average of spikes before joining the tips. The smoothed periodogram is also known as the sample spectrum, which is denoted as $C_{y y}()$, which had domain frequency given in radians $\omega$ or cycles per unit time. Another disadvantage is that smoothing will reduce the heights of the spikes; thus, additional smoothing blurs the features sought. Thus, one approach is present spectra with varying amounts of smoothing, which is easily implemented with the $\mathrm{R}$ function called spectrum.

The spectrum function in $\mathrm{R}$ has as an argument is the number of spikes in the moving average, which is a useful hint for the initial value for time series with a large number of observations.

# 贝叶斯分析代写

## 统计代写|贝叶斯分析代考Bayesian Analysis代写|Unit of Measurement of Frequency

$$\omega=2 \pi f \Leftrightarrow f=\omega / 2 \pi$$

## 统计代写|贝叶斯分析代考Bayesian Analysis代写|The Spectrum

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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。