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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

## 数学代写|傅里叶分析代写Fourier analysis代考|Energy and Power Signals

Power is the rate of doing work, typically measured in watts. It is common to specify devices by their power handling capacity. Devices, such as an electric motor, heater, amplifier and a diesel engine, are characterized by their power rating. The energy of a signal $x(t)$ is measured by the power dissipated in a $1 \Omega$ resister due to a voltage applied across it or a current passing through. The energy dissipated is
$$E=\int_{-\infty}^{\infty}|x(t)|^{2} d t$$
assuming that $E$ is finite. Signals satisfying the condition $E<\infty$ are called energy signals. All practical signals are energy signals. The energy of $x(t)=2 e^{-3 t}, t \geq 0$ is
$$E=\int_{0}^{\infty}\left|2 e^{-3 t}\right|^{2} d t=\frac{2}{3}$$
For discrete signals,
$$E=\sum_{n=-\infty}^{\infty}|x(n)|^{2}$$
The energy of $x(n)=3(0.8)^{n} u(n)$ is
$$E=\sum_{n=0}^{\infty}\left|3(0.8)^{n}\right|^{2}=\frac{9}{1-0.64}=\frac{9}{0.36}=25$$
Sinusoids are not energy signals, since they have infinite energy. Such signals are characterized by their power. The average power of a continuous signal is defined as $P=\lim {T \rightarrow \infty} \frac{1}{T} \int{-\frac{T}{2}}^{\frac{T}{2}}|x(t)|^{2} d t$

## 数学代写|傅里叶分析代写Fourier analysis代考|Complex Numbers

Complex number system is an extension of the real number system that suits a large number of applications in science and engineering. The simplest number system is the set of natural numbers ${1,2,3, \ldots}$, the system we use to count things. By including the negative numbers, we get the integers. Further, the number system is extended by including rational and irrational numbers. With this system, we can only specify the location of a point on a line. There is a necessity in several applications to represent a point on a plane. For example, a sinusoid at a given frequency is characterized by its amplitude and phase. That requires a pair of ordered numbers, a two-element vector. While it is possible to represent a sinusoid with two scalars, the vector representation is so much advantageous that it is used in most of the Fourier analysis, the subject of this book. Another advantage of the complex number system is that it provides solution to all polynomial equations. Further, real integrals, which may or may not be Except that the system is, unfortunately, named as complex number system, there is nothing complex about it and it is just another extension of the number system.
A complex number $z=(x, y)$ is a two-element vector of real numbers, in which the first and second elements are, respectively, called the real and imaginary parts of z. A more commonly used notation for the complex number is $z=x+j y$, where $j$ is the imaginary unit. For example, the real part of $z=(3-j 2)$ is 3 and the imaginary part is $-2$. This form of a complex number is called its rectangular form. Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are also equal.

# 傅里叶分析代写

## 数学代写|傅里叶分析代写Fourier analysis代考|Energy and Power Signals

$$E=\int_{-\infty}^{\infty}|x(t)|^{2} d t$$

$$E=\int_{0}^{\infty}\left|2 e^{-3 t}\right|^{2} d t=\frac{2}{3}$$

$$E=\sum_{n=-\infty}^{\infty}|x(n)|^{2}$$

$$E=\sum_{n=0}^{\infty}\left|3(0.8)^{n}\right|^{2}=\frac{9}{1-0.64}=\frac{9}{0.36}=25$$

## 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。

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