## 物理代写|电磁学代写electromagnetism代考|PHYC20014

statistics-lab™ 为您的留学生涯保驾护航 在代写电磁学electromagnetism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。我们的专家在代写电磁学electromagnetism代写方面经验极为丰富，各种代写电磁学electromagnetism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

## 物理代写|电磁学代写electromagnetism代考|Electric Field Lines

By definition, electric field lines are drawn to follow the same direction as the electric field vector at any point. Furthermore, the electric field vector is tangent to the line at every point along the field line.

The electric field lines are such that $\mathbf{E}$ is tangent to the electric field line at each point. The number of lines per unit surface area passing a surface perpendicular to the lines is proportional to the magnitude $|\mathbf{E}|$ in that region. Furthermore, the lines are directed radially away from the positive point charge. Moreover, the lines are directed radially toward the negative point charge.

In Fig. 1.7, we show the electric field lines of a negative and positive point charge. It can be seen that for a negative point charge, $-q$, the electric field lines are drawn toward the charge (see Fig. 1.7a). On the other hand, for a positive point charge, $+q$, electric field lines are leaving the charge, as shown in Fig. 1.7b.

The following general rules for drawing electric field lines apply:
The lines start from a positive charge and end on a negative charge. Also, the number of lines drawn, leaving a positive charge, or approaching a negative charge is proportional to the magnitude of the charge. Moreover, no two field lines can cross.

In Fig. 1.8, we show the electric field vector for a positive point charge $+q$ located at the point $(0,3,0)$ (Fig. 1.8b) and a negative point charge $-q$ located at $(0,-3,0)$ (Fig. 1.8a), colored according to the magnitude of the electric field $\mathbf{E}$ using a color scaling. as depicted in Fig. 1.8. Besides, the electric field lines of the resultant electric field are shown in Fig. 1.8c.

## 物理代写|电磁学代写electromagnetism代考|Motion in Uniform Electric Field

Suppose a charge particle of mass $m$ and charge $q$ is moving in a uniform electric field $\mathbf{E}$. Electric field $\mathbf{E}$ exerts on a particle placed in it the force
$$\mathbf{F}=q \mathbf{E}$$

If that force is equal to the resultant force exerted on the particle, it causes the particle to accelerate, based on Newton’s second law:
$$m \mathbf{a}=q \mathbf{E}$$
The acceleration gained by the charge is given as
$$\mathbf{a}=\frac{q}{m} \mathbf{E}$$
Therefore, if $\mathbf{E}$ is uniform (that is, constant in magnitude and direction), then a is constant. Furthermore, if the particle has a positive charge, then its acceleration is in the direction of the electric field. On the other hand, if the particle has a negative charge, then its acceleration is in the direction opposite the electric field.

# 电磁学代考

## 物理代写|电磁学代写electromagnetism代考|Motion in Uniform Electric Field

$$\mathbf{F}=q \mathbf{E}$$

$$m \mathbf{a}=q \mathbf{E}$$

$$\mathbf{a}=\frac{q}{m} \mathbf{E}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|电磁学代写electromagnetism代考|ELEC3104

statistics-lab™ 为您的留学生涯保驾护航 在代写电磁学electromagnetism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。我们的专家在代写电磁学electromagnetism代写方面经验极为丰富，各种代写电磁学electromagnetism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

## 物理代写|电磁学代写electromagnetism代考|Force Fields

The field forces act through space, producing an effect even when no physical contact between the objects occurs. As an example, we can mention the gravitational field. Michael Faraday developed a similar approach to electric forces. That is, an electric field exists in the region of space around any charged body, and when another charged body is inside this region of the electric field, an electric force acts on it.

Definition 1.2 The electric field $\mathbf{E}$ at a point in space is defined as the electric force $\mathbf{F}_e$ acting on a positive test charge $q_0$ placed at that point divided by the magnitude of the test charge:
$$\mathbf{E}=\frac{\mathbf{F}_e}{q_0}$$

The vector $\mathbf{E}$ has the SI units of newtons per coulomb (N/C). Figure $1.3$ illustrates the electric field $\mathbf{E}$ created by a positively charged sphere with total charge $Q$ at the positive test charge $q_0$. Here, we have assumed that the test charge $q_0$ is small enough that it does not disturb the charge distribution of the sphere responsible for the electric field.

Note that $\mathbf{E}$ is the field produced by some charge external to the test charge, and it is not the field produced by the test charge itself. Also, note that the existence of an electric field is a property of its source. For example, every electron comes with its electric field. An electric field exists at a point if a test charge at rest at that point experiences an electric force. The electric field direction is the direction of the force on a positive test charge placed in the field. Once we know the magnitude and direction of the electric field at some point, the electric force exerted on any charged particle (either positive or negative) placed at that point can be calculated. The electric field exists at some point space, including the free space, independent of the existence of another test charge at that point.

To determine the direction of electric field, consider a point charge $q$ located some distance $r$ from a test positive charge $q_0$ located at a point $P$, as shown in Fig. 1.4. Coulomb’s law defines the force exerted by $q$ on $q_0$ as
$$\mathbf{F}_e=k_e \frac{q q_0}{r^2} \hat{\mathbf{r}}$$
where $\hat{\mathbf{r}}$ represents the usual unit vector directed from $q$ toward $q_0$ (see Fig. 1.4). Electric field created by $q$ (positive or negative) is $$\mathbf{E}=\frac{\mathbf{F}_e}{q_0}=k_e \frac{q}{r^2} \hat{\mathbf{r}}$$
From Eq. (1.11), when $q<0$, then $\mathbf{E}$ is pointing opposite to vector $\hat{\mathbf{r}}$, and hence the electric field of a negative charge is pointing toward that charge, see Fig. 1.4a. On the other hand, when $q>0, \mathbf{E}$ and $\hat{\mathbf{r}}$ are parallel, and hence the electric field of a positive charge is pointing away from that charge, as shown in Fig. 1.4b.

## 物理代写|电磁学代写electromagnetism代考|Superposition Principle

According to superposition principle, at any point $P$, the total electric field due to a set of discrete point charges, $q_1, q_2, \ldots, q_N$, positive and negative charges, is equal to the sum of the individual charge electric field vectors (see Fig. 1.5). Mathematically, we can write
$$\mathbf{E}(\mathbf{r})=\sum_{i=1}^N \mathbf{E}i=\sum{i=1}^N k_e \frac{q_i}{\left|\mathbf{r}-\mathbf{r}_i\right|^2} \hat{\mathbf{r}}_i$$
In Eq. (1.12), $\left|\mathbf{r}-\mathbf{r}_i\right|$ is the distance from $q_i$ to the point $P$ (the location of a test charge), where $\mathbf{r}$ is the position vector of the point $P$ with respect to some reference frame, as indicated in Fig. 1.5, and $\mathbf{r}_i$ is the position vector of the charge $i$ in that reference frame. Furthermore, $\hat{\mathbf{r}}_i$ is a unit vector directed from $q_i$ toward $P$.

Note that in Eq. (1.12) the dependence of $\mathbf{E}$ on only position vector of point $P$. r. assumes a static configuration of the charges in space. That is, for some other configuration distribution of charges in space, $\mathbf{E}$ at the same point $P$ may be different. Note that often for convenience, Eq.(1.12) is also written as $$\mathbf{E}(\mathbf{r})=\sum_{i=1}^N k_e \frac{q_i\left(\mathbf{r}-\mathbf{r}_i\right)}{\left|\mathbf{r}-\mathbf{r}_i\right|^3}$$
where
$$\hat{\mathbf{r}}_i=\frac{\mathbf{r}-\mathbf{r}_i}{\left|\mathbf{r}-\mathbf{r}_i\right|}$$
If the distances between charges in a set of charges are much smaller, compare with the distance of the set from a point where the electric field is to be calculated, then charge distribution is continuous.

To calculate the net electric field created by a continuous charge distribution in some volume $V$, we follow these steps. First, we divide the charge distribution into macroscopically small elements with small charge $\Delta q_i$, as shown in Fig. 1.6a. $\Delta q_i=\rho_i \Delta V$, where $\rho_i$ is seen from a microscopic viewpoint as a uniform charge density within the volume element $i$, which represents one of the possible configurations of microscopic description. It is important to note that with “macroscopically small” we should understand a small volume in space with a characteristic microscopic configuration of the charges inside it that can, on average, macroscopically be represented as a point-like charge, $\Delta q_i$. Then, we calculate the electric field due to one of these macroscopically point charges, $\Delta q_i$, at some point $P$ at distance $\left|\mathbf{r}-\mathbf{r}_i\right|$ from the charge element, $\Delta q_i$, as
$$\Delta \mathbf{E}\left(\mathbf{r}, \mathbf{r}_i\right)=k_e \frac{\Delta q_i}{\left|\mathbf{r}-\mathbf{r}_i\right|^2} \hat{\mathbf{r}}_i$$
where $\hat{\mathbf{r}}_i$ is a unit vector directed from the charge element $\Delta q_i$ toward $P$. Here, $\mathbf{r}$ is position vector of point $P$ in some reference frame, and $\mathbf{r}_i$ is the position vector of the macroscopically point charge $\Delta q_i$.

# 电磁学代考

## 物理代写|电磁学代写electromagnetism代考|Force Fields

$$\mathbf{E}=\frac{\mathbf{F}_e}{q_0}$$

$$\mathbf{F}_e=k_e \frac{q q_0}{r^2} \hat{\mathbf{r}}$$

$$\mathbf{E}=\frac{\mathbf{F}_e}{q_0}=k_e \frac{q}{r^2} \hat{\mathbf{r}}$$

## 物理代写|电磁学代写electromagnetism代考|Superposition Principle

$$\mathbf{E}(\mathbf{r})=\sum_{i=1}^N \mathbf{E} i=\sum i=1^N k_e \frac{q_i}{\left|\mathbf{r}-\mathbf{r}i\right|^2} \hat{\mathbf{r}}_i$$ 在等式中。(1.12)， $\left|\mathbf{r}-\mathbf{r}_i\right|$ 是距离 $q_i$ 直截了当 $P$ (测试电荷的位置)，其中 $\mathbf{r}$ 是点的位置向量 $P$ 关于一些 参考系，如图 1.5 所示，以及 $\mathbf{r}_i$ 是电荷的位置向量 $i$ 在那个参考系中。此外， $\hat{\mathbf{r}}_i$ 是指向的单位向量 $q_i$ 朝向 $P$. 请注意，在等式中。(1.12) 的依赖 $\mathbf{E}$ 仅在点的位置向量上 $P$. 河 假定空间中电荷的静态配置。也就是说， 对于空间中电荷的一些其他配置分布， $\mathbf{E}$ 在同一时间 $P$ 可能不同。请注意，通常为方便起见，Eq.(1.12) 也写为 $$\mathbf{E}(\mathbf{r})=\sum{i=1}^N k_e \frac{q_i\left(\mathbf{r}-\mathbf{r}_i\right)}{\left|\mathbf{r}-\mathbf{r}_i\right|^3}$$

$$\hat{\mathbf{r}}_i=\frac{\mathbf{r}-\mathbf{r}_i}{\left|\mathbf{r}-\mathbf{r}_i\right|}$$

$$\Delta \mathbf{E}\left(\mathbf{r}, \mathbf{r}_i\right)=k_e \frac{\Delta q_i}{\left|\mathbf{r}-\mathbf{r}_i\right|^2} \hat{\mathbf{r}}_i$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|电磁学代写electromagnetism代考|PHYS3040

statistics-lab™ 为您的留学生涯保驾护航 在代写电磁学electromagnetism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。我们的专家在代写电磁学electromagnetism代写方面经验极为丰富，各种代写电磁学electromagnetism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

## 物理代写|电磁学代写electromagnetism代考|Electrical Charges

There exist several simple experiments to demonstrate the existence of electrical charges and forces. For example,

1. When we comb our hair on a dry day, we find that the comb attracts pieces of paper.
2. The same effect of attracting pieces of paper occurs when materials such as glass or rubber are rubbed with silk or fur.

As a general rule, for every material behaving in that way, we can say that it is electrified, or it becomes electrically charged.

Benjamin Franklin (1706-1790) found that there exist two types of electric charges, namely positive and negative. The following experiment can be used to demonstrate his finding. Suppose that we rubber with fur a hard rubber rod. In addition, we rub a glass rod with silk material. Then, if the glass rod is brought near the rubber rod, we will observe that the two attract each other. However, if we bring near each other two charged rubber rods or two charged glass rods, then the two repel each other. This experiment indicates the existence of two different states of electrification for the rubber and glass. Furthermore, it finds that like charges repel each other and unlike charges attract each other.

By convention, the electric charge on the glass rod is positive, and that on the rubber rod is negative. Based on that convention, any charged object repelled by another charged object must have the same sign of charge with it, and any charged object attracted by another charged object must have an opposite sign of charge. It is important to note that the electricity model of Franklin implies that electric charge is always conserved. That is, an electrified state (positive or negative) is due to the charge transfer from one object to the other. In other words, when an object gains some amount of positive/negative charge, then the other gains an equal amount of the electric charge of the opposite sign.

Robert Millikan (1868-1953), in 1909, discovered that electric charge always appears as a multiple integer of a fundamental amount of charge, called $e$ such that the electric charge $q$, which is a standard symbol for the charge, is quantized as
$$q=N e$$
Here, $N$ is an integer number, $N=0, \pm 1, \pm 2, \ldots$.

## 物理代写|电磁学代写electromagnetism代考|Coulomb’s Law

Based on an experiment performed by Coulomb, the electric force between two charged particles at rest is proportional to the inverse of the square of distance $r$ between them and directed along the line joining the two particles. In addition, the electric force is proportional to the charges $q_1$ and $q_2$ on each particle. Also, the electric force is attractive if the charges are of opposite sign and repulsive if the charges have the same sign. That is known as Coulomb’s Law.

Definition 1.1 Force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. Mathematically, the law may be written as
$$F=k_e \frac{\left|q_1\right|\left|q_2\right|}{r^2}$$
In Eq. (1.2), $k_e$ is the Coulomb constant. Note that, in SI, the unit of charge is the coulomb (C). Therefore, the Coulomb constant $k_e$ in SI units has the value
$$k_e=8.9875 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2$$
Often, the constant is written as $$k_e=\frac{1}{4 \pi \epsilon_0}$$
where $\epsilon_0$ is the permittivity of free space given by
$$\epsilon_0=8.8542 \times 10^{-12} \mathrm{C}^2 / \mathrm{N} \cdot \mathrm{m}^2$$
Coulomb’s force is a vector; hence it has a magnitude expressed by Eq. (1.2) and a direction. Therefore, the Coulomb’s law can be expressed in vector form concerning the electric force, $\mathbf{F}{12}$, exerted by the charge $q_1$ (positive or negative) on another charge $q_2$ (positive or negative) as $$\mathbf{F}{12}=k_e \frac{q_1 q_2}{r^2} \hat{\mathbf{r}}$$
In Eq. (1.6), $\hat{\mathbf{r}}$ denotes a unit vector pointing from $q_1$ to $q_2$. Note that based on the Newton’s third law, the electric force, $\mathbf{F}{21}$, exerted by a charge $q_2$ (positive or negative) on a second charge $q_2$ (positive or negative) is $$\mathbf{F}{21}=-\mathbf{F}_{12}$$
Figure $1.1$ illustrates graphically the direction of Coulomb’s force vectors for different combinations of the pairs of positive and negative charges, namely negativenegative, positive-positive, and negative-positive charge-charge interactions.

# 电磁学代考

## 物理代写|电磁学代写electromagnetism代考|Electrical Charges

1. 当我们在干燥的日子㓍头时，我们发现㓍子会吸引纸片。
2. 当玻璃或橡胶等材料与丝绸或毛皮摩擦时，也会产生吸引纸片的相同效果。
作为一般规则，对于以这种方式表现的每种材料，我们可以说它带电，或者带电。
本杰明·富兰克林 (1706-1790) 发现存在两种电荷，即正电荷和负电荷。下面的实验可以用来证明他的 发现。假设我们用毛皮橡胶一根硬橡胶棒。此外，我们用丝绸材料摩擦玻璃棒。然后，如果将玻璃棒靠 近橡胶棒，我们会观察到两者相互吸引。但是，如果我们将两根带电的橡胶棒或两根带电的玻璃棒靠 近，那么两者就会相互排斥。该实验表明橡胶和玻璃存在两种不同的带电状态。此外，它发现同种电荷 相互排斥，不同种电荷相互吸引。
按照惯例，玻璃棒上的电荷为正，橡胶棒上的电荷为负。根据该约定，任何被另一个带电物体排斥的带 电物体必须具有与其相同的电荷符号，而任何被另一个带电物体吸引的带电物体必须具有相反的电荷符 号。重要的是要注意富兰克林的电模型意味着电荷总是守恒的。也就是说，带电状态 (正或负) 是由于 电荷从一个物体转移到另一个物体。换句话说，当一个物体获得一定量的正/负电荷时，另一个物体获得 等量的相反符号的电荷。

Robert Millikan (1868-1953) 在 1909 年发现电荷总是以基本电荷量的整数倍形式出现，称为 $e$ 这样电荷 $q$ ，这是电荷的标准符号，被量化为
$$q=N e$$

## 物理代写|电磁学代写electromagnetism代考|Coulomb’s Law

$$F=k_e \frac{\left|q_1\right|\left|q_2\right|}{r^2}$$

$$k_e=8.9875 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2$$

$$k_e=\frac{1}{4 \pi \epsilon_0}$$

$$\epsilon_0=8.8542 \times 10^{-12} \mathrm{C}^2 / \mathrm{N} \cdot \mathrm{m}^2$$

$$\mathbf{F} 12=k_e \frac{q_1 q_2}{r^2} \hat{\mathbf{r}}$$

$$\mathbf{F} 21=-\mathbf{F}_{12}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|ECE310

statistics-lab™ 为您的留学生涯保驾护航 在代写数字信号处理Digital Signal Processing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。我们的专家在代写数字信号处理Digital Signal Processing方面经验极为丰富，各种代写数字信号处理Digital Signal Processing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 高等楖率论
• 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

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|What is Signal Processing

In short, signal processing applies mathematical operations to a signal. Signal processing is applied in many disciplines in practice. Here are some top-level examples:
(a) Image and video processing. Used in industrial machine vision, target tracking, media compression, social media photo filters, etc.
(b) Communication systems. Used to package information for transmission over a noisy channel (wired or wireless) and recover at a destination.
(c) Audio mixing. Used to amplify sounds at different frequencies, noise cancellation, karaoke, introduce effects such as reverb, distortion, and delay, etc.
(d) Biomedical systems. Used to monitor vital signs, diagnose diseases, guide surgical procedures, etc.
(e) Artificial intelligence. Self-driving cars, speech/pattern recognition, smart homes (heating, appliances), video games, etc.
(f) Financial markets. Predict future prices (of currencies, stocks, options, houses, etc.) and optimise portfolio asset allocations.

We will not be covering all of these applications in this module, particularly as some of them rely on more advanced methods than what we will learn about. But we will use a diverse range of applications for our examples.

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Linear Time Invariant Systems

This is a module on signal processing, and in this context we perform signal processing through systems, which take a signal as an input and then return a signal as an output. We will focus on systems that we can design as engineers, i.e., with particular system processing goals in mind. For example, in communication problems, there is a natural system that distorts our communication signal, and we design a receiver system to help us recover the original signal.

We will focus our study of analogue systems in this part of the module on a particular class of systems: those that are Linear Time Invariant (LTI). LTI systems have particular properties when acting on input signals. Given an LTI system that is defined by the functional (i.e., function of a function) $\mathcal{F}{\cdot}$ acting on time-varying input signals $x_1(t)$ and $x_2(t)$, where $t$ is time, the properties are as follows:

1. The system is linear, meaning that:
(a) The system is additive, i.e.,
$$\mathcal{F}\left{x_1(t)+x_2(t)\right}=\mathcal{F}\left{x_1(t)\right}+\mathcal{F}\left{x_2(t)\right}$$
(b) The system is scalable (or homogeneous), i.e.,
$$\mathcal{F}\left{a x_1(t)\right}=a \mathcal{F}\left{x_1(t)\right}$$
for any real or complex constant $a$.
2. The system is time-invariant, i.e., if output $y(t)=\mathcal{F}\left{x_1(t)\right}$, then
$$y(t-\tau)=\mathcal{F}\left{x_1(t-\tau)\right}$$
In other words, delaying the input by some constant time $\tau$ will delay the output and make no other changes.

Part of the convenience of working with L’l’ systems is that we can derive the ontipit. $y$ (t) given the inpit $x(t)$, if wé know the system’s impilse response $h$ (t.) The impulse response is the system output when the input is a Dirac delta, i.e.,
$$h(t)=\mathcal{F}{\delta(t)} .$$
Given the impulse response $h(t)$ of a system, the output is the convolution of the input signal with the impulse response, i.e.,
$$y(t)=\int_0^t x(\tau) h(t-\tau) d \tau=x(t) * h(t)=h(t) * x(t)$$

# 数字信号处理代考

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|What is Signal Processing

(a) 图像和视频处理。用于工业机器视觉、目标跟踪、媒体压缩、社交媒体照片过滤器等。
(b) 通信系统。用于打包信息以通过嘈杂的信道（有线或无线）传输并在目的地恢复。
(c) 音频混合。用于放大不同频率的声音、消除噪音、卡拉 OK，引入混响、失真和延迟等效果。
(d) 生物医学系统。用于监测生命体征、诊断疾病、指导手术操作等。
(e) 人工智能。自动驾驶汽车、语音/模式识别、智能家居（供暖、电器）、视频游戏等。
(f) 金融市场。预测未来价格（货币、股票、期权、房屋等）并优化投资组合资产配置。

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Linear Time Invariant Systems

1. 该系统是线性的，这意味着:
(a) 该系统是可加的，即，
(b) 该系统是可扩展的（或同类的），即，
对于任何实数或复数常数 $a$.
2. 该系统是时不变的，即如果输出 $y(t)=\backslash m a t h c a \mid{F} \backslash l$ eft $\left{x_{-} 1(t) \backslash r i g h t\right}$, 然后
$y(t-\backslash t a u)=\backslash$ mathcal ${F} \backslash l$ eft $\left{x_{-} 1(t-1\right.$ Itau $) \backslash$ right $}$
换句话说，将输入延迟某个常数时间 $\tau$ 将延迟输出并且不进行其他更改。
使用 L’l’ 系统的部分便利在于我们可以导出 ontipit。 $y(\mathrm{t})$ 给定 inpit $x(t)$ ，如果我们知道系统的即时响应 $h$ (t.) 当输入是 Dirac delta 时，脉冲响应是系统输出，即
$$h(t)=\mathcal{F} \delta(t) .$$
给定脉冲响应 $h(t)$ 对于一个系统，输出是输入信号与脉冲响应的卷积，即
$$y(t)=\int_0^t x(\tau) h(t-\tau) d \tau=x(t) * h(t)=h(t) * x(t)$$

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|EE615

statistics-lab™ 为您的留学生涯保驾护航 在代写数字信号处理Digital Signal Processing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。我们的专家在代写数字信号处理Digital Signal Processing方面经验极为丰富，各种代写数字信号处理Digital Signal Processing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 高等楖率论
• 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

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Textbooks

The following textbooks are the most relevant for this module:

• “Essentials of Digital Signal Processing,” B.P. Lathi and R.A. Green, Cambridge University Press, 2014. Lathi has authored several popular textbooks on signals and systems. This recent text is quite accessible and features strong integration with MATLAB.
• “Essential MATLAB for engineers and scientists,” B. Hahn and D. Valentine, Academic Press, 7th Edition, 2019. There are many excellent free re-
• sources for MATLAB, including the official software documentation (go to the help browser within the software or visit https://uk . mathworks. com/help/ matlab/index.html). While this book has only a very brief chapter on signal processing, it is good for a broad overview of MATLAB if you are seeking a general reference. It is also up to date as of MATLAB release $2018 \mathrm{~b}$.
• “Discrete-Time Signal Processing,” Oppenheim and Schafer, Pearson, 3rd Edition, 2013. Every signal processing textbook will have its relative strengths and weaknesses. This book serves as an alternative to Lathi and Green’s “Essentials of Digital Signal Processing.” While MATLAB is used for some of the examples, it is not thoroughly integrated, but overall this book has greater depth and breadth of topics. For example, it provides better coverage of random processes and signals.
• We will refer to several other textbooks and resources throughout the module, but they will only be relevant for 1 or 2 lessons each. Please see “Further Reading” at the end of each lesson for details.

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Signals and Signal Classification

So what are signals? A signal is a quantity that can be varied in order to convey information. If a signal does not contain useful information (at least not in the current context), then the signal is regarded as noise. You may have a useful audio signal for your neighbour in a lecture, but this could be noise to anyone nearby that is trying to listen to the instructor!

Practically any physical phenomena can be understood as a signal (e.g., temperature, pressure, concentration, voltage, current, impedance, velocity, displacement, vibrations, colour). Immaterial quantities can also be signals (e.g., words, stock prices, module marks). Signals are usually described over time, frequency, and/or spatial domains. Time and frequency will be the most common in the context of this module, but our brief introduction to image processing will treat images as two-dimensional signals.

There are several ways of classifying signals. We will classify according to how they are defined over time and in amplitude. Over time we have:

1. Continuous-time signals – signals that are specified for every value of time $t$ (e.g., sound level in a classroom).
2. Discrete-time signals – signals that are specified at discrete values of time (e.g., the average daily temperature). The times are usually denoted by the integer $n$.
In amplitude we have:
3. Analogue signals – signals can have any value over a continuous range (e.g., body temperature).
4. Digital signals – signals whose amplitude is restricted to a finite number of values (e.g., the result of rolling a die).

While we can mix and match these classes of signals, in practice we most often see continuous-time analogue signals (i.e., many physical phenomena) and discrete-time digital signals (i.e., how signals are most easily represented in a computer); see Fig. 1.1. However, digital representations of data are often difficult to analyse mathematically, so we will usually treat them as if they were analogue. Thus, the key distinction is actually continuous-time versus discrete-time, even though for convenience we will refer to these as analogue and digital. The corresponding mathematics for continuous-time and discrete-time signals are distinct, and so they also impose the structure of this module.

# 数字信号处理代考

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Textbooks

• “Essentials of Digital Signal Processing”，BP Lathi 和 RA Green，剑桥大学出版社，2014 年。Lathi 撰写了多本关于信号和系统的热门教科书。这篇最近的文章很容易理解，并且与 MATLAB 紧密集成。
• “工程师和科学家的基本 MATLAB”，B. Hahn 和 D. Valentine，Academic Press，第 7 版，2019 年。
• MATLAB 的资源，包括官方软件文档（转到软件内的帮助浏览器或访问 https://uk.mathworks.com/help/matlab/index.html）。虽然这本书只有一个非常简短的章节介绍信号处理，但如果您正在寻找一般参考资料，那么它有助于对 MATLAB 进行广泛的概述。它也是最新的 MATLAB 版本2018 b.
• “离散时间信号处理”，Oppenheim 和 Schafer，Pearson，第 3 版，2013 年。每本信号处理教科书都有其相对优势和劣势。本书可替代 Lathi 和 Green 的“数字信号处理基础”。虽然 MATLAB 用于某些示例，但并未完全集成，但总体而言，本书的主题具有更大的深度和广度。例如，它可以更好地覆盖随机过程和信号。
• 我们将在整个模块中参考其他几本教科书和资源，但它们每本仅与 1 或 2 节课相关。详情请见每课后的“延伸阅读”。

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Signals and Signal Classification

1. 连续时间信号——为每个时间值指定的信号吨（例如，教室中的声级）。
2. 离散时间信号——以离散时间值指定的信号（例如，日平均温度）。次数通常用整数表示n.
在幅度方面，我们有：
3. 模拟信号——信号可以在连续范围内具有任何值（例如，体温）。
4. 数字信号——其幅度被限制在有限数量值内的信号（例如，掷骰子的结果）。

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|ELEC3104

statistics-lab™ 为您的留学生涯保驾护航 在代写数字信号处理Digital Signal Processing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。我们的专家在代写数字信号处理Digital Signal Processing方面经验极为丰富，各种代写数字信号处理Digital Signal Processing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 高等楖率论
• 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

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Learning Outcomes

Welcome to ES3C5: Signal Processing. This document is the official set of notes to supplement the lecture videos. It is written as a series of lessons that correspond to the lectures. Each lesson will align with one to several video lectures. The video lectures focus on highlighting the main theoretical ideas and presenting example problems that are worked on in the videos. These notes are intended to provide a precise, self-contained presentation of all technical material needed for ES3C5, including formal definitions and descriptions of the theoretical ideas. These notes also present additional applications, example problems, code snippets, etc.
This raises two important questions:

1. Do you need to read these notes if you watch the video lectures?
2. Do you need to watch the video lectures if you read these notes?
In practice, depending on your personal approach to learning, you may find the videos more helpful than the notes, or vice versa. Nevertheless, it is recommended that you use both.
A few reasons to watch the video lectures:
• Keep on top of the material. While you may have been exposed to many of the mathematical concepts in previous modules, ES3C5 covers a lot of ground and ties together a lot of ideas from a design perspective. The video lectures will help you keep up.
• Emphasize what’s most important. The video lectures won’t cover all of the material in the same detail as the notes, but they will highlight the most important content and the most challenging ideas that you will be assessed on.
• Be guided through problems. We will work through a lot of examples and they can be easier to follow in the video lectures than to read through solutions yourself.
• See software demonstrations. The coursework has a software (MATLAB) component and there will be regular video lectures with MATLAB demonstrations.
A few reasons to use the notes:
• Preview lecture material. The notes can help set the stage for what will be covered in the video lectures.
• Clarify details about what was covered in a video lecture. After a video lecture, the notes might help you to resolve lingering questions.
• The notes are self-contained. There will be no concept that you need to know for the exam that isn’t in the notes (though the coursework may require you to do some additional research). This can make the notes very useful for exam revision.
• More accessible than the textbooks. Although the notes are self-contained, they are written to be more concise and accessible than the module textbooks. Furthermore, the scope of the module is larger than what can be found in any one of the module textbooks.
• Additional study aides. The notes include many example problems; many but not all of these will be covered during video lectures and revision classes.

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|ES3C5 Overview

ES3C5 has several formal learning outcomes. By the end of the module you should be able to …

1. Apply mathematics to analyse deterministic and random signals and to analyse processing systems.
2. Apply signal processing systems to classify signals and extract information.
3. Critique practical issues behind signal processing and information retrieval.
4. Design signal processing systems.
5. Model signals, filters and processes using computer packages.
1. Evaluate signals and systems using laboratory test and measurement equipment.

The learning objectives mention signals but not what kinds of signals (besides deterministic vs random). This module and these notes are organized according to the signal type. We will consider deterministic analog signals, deterministic digital signals, and random digital signals. Although most practical signals have a random component, we first consider deterministic signals because they are simpler to analyse. We also focus on signal processing systems that are filters, which are broadly applicable to a very wide range of signal processing applications.

This module will not teach you everything there is or everything you will ever need to know about signal processing. But it will help you to develop a skill set to understand signal processing, design (relatively) simple signal processing systems, and be aware of some more advanced signal processing techniques.

ES3C5: Signal Processing is a core module for the Systems, Biomedical, and EE/EEE streams, and optional for students in the General engineering program. It can also be taken by MSe students who do not have a background in signal processing. It builds most directly on material that is covered in ES2C7 (Engineering Mathematics and Technical Computing) and is the foundation for all of the subsequent signal processing modules in the School.

The broad applicability of signal processing is reflected in the diverse modules that build on this one, including ES335 (Communications Systems), ES4A4 (Biomedical Signal Processing), ES4E9 (Affective Computing), etc.

You will also find that many 3 rd and 4 th year projects include a signal processing component, so you may pick up some skills or discover methods that you can apply in your project work. Of course, you should also find this module relevant as a practising engineer.

# 数字信号处理代考

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Learning Outcomes

1. 如果您观看视频讲座，是否需要阅读这些笔记？
2. 如果你看了这些笔记，你需要看视频讲座吗？
在实践中，根据您个人的学习方法，您可能会发现视频比笔记更有帮助，反之亦然。尽管如此，还是建议您同时使用两者。
观看视频讲座的几个原因：
• 保持在材料之上。虽然您可能已经接触过前面模块中的许多数学概念，但 ES3C5 涵盖了很多基础知识，并且从设计的角度将很多想法联系在一起。视频讲座将帮助您跟上进度。
• 强调最重要的。视频讲座不会像笔记一样详细地涵盖所有材料，但它们会突出显示最重要的内容和将对您进行评估的最具挑战性的想法。
• 被引导解决问题。我们将研究大量示例，在视频讲座中理解它们比自己通读解决方案更容易。
• 查看软件演示。该课程有一个软件 (MATLAB) 组件，并且将定期提供带有 MATLAB 演示的视频讲座。
使用注释的几个原因：
• 预览讲座材料。这些笔记可以帮助为视频讲座中的内容奠定基础。
• 澄清有关视频讲座中所涵盖内容的详细信息。视频讲座结束后，这些笔记可能会帮助您解决挥之不去的问题。
• 注释是独立的。对于笔记中没有的考试，您不需要了解任何概念（尽管课程作业可能需要您做一些额外的研究）。这可以使笔记对考试复习非常有用。
• 比教科书更通俗易懂。尽管笔记是独立的，但它们比模块教科书更简洁易懂。此外，该模块的范围比任何一本模块教科书中的内容都要大。
• 额外的学习助手。注释包括许多示例问题；在视频讲座和复习课程中将涵盖其中的许多但不是全部。

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|ES3C5 Overview

ES3C5 有几个正式的学习成果。在本模块结束时，您应该能够……

1. 应用数学来分析确定性和随机信号以及分析处理系统。
2. 应用信号处理系统对信号进行分类并提取信息。
3. 批判信号处理和信息检索背后的实际问题。
4. 设计信号处理系统。
5. 使用计算机包对信号、过滤器和过程进行建模。
6. 使用实验室测试和测量设备评估信号和系统。

ES3C5：信号处理是系统、生物医学和 EE/EEE 流的核心模块，对于通用工程计划的学生来说是可选的。没有信号处理背景的 MSe 学生也可以参加。它最直接地建立在 ES2C7（工程数学和技术计算）涵盖的材料之上，并且是学校所有后续信号处理模块的基础。

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|ECE310

statistics-lab™ 为您的留学生涯保驾护航 在代写数字信号处理Digital Signal Processing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。我们的专家在代写数字信号处理Digital Signal Processing方面经验极为丰富，各种代写数字信号处理Digital Signal Processing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 高等楖率论
• 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

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Time Invariant and Time Varying DT Systems

Consider the discrete time system represented in block diagram of Fig. 1.32a. If the input is $x[n]$, then the output is $y[n]$. If the input is time delayed by $n_0$, which becomes $x\left[n-n_0\right]$, the output becomes $y\left[n-n_0\right]$. The signal representation and the delayed signals are shown in Fig. 1.32b, c, respectively. Such systems are called time invariant.

If an arbitrary excitation $x[n]$ of a system causes a response $y[n]$ and the delayed excitation $x\left[n-n_0\right]$ where $n_0$ is any arbitrary integer causes $y\left[n-n_0\right]$, then the system is said to be time invariant.
Procedure to Check Time Invariancy of DT Systems

1. For the delayed input $x\left[n-n_0\right]$, find the output $y\left[n, n_0\right]$.
2. Obtain the delayed output $y\left[n-n_0\right]$ by substituting $n=n-n_0$ in $y[n]$.
3 . If $y\left[n, n_0\right]=y\left[n-n_0\right]$, the system is time invariant. Otherwise the system is time varying.

The following examples illustrate the method of testing the time invariancy of DT systems.

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Causal and Non-causal DT Systems

A discrete time system is said to be causal if the response of the system depends on the present or the past inputs applied. The systems is non-causal if the output depends on the future input.

The following examples illustrate the method of identifying causal and non-causal systems.
Example 1.30
Determine whether the following systems are causal or not:
(a) $y[n]=x[n-1]$
(b) $y[n]=x[n]+x[n-1]$
(c) $y[n-1]=x[n]$
(d) $y[n]=\sin (x[n])$
(e) $y[n]=\sum_{k=-\infty}^{n+4} x(k)$
(f) $y[n]=\sum_{k=0}^{-3} x(k)$
Solution
(a) $y[n]=x[n-1]$
\begin{aligned} & y[0]=x[-1] \ & y[1]=x[0] \end{aligned}
The output depends on the past value of $x[n]$. Hence
The system is causall.

(b) $y[n]=x[n]+x[n-1]$
\begin{aligned} & y[0]=x[0]+x[-1] \ & y[1]=x[1]+x[0] \end{aligned}
here $x[1]$ is present value and $x[0]$ is past value. The output depends on the present and past inputs. Hence
The system is causal.

# 数字信号处理代考

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Time Invariant and Time Varying DT Systems

1. 对于延迟输入 $x\left[n-n_0\right]$, 找到输出 $y\left[n, n_0\right]$.
2. 获取延迟输出 $y\left[n-n_0\right]$ 通过替换 $n=n-n_0$ 在 $y[n]$.
3. 如果 $y\left[n, n_0\right]=y\left[n-n_0\right]$ ，系统是时不变的。否则系统是随时间变化的。
下面举例说明测试DT系统时不变性的方法。

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Causal and Non-causal DT Systems

(a) $y[n]=x[n-1]$
(乙) $y[n]=x[n]+x[n-1]$
(C) $y[n-1]=x[n]$
(四) $y[n]=\sin (x[n])$
(和) $y[n]=\sum_{k=-\infty}^{n+4} x(k)$
(F) $y[n]=\sum_{k=0}^{-3} x(k)$

$$\text { (一) } y[n]=x[n-1]$$
$$y[0]=x[-1] \quad y[1]=x[0]$$

(乙) $y[n]=x[n]+x[n-1]$
$$y[0]=x[0]+x[-1] \quad y[1]=x[1]+x[0]$$

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|EE615

statistics-lab™ 为您的留学生涯保驾护航 在代写数字信号处理Digital Signal Processing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。我们的专家在代写数字信号处理Digital Signal Processing方面经验极为丰富，各种代写数字信号处理Digital Signal Processing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 高等楖率论
• 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

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Energy and Power of DT Signals

For a discrete time signal $x[n]$, the total energy is defined as $$E=\sum_{n=-\infty}^{\infty}|x[n]|^2$$
The average power is defined as
$$P=\operatorname{Lt}{N \rightarrow \infty} \frac{1}{(2 N+1)} \sum{n=-N}^N|x[n]|^2$$
From the definitions of energy and power, the following inferences are derived:

1. $x[n]$ is an energy sequence if $0<E<\infty$. For finite energy signal, the average power $P=0$.
2. $x[n]$ is a power sequence if $0<P<\infty$. For a sequence with average power $P$ being finite, the total energy $E=\infty$.
3. Periodic signal is a power signal, and vice versa is not true. Here, the energy of the signal per period is finite.
4. Signals which do not satisfy the definitions of total energy and average power are neither termed as power signal nor energy signal. The following summation formulae are very often used while evaluating the average power and total energy of DT sequence.
1.
$$\begin{array}{rlrl} \sum_{n=0}^{N-1} a^n & =\frac{\left(1-a^n\right)}{(1-a)} & & a \neq 1 \ & =N & a & =1 \end{array}$$
2.
$$\sum_{n=0}^{\infty} a^n=\frac{1}{(1-a)} \quad a<1$$

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Linear and Nonlinear Systems

A linear discrete time system obeys the property of superposition. As discussed for CT system, the superposition property is composed of homogeneity and additivity. Let $x_1[n]$ excitation produce $y_1[n]$ response and $x_2[n]$ produce $y_2[n]$ response. According to additivity property of superposition theorem, if both $x_1[n]$ and $x_2[n]$ are applied simultaneously, then
$$x_1[n]+x_2[n]=y_1[n]+y_2[n]$$
Let $a_1 x_1[n]$ and $a_2 x_2[n]$ be the inputs. According the homogeneity (scaling) property, when these signals are separately applied,
\begin{aligned} & a_1 x_1[n]=a_1 y_1[n] \ & a_2 x_2[n]=a_2 y_2[n] \end{aligned}
If $a_1 x_1[n]+a_2 x_2[n]$ are simultaneously applied, the output is obtained by applying superposition theorem as,
$$a_1 x_1[n]+a_2 x_2[n]=a_1 y_1[n]+a_2 y_2[n]$$
In the above equation, $a_1 x_1[n]+a_2 x_2[n]$ is called the weighted sum of input, and $a_1 y_1[n]+a_2 y_2[n]$ is called the weighted sum of the output. Therefore, the following procedure is followed to test the linearity of a DT system.

1. Express
\begin{aligned} & y_1[n]=f\left(x_1[n]\right) \ & y_2[n]=f\left(x_2[n]\right) \end{aligned}
2. Find the weighted sum of the output as
$$y_3[n]=a_1 y_1[n]+a_2 y_2[n]$$
3. Find the output $y_4[n]$ due to the weighted sum of input as
$$y_4[n]-f\left(a_1 x_1[n]+a_2 x_2[n]\right)$$
4. If $y_3\lfloor n\rfloor=y_4\lfloor n\rfloor$, then given DI’ system is linear. Otherwise it is nonlinear.
The following examples illustrate the method of testing a DT system for its linearity.

# 数字信号处理代考

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Energy and Power of DT Signals

$$E=\sum_{n=-\infty}^{\infty}|x[n]|^2$$

$$P=\operatorname{Lt} N \rightarrow \infty \frac{1}{(2 N+1)} \sum n=-N^N|x[n]|^2$$

1. $x[n]$ 是一个能量序列，如果 $0<E<\infty$. 对于有限能量信号，平均功率 $P=0$.
2. $x[n]$ 是一个幂序列，如果 $0<P<\infty$. 对于具有平均功率的序列 $P$ 是有限的，总能量 $E=\infty$.
3. 周期信号就是功率信号，反之则不然。这里，每个周期信号的能量是有限的。
4. 不满足总能量和平均功率定义的信号既不称为功率信号也不称为能量信号。在评估 DT 序列的平均功 率和总能量时，经常使用以下求和公式。
1.
$$\sum_{n=0}^{N-1} a^n=\frac{\left(1-a^n\right)}{(1-a)} \quad a \neq 1 \quad=N \quad a=1$$
2.
$$\sum_{n=0}^{\infty} a^n=\frac{1}{(1-a)} \quad a<1$$

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Linear and Nonlinear Systems

$$x_1[n]+x_2[n]=y_1[n]+y_2[n]$$

$$a_1 x_1[n]=a_1 y_1[n] \quad a_2 x_2[n]=a_2 y_2[n]$$

$$a_1 x_1[n]+a_2 x_2[n]=a_1 y_1[n]+a_2 y_2[n]$$

1. 表达
$$y_1[n]=f\left(x_1[n]\right) \quad y_2[n]=f\left(x_2[n]\right)$$
2. 找到输出的加权和作为
$$y_3[n]=a_1 y_1[n]+a_2 y_2[n]$$
3. 找到输出 $y_4[n]$ 由于输入的加权和为
$$y_4[n]-f\left(a_1 x_1[n]+a_2 x_2[n]\right)$$
4. 如果 $y_3\lfloor n\rfloor=y_4\lfloor n\rfloor$ ，那么给定的 DI’ 系统是线性的。否则它是非线性的。 以下示例说明了测试 DT 系统线性度的方法。

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|ELEC3104

statistics-lab™ 为您的留学生涯保驾护航 在代写数字信号处理Digital Signal Processing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。我们的专家在代写数字信号处理Digital Signal Processing方面经验极为丰富，各种代写数字信号处理Digital Signal Processing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 高等楖率论
• 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

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Periodic and Non-periodic DT Signals

A discrete time signal (sequence) $x[n]$ is said to be periodic with period $N$ which is a positive integer if
$$x[n+N]=x[n] \text { for all } n$$
Consider the DT sequence shown in Fig. 1.24. The signal gets repeated for every $N$. For Fig. 1.24, the following equation is written:
$$x[n+m N]=x[n] \text { for all } n$$
where $m$ is any integer. The smallest positive integer $N$ in Eq. (1.9) is called the fundamental period $N_0$. Any sequence which is not periodic is said to be non-periodic or aperiodic.

Example 1.10
Show that complex exponential sequence $x[n]=\mathrm{e}^{j \omega_0 n}$ is periodic and find the fundamental period.
Solution
\begin{aligned} x[n] & =\mathrm{e}^{j \omega_0 n} \ x[n+N] & =\mathrm{e}^{j \omega_0(n+N)} \ & =\mathrm{e}^{j \omega_0 n} \mathrm{e}^{j \omega_0 N} \ & =\mathrm{e}^{j \omega_0 n} \quad \text { if } \mathrm{e}^{j \omega_0 N}=1 \ \omega_0 N & =m 2 \pi \text { where } m \text { is any integer. } \ & N=m \frac{2 \pi}{\omega_0} \end{aligned}
or
$$\frac{\omega_0}{2 \pi}=\frac{m}{N}=\text { rational number. }$$
Thus, $\mathrm{e}^{j \omega_0 n}$ is periodic if $\frac{m}{N}$ is rational. For $m=1, N=N_0$. The corresponding frequency $F_0=\frac{1}{N_0}$ is the fundamental frequency. $F_0$ is expressed in cycles and not $\mathrm{Hz}$. Similarly $\omega_0$ is expressed in radians and not in radians per second.
Example 1.11
Consider the following DT signal.
$$x[n]=\sin \left(\omega_0 n+\phi\right)$$
Under what condition, the above signal is periodic?

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Odd and Even DT Signals

DT signals are classified as odd and even signals. The relationships are analogous to CT signals.
A discrete time signal $x[n]$ is said to be an even signal if
$$x[-n]=x[n]$$
A discrete time signal $x[n]$ is said to be an odd signal if
$$x[-n]=-x[n]$$
The signal $x[n]$ can be expressed as the sum of odd and even signals as
$$x[n]=x_e[n]+x_0[n]$$
The even and odd components of $x[n]$ can be expressed as
\begin{aligned} x_e[n] & =\frac{1}{2}[x[n]+x[-n]] \ x_0[n] & =\frac{1}{2}[x[n]-x[-n]] \end{aligned}

It is to be noted that

• An even function has an odd part which is zero.
• An odd function has an even part which is zero.
• The product of two even signals or of two odd signals is an even signal.
• The product of an odd and an even signal is an odd signal.
• At $n=0$, the odd signal is zero.
The even and odd signals are represented in Fig. 1.25a, b, respectively.

# 数字信号处理代考

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Periodic and Non-periodic DT Signals

$$x[n+N]=x[n] \text { for all } n$$

$$x[n+m N]=x[n] \text { for all } n$$

$$x[n]=\mathrm{e}^{j \omega_0 n} x[n+N] \quad=\mathrm{e}^{j \omega_0(n+N)}=\mathrm{e}^{j \omega_0 n} \mathrm{e}^{j \omega_0 N} \quad=\mathrm{e}^{j \omega_0 n} \quad \text { if } \mathrm{e}^{j \omega_0 N}=1 \omega_0 N=m 2 \pi$$

$$\frac{\omega_0}{2 \pi}=\frac{m}{N}=\text { rational number. }$$

$$x[n]=\sin \left(\omega_0 n+\phi\right)$$

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Odd and Even DT Signals

DT 信号分为奇信号和偶信号。这些关系类似于 CT 信号。

$$x[-n]=x[n]$$

$$x[-n]=-x[n]$$

$$x[n]=x_e[n]+x_0[n]$$

$$x_e[n]=\frac{1}{2}[x[n]+x[-n]] x_0[n] \quad=\frac{1}{2}[x[n]-x[-n]]$$

• 偶函数有奇数部分为零。
• 奇函数有偶数部分为零。
• 两个偶信号或两个奇信号的乘积是偶信号。
• 奇信号和偶信号的乘积是奇信号。
• 在 $n=0$, 奇数信号为零。
偶数和奇数信号分别如图 1.25a、b 所示。

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|电磁学代写electromagnetism代考|ELEC3104

statistics-lab™ 为您的留学生涯保驾护航 在代写电磁学electromagnetism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。我们的专家在代写电磁学electromagnetism代写方面经验极为丰富，各种代写电磁学electromagnetism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

## 物理代写|电磁学代写electromagnetism代考|Electric Current

Consider the motion in a system of electric charges, as presented in Fig.5.1. A current will exist, if there is a net flow of charge through a region. To define current, we consider the charges moving as in Fig. $5.1$ and a surface of area $A$ perpendicular to the direction of motion of the charges.

By definition, the ratio of the amount of charge $\Delta Q$ that passes through the surface area $A$ in a time interval $\Delta t$ is the average current $I_{a v}$ :
$$I_{a v}=\frac{\Delta Q}{\Delta t}$$
which represents the charge that passes through $A$ per unit time. If the charge flow rate, $\Delta Q / \Delta t$ varies in time, then the current varies in time.

Then, the instantaneous current $I$ is define as
$$I=\lim _{\Delta t \rightarrow 0} \frac{\Delta Q}{\Delta t}=\frac{d Q}{d t}$$
Note that the instantaneous current $I$ is simply called electric current or current. In the SI units, the current has a unit of the ampere (A):
$$1 \mathrm{~A}=1 \frac{\mathrm{C}}{\mathrm{s}}$$
Equation (5.2) implies that a current of $1 \mathrm{~A}$ is equivalent to a charge of $1 \mathrm{C}$ passing through the surface area in $1 \mathrm{~s}$.

## 物理代写|电磁学代写electromagnetism代考|Microscopic Model of Current

In the following, we describe a microscopic model of conduction in a conductor to relate the current to the motion of the charge carriers. In particular, we will consider the current in a conductor with a cross-sectional area $A$, as shown in Fig. 5.3. Consider a section of the conductor with a length $\Delta x$. The volume of that section is
$$\Delta V=A \Delta x=A v_d \Delta t$$
Suppose that $n$ is the volume number density of mobile charge carriers (or the charge carrier density), then, the total number of carriers in the volume $\Delta V$ is
$$N=n A \Delta x=n A v_d \Delta t$$

Therefore, the charge $\Delta Q$ in this volume is
$$\Delta Q=N q=q n A \Delta x=q n A v_d \Delta t$$
From Eq. (5.1), the average current in the conductor is
$$I_{a v}=\frac{\Delta Q}{\Delta t}=q n A v_d$$
By definition, the drift speed represents the average speed of the charge carriers, denoted as $v_d$. To understand the drift speed, we will consider a conductor, and hence the charge carriers are free electrons. For an isolated conductor, the potential difference across it is zero, as described above for Fig. $5.3$, thus these electrons move randomly as the motion of molecules of the gas in a container. If we apply a potential difference across the conductor utilizing a battery, as also described above in Fig. 5.4, an electric field sets up in the conductor. That field exerts an electric force on the electrons, accelerating them in a given direction. That directed movement of electrons produces a current, as shown in Fig. 5.4. It is important to note that the electrons do not move in straight lines along the conductor. Indeed, they collide regularly with the atoms of the conductor, and hence their resultant motion is a complicated movement, considered here as a spiral motion. However, the collision just slows down the motion, because the electrons move slowly along the conductor (in a direction opposite to $\mathbf{E}$ ) with a drift velocity $\mathbf{v}_d$, as shown in Fig. 5.4.

# 电磁学代考

## 物理代写|电磁学代写electromagnetism代考|Electric Current

$$I_{a v}=\frac{\Delta Q}{\Delta t}$$

$$I=\lim _{\Delta t \rightarrow 0} \frac{\Delta Q}{\Delta t}=\frac{d Q}{d t}$$

$$1 \mathrm{~A}=1 \frac{\mathrm{C}}{\mathrm{s}}$$

## 物理代写|电磁学代写electromagnetism代考|Microscopic Model of Current

$$\Delta V=A \Delta x=A v_d \Delta t$$

$$N=n A \Delta x=n A v_d \Delta t$$

$$\Delta Q=N q=q n A \Delta x=q n A v_d \Delta t$$

$$I_{a v}=\frac{\Delta Q}{\Delta t}=q n A v_d$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。