## 电气工程代写|通讯系统作业代写communication system代考|ELN234

statistics-lab™ 为您的留学生涯保驾护航 在代写通讯系统communication system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。我们的专家在代写通讯系统communication system方面经验极为丰富，各种代写通讯系统communication system相关的作业也就用不着说。

• 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

## 电气工程代写|通讯系统作业代写communication system代考|Over-rotation during electro-optical sampling

It is noted in Formula (7) that the modulation is bounded by $-1$ and 1 for phase differences of $-\pi / 2$ and $\pi / 2$, respectively. If the phase difference exceeds $\pi / 2$, the modulation decreases instead of increases since it has a sinusoidal behavior. This problem related to electro-optical detection is called over-rotation. Since a large phase difference is usually caused by a high electric field, EOS can only be used for detecting weak THz fields if over-rotation is to be avoided.

There are of course ways to work around the over-rotation problem and detect high THz fields. According to Formula (6), a smaller phase difference can be obtained by using a thinner detection crystal or having a lower electro-optical coefficient. In the first case, it should be known that a THz pulse incident on a crystal always generates reflections, which can also be detected. The thinner the crystal, the closer the reflection is temporally to the main pulse, and therefore, the more it is necessary to reduce the time window of the measurement in order to avoid measuring the reflection. However, a short time window also means a low frequency resolution, which is generally undesirable. In addition, a thinner crystal also means a shorter interaction length of the waves in the crystal, which results in a decrease in the Signalto-Noise Ratio (SNR). In the second case, it is actually possible to use a crystal with a lower electro-optical coefficient than $\mathrm{ZnTe}$, for example, gallium phosphide (GaP), and with which it is much more difficult to obtain over-rotation. On the other hand, the measured signal-to-noise ratio is then lower.

The most common solution to over-rotation is the addition of silicon waffles in the mounting just before the detection crystal (see Fig. 3). Part of the THz pulse (30\%) is reflected on each silicon waffle. The goal is to add enough silicon waffles so that the THz field reaching the crystal is both under the over-rotation limit and in the linear regime $(\sin (\Delta \varphi)=\Delta \varphi)$. However, adding several silicon waffles may cause some deformations in the detected THz field. In addition, a high THz field can induce nonlinear effects in silicon and the reflection on each waffle is then lower than $30 \%$. Also, multiple $\mathrm{THz}$ reflections on the silicon waffles are always at the tail of the main pulse in a measurement, which limits the time acquisition length and therefore the frequency resolution.

Of course, if silicon waffles are added to the assembly, this must be taken into account when calculating the THz field. By also adding the reflection losses on the detection crystal, we obtain:
$$E_{\mathrm{THz}}=\frac{d M}{2 \pi n_0^3 L r_{41} \Gamma 0.7^N}$$
where $\Gamma$ is the transmission coefficient through the detection crystal and $N$ is the number of waffles of Si. Each waffle transmits $70 \%$ of the THz wave.

## 电气工程代写|通讯系统作业代写communication system代考|THz Detection by Plasma in Air

There are two methods of plasma THz detection in air called THz-ABCD. The first is $\mathrm{THz}$ Air Breakdown Coherent Detection. The principle is very similar to $\mathrm{THz}$ generation by plasma in the air: A femtosecond laser is focused in the air, which generates a plasma whose charges are accelerated. If one sends a $\mathrm{THz}$ pulse to be detected on the plasma at the same time (or almost) as the laser pulse, there will be generation of the second harmonic of the laser beam. By detecting this second harmonic using a photomultiplier tube, the THz field can be deduced:
$$I_{2 \omega} \propto\left|E_{2 \omega}\right|^2 \propto\left(W^{(3)} E_\omega E_\omega\right)^2 E_{\mathrm{THz}}^2$$
where $I_{2 \omega}$ is the intensity of the second harmonic of the laser, $W^{(3)}$ is the 3rd order nonlinear coefficient of the plasma, $E_\omega$ is the laser electric field, $E_{2 \omega}$ is the electric field of the second harmonic of the laser, and $E_{\mathrm{THz}}$ is the electric field THz.

Unfortunately, since we only measure the intensity of the second harmonic, we cannot measure the electric field coherently. To achieve consistent detection, a very intense laser intensity must be used. At high pump intensity, the white light generated by the plasma contains a non-negligible second harmonic component that must be considered in the calculation [31]:
$$I_{2 \omega} \propto\left|E_{2 \omega}\right|^2 \propto\left(W^{(3)} E_\omega E_\omega\right)^2 E_{\mathrm{THz}}^2+2\left(W^{(3)} E_\omega E_\omega\right) E_{\mathrm{THz}} E_{\mathrm{SH}}^{2 \omega}+\left(E_{\mathrm{SH}}^{2 \omega}\right)^2$$
where $E_{\mathrm{SH}}^{2 \omega}$ is the electric field of the second harmonic from the plasma.
If the field of the second harmonic coming from the plasma is high enough, the first term of Formula (11) becomes negligible and the intensity detected by the photomultiplier tube is then proportional to the electric field $\mathrm{THz}$, making the detection method consistent. Of course, a drawback is that it is not possible to detect a $\mathrm{THz}$ field that is too large (or it is necessary to compensate with the intensity of the pump laser) since the first term of Formula (11) would then no longer be negligible. The second THz method is THz Air Bias Coherent Detection (THz-ABCD). This method requires a lower laser intensity, but an $\mathrm{AC}$ electric field must be applied close to the focal point.

## 电气工程代写|通讯系统作业代写communication system代考|Over-rotation during electro-optical sampling

$$E_{\mathrm{THz}}=\frac{d M}{2 \pi n_0^3 L r_{41} \Gamma 0.7^N}$$

## 电气工程代写|通讯系统作业代写communication system代考|THz Detection by Plasma in Air

$$I_{2 \omega} \propto\left|E_{2 \omega}\right|^2 \propto\left(W^{(3)} E_\omega E_\omega\right)^2 E_{\mathrm{THz}}^2$$

$$I_{2 \omega} \propto\left|E_{2 \omega}\right|^2 \propto\left(W^{(3)} E_\omega E_\omega\right)^2 E_{\mathrm{THz}}^2+2\left(W^{(3)} E_\omega E_\omega\right) E_{\mathrm{THz}} E_{\mathrm{SH}}^{2 \omega}+\left(E_{\mathrm{SH}}^{2 \omega}\right)^2$$

## 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。

## 电气工程代写|通讯系统作业代写communication system代考|ECE3614

statistics-lab™ 为您的留学生涯保驾护航 在代写通讯系统communication system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。我们的专家在代写通讯系统communication system方面经验极为丰富，各种代写通讯系统communication system相关的作业也就用不着说。

• 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

## 电气工程代写|通讯系统作业代写communication system代考|THz Detection by Photoconductive Antennas

The principle of detection by photoconductive antennas is similar to that of generation. As for the generation, a laser pulse (visible or infrared) is sent to the semiconductor component of the antenna, between the two electrodes, in order to reduce its resistance. On the other hand, unlike the generation, no potential difference is imposed between the electrodes; here, it is the incident THz field which acts on the displacement of the photoporters. A current can then pass between the two electrodes. By measuring this current, we can determine the $\mathrm{THz}$ field using the expression that binds the two, i.e., [25]:
$$I(t)=\int_{-\infty}^t \epsilon\left(t-t^{\prime}\right) E_{\mathrm{THz}} \mathrm{d} t^{\prime}$$
where $I(t)$ is the current induced by the $\mathrm{THz}$ field, $\epsilon$ is the surface conductivity of the semiconductor, and $E_{\mathrm{TH} z}$ is the electric field $\mathrm{THz}$.

Photoconductive antennas are mainly used for the detection of low and medium high $\mathrm{THz}$ electric fields. Indeed, a strong $\mathrm{THz}$ electric field could induce nonlinear effects in the semiconductor and the above formula would then no longer be valid [13].

Generally, the detection of terahertz radiation using photoconductive antennas is quite similar to its emission: This time it is the incident terahertz electric field which induces a voltage between two arms of the antenna connected by a transmission line to a current amplifier. Indeed, a laser pulse excites charge carriers beyond the bandgap of the semiconductor photoswitch. The charge carriers are accelerated by the external terahertz field to be detected, such that, still in the context of the Drude model. The current measured by an ammeter is then the convolution of the sampling field $E_S^{(d)}$ and the flow of charge carriers in the detector antenna:
$$I^{(d)}(t)=E_S^{(d)} *\left(e n^{(d)}(t) V(t)\right)$$

## 电气工程代写|通讯系统作业代写communication system代考|THz Detection by Electro-Optical Sampling

Electro-optical sampling (EOS) is a technique based on the Pockels effect, which is the inverse of optical rectification. The Pockels effect is the induction of birefringence in a nonlinear crystal by a DC wave. In the case of THz detection by electro-optical sampling, it will be approximated that the $\mathrm{THz}$ wave is a DC wave since its frequency is much smaller than the visible or near infrared wave used as a probe. The THz wave is therefore sent on a non-centrosymmetric crystal, which induces a change in the polarization ellipsoid in the crystal, and therefore in the ellipsoid of the refractive indices of the crystal. For example, for a ZnTe crystal (or any other crystal with a blende-like structure), the ellipsoid of indices becomes [28]:
$$\frac{\alpha^2+\beta^2+\gamma^2}{n_0^2}+2 r_{41} E_\alpha \beta \gamma+2 r_{41} E_\beta \alpha \gamma+2 r_{41} E_\gamma \alpha \beta=1$$
where $\alpha, \beta, \gamma$ are the spatial coordinates corresponding to the axes of the crystal, $n_0$ is the refractive index of the crystal without exposure $\mathrm{THz}, r_{41}$ is the electro-optical coefficient of the crystal and $E_\alpha, E_\beta, E_\gamma$, are the electric fields $\mathrm{THz}$ applied along the axes $\alpha, \beta, \gamma$.

The THz wave thus induces a birefringence in the nonlinear crystal. This birefringence is probed by a second beam sent on the crystal. This beam, visible, or near infrared undergoes a change in polarization during its passage in the birefringent crystal since the optical component parallel to the slow axis of the crystal undergoes a phase delay with respect to the optical component parallel to the fast axis of the crystal [28]:
$$\Delta \varphi=\frac{2 \pi L}{d} \Delta n$$
where $\Delta \varphi$ is the induced phase difference, $L$ is the thickness of the crystal $d$ is the central wavelength of the probe pulse and $\Delta n$ is the difference between the refractive indices of the slow and fast axes of the crystal. For a beam orthogonal to an oriented ZnTe crystal (110) with an electric field oriented along the axis $(-110)$ of the crystal, i.e., the optimal position [29]:
$$\Delta \varphi=\frac{2 \pi n_0^3 L r_{41} E_{\mathrm{THz}}}{d}$$

## 电气工程代写|通讯系统作业代写communication system代考|THz Detection by Photoconductive Antennas

$$I(t)=\int_{-\infty}^t \epsilon\left(t-t^{\prime}\right) E_{\mathrm{THz}} \mathrm{d} t^{\prime}$$

$$I^{(d)}(t)=E_S^{(d)} *\left(e n^{(d)}(t) V(t)\right)$$

## 电气工程代写|通讯系统作业代写communication system代考|THz Detection by Electro-Optical Sampling

$$\frac{\alpha^2+\beta^2+\gamma^2}{n_0^2}+2 r_{41} E_\alpha \beta \gamma+2 r_{41} E_\beta \alpha \gamma+2 r_{41} E_\gamma \alpha \beta=1$$

$$\Delta \varphi=\frac{2 \pi L}{d} \Delta n$$

$$\Delta \varphi=\frac{2 \pi n_0^3 L r_{41} E_{\mathrm{THz}}}{d}$$

## 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。

## 电气工程代写|通讯系统作业代写communication system代考|ENG307

statistics-lab™ 为您的留学生涯保驾护航 在代写通讯系统communication system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。我们的专家在代写通讯系统communication system方面经验极为丰富，各种代写通讯系统communication system相关的作业也就用不着说。

• 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

## 电气工程代写|通讯系统作业代写communication system代考|Impact of THz on 6G Wireless Communication

The 5G network, with its additional new techniques, such as millimeter wave, massive MIMO, beamforming, small cells, and full duplex, will offer revolutionary new features compared to previous generations. Nevertheless, the explosive growth in the number of connected systems could overcome the capabilities of $5 \mathrm{G}$ wireless networks. Some recently developed applications, such as virtual reality systems, are required to go beyond $5 \mathrm{G}$ because they need a minimum data rate of ten $\mathrm{Gbps}$, which exceeds the capacity of 5G systems [43]. In addition, high-definition video, ultrahigh-definition (UHD) devices, and 3-D video are becoming increasingly valuable for mobile users. Uncompressed UHD video can achieve $24 \mathrm{~Gb} / \mathrm{s}$ data rate, while uncompressed 3-D video with UHD can achieve $100 \mathrm{G} / \mathrm{ps}$ [26].

Research into the use of $\mathrm{THz}$ radiation in $6 \mathrm{G}$ wireless networks has become a daily occupation for researchers and players in the telecommunications field. This technology will revolutionize not only communication systems and their applications, but also business, personal life, lifestyle, and thus society [44]. To meet the expectations of the intelligent information society of 2030. China has launched the “Broadband Communications and New Networks” project for 2030 and beyond. The European Commission’s Horizon 2020 program has sponsored multiple B5G projects, like TERRANOVA; a project that aims to develop architectures and technologies capable of delivering optical network quality of experience in 6G wireless communication networks [45]. In the USA, the FCC has already launched studies of $6 \mathrm{G}$ networks, and the THz band has already opened. For the FCC, frequencies beyond $5 \mathrm{G}$ are reserved for 6G. In Japan, the first 6G projects have already been launched in 2020 [46]. Finland organized the first global summit on 6G wireless technology and launched the 6Genesis project, the first $6 \mathrm{G}$ project. The project supports the development of several aspects of wireless communication [47]. The International

## 电气工程代写|通讯系统作业代写communication system代考|VCO Design for THz Band

Various electronic and/or photonic systems and technologies have been developed to achieve the first demonstrations of THz communication. Due to the limitation of the operating frequency of the transistors developed by different foundries, most of the published works in the literature propose photonic solutions. Recently, electronic techniques are being developed, and our work is part of the development of an efficient wireless communication system for the terahertz frequency band.

Due to the behavior of passive elements at high frequencies, and the limited cutoff frequency for transistors, the VCO presents one of the most difficult blocks to design in a transceiver system. In this section, we propose the study and design of a $\mathrm{VCO}$, capable to generate a signal with frequencies around $104 \mathrm{GHz}$.

For the design of a local oscillator that delivers a high-power signal with minimal phase noise, we have opted for the pHEMT (pseudomorphic High Electron Mobility Transistor) of the PH15 process from the UMS foundry. It is characterized by a transition frequency $\mathrm{fT}=110 \mathrm{GHz}$ and a gate length of $0.15 \mu \mathrm{m}$ [48]. In this regard, considering the limitation of the operating frequency of most of the transistors developed so far, we have focused in this chapter on the choice of a structure that favors the second harmonic (Fig. 3). It consists of a LO (Fig. 4) whose fundamental oscillation frequency is $52 \mathrm{GHz}$ and a bandpass filter (Fig. 7), whose passband is around $104 \mathrm{GHz}$.

## 电气工程代写|通讯系统作业代写communication system代考|Impact of THz on 6G Wireless Communication

5G 网络及其附加新技术，如毫米波、大规模 MIMO、波束成形、小型蜂窝和全双工，将提供与前几代相比具有革命性的新功能。然而，连接系统数量的爆炸式增长可能会克服5G无线网络。一些最近开发的应用程序，例如虚拟现实系统，需要超越5G因为他们需要 10 的最低数据速率Gbps，这超过了 5G 系统的容量 [43]。此外，高清视频、超高清 (UHD) 设备和 3-D 视频对移动用户的价值越来越高。未压缩的超高清视频可以实现24 Gb/s数据速率，而 UHD 的未压缩 3-D 视频可以实现100G/ps [26].

## 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。

## 电气工程代写|数字系统设计作业代写Digital System Design代考|COE328

statistics-lab™ 为您的留学生涯保驾护航 在代写数字系统设计Digital System Design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系统设计Digital System Design方面经验极为丰富，各种代写数字系统设计Digital System Design相关的作业也就用不着说。

• 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

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Transmitter Antenna Losses

Several losses are associated with the antenna. Some of the possible losses, which may or may not be present in each antenna, are as follows:

• $L_{t r}$, radome losses on the transmitter antenna. The radome is the covering over the antenna that protects the antenna from the outside elements. Most antennas do not require a radome.
• $L_{t p o l}$, polarization mismatch losses. Many antennas are polarized (i.e., horizontal, vertical, or circular). This defines the spatial position or orientation of the electric and magnetic fields. A mismatch loss is due to the polarization of the transmitter antenna being spatially off with respect to the receiver antenna. The amount of loss is equal to the angle difference between them. For example, if both the receiver and transmitter antennas are vertically polarized, they would be at $90^{\circ}$ from the earth. If one is positioned at $80^{\circ}$ and the other is positioned at $100^{\circ}$, the difference is $20^{\circ}$. Therefore, the loss due to polarization would be
$$20 \log (\cos \theta)=20 \log (\cos 20)=0.54 \mathrm{~dB}$$
• $L_{t f o c}$, focusing loss or refractive loss. This is caused by imperfections in the shape of the antenna so that the energy is focused toward the feed. This is often a factor when the antenna receives signals at low elevation angles.
• $L_{\text {tpoint }}$, mispointed loss. This is caused by transmitting and receiving directional antennas that are not exactly lined up and pointed toward each other. Thus, the gains of the antennas do not add up without a loss of signal power.
• $L_{\text {tcon, }}$ conscan crossover loss. This loss is present only if the antenna is scanned in a circular search pattern, such as a conscan (conical scan) radar searching for a target. Conscan means that the antenna system is either electrically or mechanically scanned in a conical fashion or in a cone-shaped pattern. This is used in radar and other systems that desire a broader band of spatial coverage but must maintain a narrow beam width. This is also used for generating the pointing error for a tracking antenna.

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Transmitted Effective Isotropic Radiated Power

An isotropic radiator is a theoretical radiator that assumes a point source radiating in all directions. Effective isotropic radiated power (EIRP) is the amount of power from a single point radiator that is required to equal the amount of power that is transmitted by the power amplifier, losses, and directivity of the antenna (antenna gain) in the direction of the receiver.

The EIRP provides a way to compare different transmitters. To analyze the output of an antenna, EIRP is used (Figure 1-2):
$$\operatorname{EIRP}=P_t-L_{t t}+G_t-L_{t o}$$
where
$P_t=$ transmitter power in $\mathrm{dBm}$
$L_{t t}=$ total negative losses in $\mathrm{dB}$; coaxial or waveguide line losses, switchers, circulators, antenna connections
$G_t=$ transmitter antenna gain in $\mathrm{dB}$ referenced to a isotropic antenna
$L_{t a}=$ total transmitter antenna losses in $\mathrm{dB}$
Effective radiated power (ERP) is another term used to describe the output power of an antenna. However, instead of comparing the effective power to an isotropic radiator, the power output of the antenna is compared to a dipole antenna. The relationship between EIRP and ERP is
$$\mathrm{EIRP}=\mathrm{ERP}+G_{\text {dipole }},$$
where $G_{\text {dipole }}$ is the gain of a dipole antenna, which is equal to approximately $2.14 \mathrm{~dB}$ (Figure 1-2). For example,
\begin{aligned} \mathrm{EIRP} &=10 \mathrm{dBm} \ \mathrm{ERP} &=\mathrm{EIRP}-G_{\text {dipole }}=10 \mathrm{dBm}-2.14 \mathrm{~dB}=7.86 \mathrm{dBm} \end{aligned}

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Transmitter Antenna Losses

• $L_{t r}$ ，发射机天线上的天线罩损耗。天线罩是天线上的覆盖物，可保护天线免受外部元件的影响。大多数天线 不需要天线罩。
• $L_{t p o l}$ ，极化失配损失。许多天线是极化的（即水平、垂直或圆形）。这定义了电场和磁场的空间位置或方 向。失配损耗是由于发射器天线的极化相对于接收器天线在空间上偏离。损失量等于它们之间的角度差。例 如，如果接收器和发射器天线都是垂直极化的，它们将在 $90^{\circ}$ 来自地球。如果一个位于 $80^{\circ}$ 另一个位于 $100^{\circ}$ ， 区别是 $20^{\circ}$. 因此，极化引起的损耗为
$$20 \log (\cos \theta)=20 \log (\cos 20)=0.54 \mathrm{~dB}$$
• $L_{t f o c}$ ，聚焦损失或屈光损失。这是由天线形状的缺陷引起的，因此能量集中在馈源上。当天线以低仰角接收 信号时，这通常是一个因素。
• $L_{\text {tpoint }}$ ，误点损失。这是由于发射和接收定向天线末完全对齐并相互指向造成的。因此，天线的增益不会在 没有信号功率损失的情况下相加。
• $L_{\text {tcon, }}$ conscan 交叉损失。仅当以圆形搜索模式扫描天线时才会出现这种损失，例如搜索目标的 conscan (锥形扫描) 雷达。Conscan 意味着天线系统以雉形方式或以雉形图案进行电气或机械扫描。这用于雷达和 其他需要更宽的空间覆盖范围但必须保持窄波束宽度的系统。这也用于生成跟踪天线的指向误差。

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Transmitted Effective Isotropic Radiated Power

EIRP 提供了一种比较不同发射机的方法。为了分析天线的输出，使用了 EIRP (图 1-2)：
$$\mathrm{EIRP}=P_t-L_{t t}+G_t-L_{t o}$$

$P_t=$ 发射机功率 $\mathrm{dBm}$
$L_{t t}=$ 总负损失 $\mathrm{dB} ;$ 同轴或波导线路损耗、开关、环行器、天线连接
$G_t=$ 发射机天线增益 $\mathrm{dB}$ 参考各向同性天线
$L_{t a}=$ 总发射机天线损耗 $\mathrm{dB}$

$$\mathrm{EIRP}=\mathrm{ERP}+G_{\text {dipole }},$$

$$\mathrm{EIRP}=10 \mathrm{dBm} \mathrm{ERP} \quad=\mathrm{EIRP}-G_{\text {dipole }}=10 \mathrm{dBm}-2.14 \mathrm{~dB}=7.86 \mathrm{dBm}$$

## 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。

## 电气工程代写|数字系统设计作业代写Digital System Design代考|EE301

statistics-lab™ 为您的留学生涯保驾护航 在代写数字系统设计Digital System Design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系统设计Digital System Design方面经验极为丰富，各种代写数字系统设计Digital System Design相关的作业也就用不着说。

• 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

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Transmitter Component Losses

Most transceiver systems contain RF components such as a circulator or a transmit/receive (T/R) switch that enable the transceiver to use the same antenna for both transmitting and receiving. Also, if the antenna arrays use multiple antennas, some of their components will interconnect the individual antenna elements. Since these elements have a loss associated with them, they need to be taken into account in the overall output power of the transmitter. These losses directly reduce the signal level or the power output of the transmitter. The component losses are labeled and are included in the analysis:
$L_{\text {tcomp }}=$ switchers, circulators, antenna connections
Whichever method is used, the losses directly affect the power output on a one-for-one basis. A $1 \mathrm{~dB}$ loss equals a $1 \mathrm{~dB}$ loss in transmitted power. Therefore, the losses after the final output power amplifier (PA) of the transmitter and the first amplifier (or low-noise amplifier [LNA]) of the receiver should be kept to a minimum. Each $\mathrm{dB}$ of loss in this path will either reduce the minimum detectable signal (MDS) by a dB or the transmitter gain will have to transmit a $\mathrm{dB}$ more power.

Since most transmitters are located at a distance from the antenna, the cable or waveguide connecting the transmitter to the antenna contains losses that need to be incorporated in the total power output:
$L_{t l l}=$ coaxial or waveguide line losses (in $\left.\mathrm{dB}\right)$
These transmitter line losses are included in the total power output analysis; a $1 \mathrm{~dB}$ loss equals a $1 \mathrm{~dB}$ loss in power output. Using larger diameter cables or higher quality cables can reduce the loss, which is a trade-off with cost. For example, heliax cables are used for very low-loss applications. However, they are generally more expensive and larger in diameter than standard cables. The total losses between the power amplifier and the antenna are therefore equal to
$$L_{t t}=L_{t l l}+L_{\text {tcomp }}$$
Another way to reduce the loss between the transmitter and the antenna is to locate the transmitter power amplifier as close to the antenna as possible. This will reduce the length of the cable, which reduces the overall loss in the transmitter.

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Transmitter Antenna Gain

Most antennas experience gain because they tend to focus energy in specified directions compared with an ideal isotropic antenna, which radiates in all directions. Antennas do not amplify the signal power but focus the existing signal in a given direction. This is similar to a magnifying glass, which can be used to focus the sun rays in a specific direction, increasing the signal level at a single point (Figure 1-4).

A simple vertical dipole antenna experiences approximately $2.14 \mathrm{dBi}$ of gain compared with an isotropic radiator because it transmits most of the signal around the antenna, with very little of the signal transmitted directly up to the sky and directly down to the ground (Figure 1-5).
A parabolic dish radiator is commonly used at high frequencies to achieve gain by focusing the signal in the direction the antenna is pointing (Figure 1-6). The gain for a parabolic antenna is
$$G_t=10 \log \left[n(\pi D / \lambda)^2\right]$$
where
\begin{aligned} G_t &=\text { gain of the antenna (in dBi) } \ n &=\text { efficiency factor }<1 \ D &=\text { diameter of the parabolic dish } \ \lambda &=\text { wavelength } \end{aligned}

The efficiency factor is the actual gain of the antenna compared with the theoretical gain. This can happen when a parabolic antenna is not quite parabolic, when the surface of the antenna combined with the feed is not uniform, and when other anomalies occur in the actual implementation of the antenna system. Typically this ranges from $0.5$ to $0.8$, depending on the design and the frequency of operation.

Notice that the antenna gain increases both with increasing diameter and higher frequency (shorter wavelength). The gain of the antenna is a direct gain where a $1 \mathrm{~dB}$ gain equals a $1 \mathrm{~dB}$ improvement in the transmitter power output. Therefore, a larger gain will increase the range of the link. In addition, the more gain the antenna can produce, the less power the power amplifier has to deliver for the same range. This is another trade-off that needs to be considered to ensure the best design and the lowest cost for a given application.

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Transmitter Component Losses

$L_{\text {tcomp }}=$ 切换器、循环器、天线连接

$$L_{t t}=L_{t l l}+L_{\text {tcomp }}$$

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Transmitter Antenna Gain

$$G_t=10 \log \left[n(\pi D / \lambda)^2\right]$$

$G_t=$ gain of the antenna (in dBi) $n=$ efficiency factor $<1 D=$ diameter of the parabolic

## 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。

## 电气工程代写|数字系统设计作业代写Digital System Design代考|ECE4110

statistics-lab™ 为您的留学生涯保驾护航 在代写数字系统设计Digital System Design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系统设计Digital System Design方面经验极为丰富，各种代写数字系统设计Digital System Design相关的作业也就用不着说。

• 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

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Frequency of Operation

In a transceiver design, we first determine the radio frequency (RF) of operation. The frequency of operation depends on the following factors:

• RF availability: This is the frequency band that is available for use by a particular system and is dependent on the communications authority for each country. For example, in the United States it is specified by the Federal Communications Commission (FCC), and in the United Kingdom it is specified by the British Approvals Board for Telecommunications (BABT). These two groups have ultimate control over frequency band allocation. Other organizations that help to establish standards are the International Telecommunications Union Standardization Sector (ITU-T), the European Conference of Postal and Telecommunications Administrations (CEPT), and the European Telecommunications Standards Institute (ETSI).
• Cost: As the frequency increases, the components in the receiver tend to be more expensive. An exception to the rule is when there is a widely used frequency band, such as the cellular radio band, where supply and demand drive down the cost of parts and where integrated circuits are designed for specific applications. These are known as application-specific integrated circuits (ASICs).
• Range and antenna size: As a general rule, decreasing the frequency will also decrease the amount of loss between the transmitter and the receiver. This loss is mainly due to free-space attenuation and is calculated using the frequency or wavelength of the transmission. This results in an increase in range for line-of-sight applications or a decrease in the output power requirement, which would also affect cost. However, another factor that affects range is the ability of the signal to reflect or bounce off the atmosphere, mainly the ionosphere and sometimes the troposphere. For specific frequencies, this can increase the range tremendously. Amateur radio operators use frequencies that can bounce off the atmosphere and travel around the world with less than 100 watts of power. Also, the size of the antenna increases as the frequency decreases. Therefore, the size of the antenna might be too big for practical considerations and could also be a factor in the cost of the design.
• Customer specified: Oftentimes the frequency of operation is specified by the customer. If the application is for commercial applications, the frequency selection must follow the rules currently in place for that specific application to obtain the approval of the FCC and other agencies.
• Band congestion: Ideally, the frequency band selected is an unused band or serves very little purpose, especially with no high-power users in the band. This also needs to be approved by the FCC and other agencies. Generally the less used bands are very high, which increases the cost. Many techniques available today allow more users to operate successfully in particular bands, and some of these techniques will be discussed further in the book.

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Power from the Transmitter

The power from the transmitter $\left(P_t\right)$ is the amount of power output of the final stage of the power amplifier. For ease in the analysis of power levels, the power is specified in $\mathrm{dBm}$ or converted to $\mathrm{dBm}$ from milliwatts $(\mathrm{mW})$. The power in $\mathrm{mW}$ is converted to power in $\mathrm{dBm}$ by
$$P_{\mathrm{dbm}}=10 \log P_{\mathrm{mW}}$$
Therefore, $1 \mathrm{~mW}$ is equal to $0 \mathrm{dBm}$. The unit $\mathrm{dBm}$ is used extensively in the industry, and a good understanding of this term and other $\mathrm{dB}$ terms is important. The term $\mathrm{dBm}$ is actually a power level related to $1 \mathrm{~mW}$ and is not a loss or gain as is the term $\mathrm{dB}$.

A decibel $(\mathrm{dB})$ is a unit for expressing the ratio of two amounts of electric or acoustic signal power. The decibel is used to enable the engineer to calculate the resultant power level by simply adding or subtracting gains and losses instead of multiplying and dividing.
Gains and losses are expressed in $\mathrm{dB} . \mathrm{A} \mathrm{dB}$ is defined as a power ratio:
$$\mathrm{dB}=10 \log \left(P_o / P_i\right)$$
where
$P_i=$ the input power (in $\mathrm{mW}$ )
$P_o=$ the output power (in $\mathrm{mW}$ )

For example:
Given:
Amplifier power input $=0.15 \mathrm{~mW}=10 \log (0.15)=-8.2 \mathrm{dBm}$ Amplifier power gain $P_o / P_i=13=10 \log (13)=11.1 \mathrm{~dB}$
Calculate the power output:
Power output $=0.15 \mathrm{~mW} \times 13=1.95 \mathrm{~mW}$ using power and multiplication Power output (in $\mathrm{dBm}$ ) $=-8.2 \mathrm{dBm}+11.1 \mathrm{~dB}=2.9 \mathrm{dBm}$ using $\mathrm{dBm}$ and $\mathrm{dB}$ and addition
Note: $2.9 \mathrm{dBm}=10 \log (1.95)$
Another example of using $\mathrm{dBm}$ and $\mathrm{dB}$ is as follows:
In many applications, $\mathrm{dB}$ and $\mathrm{dBm}$ are misused, which can cause errors in the results. The unit $\mathrm{dB}$ is used for a change in power level, which is generally a gain or a loss. The unit $\mathrm{dBm}$ is used for absolute power; for example, $10 \log (1$ milliwatt $)=0 \mathrm{dBm}$. The unit $\mathrm{dBw}$ is also used for absolute power; for example, $10 \log (1 \mathrm{watt})=0 \mathrm{dBw}$. The terms $\mathrm{dBm}$ and $\mathrm{dBw}$ are never used for expressing a change in signal level. The following examples demonstrate this confusion.

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Frequency of Operation

• RF 可用性：这是可供特定系统使用的频段，取决于每个国家/地区的通信机构。例如，在美国由联邦通信委员会 (FCC) 指定，在英国由英国电信认证委员会 (BABT) 指定。这两组对频带分配具有最终控制权。其他帮助制定标准的组织包括国际电信联盟标准化部门 (ITU-T)、欧洲邮政和电信管理会议 (CEPT) 和欧洲电信标准协会 (ETSI)。
• 成本：随着频率的增加，接收器中的组件往往更昂贵。该规则的一个例外是当存在广泛使用的频段时，例如蜂窝无线电频段，供需降低了零件成本，并且集成电路是为特定应用设计的。这些被称为专用集成电路（ASIC）。
• 范围和天线尺寸：作为一般规则，降低频率也会减少发射器和接收器之间的损耗量。这种损耗主要是由于自由空间衰减造成的，并且是使用传输的频率或波长计算得出的。这导致视距应用范围的增加或输出功率要求的降低，这也会影响成本。然而，影响范围的另一个因素是信号反射或反射大气层的能力，主要是电离层，有时是对流层。对于特定频率，这可以极大地增加范围。业余无线电操作员使用的频率可以从大气层反弹并以不到 100 瓦的功率环游世界。此外，天线的尺寸随着频率的降低而增加。
• 客户指定：通常操作频率由客户指定。如果申请是用于商业应用，则频率选择必须遵循该特定应用的现行规则，以获得 FCC 和其他机构的批准。
• 频段拥塞：理想情况下，所选频段是未使用的频段或用途很少，尤其是频段内没有高功率用户。这也需要得到 FCC 和其他机构的批准。通常较少使用的频段非常高，这增加了成本。当今可用的许多技术允许更多用户在特定频段成功操作，其中一些技术将在本书中进一步讨论。

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Power from the Transmitter

$$P_{\mathrm{dbm}}=10 \log P_{\mathrm{mW}}$$

$$\mathrm{dB}=10 \log \left(P_o / P_i\right)$$

$P_i=$ 输入功率 (在 $\left.\mathrm{mW}\right)$
$P_o=$ 输出功率 (在 $\mathrm{mW}$ )

$P_o / P_i=13=10 \log (13)=11.1 \mathrm{~dB}$

$=-8.2 \mathrm{dBm}+11.1 \mathrm{~dB}=2.9 \mathrm{dBm}$ 使用 $\mathrm{dBm}$ 和 $\mathrm{dB}$ 和补充

## 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。

## 电气工程代写|数字信号过程代写digital signal process代考|ECE4624

statistics-lab™ 为您的留学生涯保驾护航 在代写数字信号过程digital signal process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过程digital signal process代写方面经验极为丰富，各种代写数字信号过程digital signal process相关的作业也就用不着说。

• 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

## 电气工程代写|数字信号过程代写digital signal process代考|Review of Linear Algebra

Linear algebra is a topic in mathematics that deals with calculations involving linear systems of equations. Although linear algebra is not required to understand the fundamentals of digital signal processing and communication engineering, a thorough command of its arithmetic and properties is paramount as we advance our skills beyond basic DSP concepts. The concept of optimization, which includes equalization, approximation, and optimal filter design, as well as the spatial multiplexing MIMO techique are built upon linear algebra.

While in-depth treatments of linear algebra are available in several text books [4], it is the goal of this section to review only those concepts that we will encounter in later chapters. Let’s start by considering a simple linear system of equations describing two lines.
\begin{aligned} &a_{11} \cdot x+a_{12} y=b_1 \ &a_{21} \cdot x+a_{22} y=b_2 \end{aligned}
Although the equation of a line is usually shown in y-intercept form $(y=m x+b)$, the formulation above, called the standard form, will be more convenient to work with. However, to get the first equation back to the more familiar $y$-intercept form, simply subtract $a_{11^{-}} x$ from both sides of the equation and divide by $a_{12}$.
$$y=-\frac{a_{11}}{a_{12}} x+\frac{b_1}{a_{12}}$$
For now, we will stay with the standard form and reformulate the systems of equations into an expressions.using matrices.
$$\left[\begin{array}{ll} a_{11} & a_{12} \ a_{21} & a_{22} \end{array}\right] \cdot\left[\begin{array}{l} x \ y \end{array}\right]=\left[\begin{array}{l} b_1 \ b_2 \end{array}\right]$$
One of the chief goals of linear algebra is to find the solution to such a system of equations, which, in the case above, means finding the $x$ and $y$ coordinate where the two lines cross (thus satisfying both equations simultaneously). We can rewrite the expression above by replacing the matrices with variables $A, X$, and $B$. Finding $X$ obviously requires that both matrices $A$ and $B$ are known.
$$A \cdot X=B$$
The variable $A$ represents a two row by two column (or $2 \times 2$ ) matrix while the other two variables are column vectors of dimension $2 x 1$. Vectors are matrices that feature either one row or one column.

## 电气工程代写|数字信号过程代写digital signal process代考|Orthogonal Vectors and Matrices

Orthogonal matrices are composed of column vectors that are themselves orthogonal. Geometrically speaking, orthogonal vectors in two and three dimensional space, $R^2$ and $R^3$, feature directions that are perpendicular to one another. The same is true for higher dimensional space, but it is more difficult to visualize. A more generalized terms, two vectors, $v_l$ and $v_2$, of length $N$ are orthogonal if the sum of their entry by entry products is equal to zero.
$$\sum_{n=0}^{N-1} v_1[n] \cdot v_2[n]=0$$
The matrices below feature column vectors that are orthogonal.
The orthogonal column vectors of each matrix – let’s call them $v_1, v_2$, and $v_3-$ are seen in the two and three dimensional coordinate systems below. $A_1$ is an identity matrix, which leaves all input vectors that it transforms unchanged. Matrix $A_2$ would cause an input vector to be rotated by 45 degrees and stretched by a factor equal to the square root of 2 . Similarly, $A_3$ produces a 45 degree rotation around the $z$ axis, stretches the $x$ and $y$ components of an input véctor by the square root of 2 but leaves the $z$ component unchanged. However, regardless of how each matrix affects its input vector, the column vectors in each matrix are perpendicular and therefore orthogonal.Orthogonal matrices, whose column vectors feature unit-length are called orthonormal. Notice that of the three matrices shown above only $A_1$ is orthonormal. We will meet orthonormal matrices later on in this chapter and discover their interesting properties.

## 电气工程代写|数字信号过程代写digital signal process代考|Review of Linear Algebra

$$a_{11} \cdot x+a_{12} y=b_1 \quad a_{21} \cdot x+a_{22} y=b_2$$

$$y=-\frac{a_{11}}{a_{12}} x+\frac{b_1}{a_{12}}$$

$$\left[\begin{array}{llll} a_{11} & a_{12} & a_{21} & a_{22} \end{array}\right] \cdot\left[\begin{array}{ll} x & y \end{array}\right]=\left[\begin{array}{ll} b_1 & b_2 \end{array}\right]$$

$$A \cdot X=B$$

## 电气工程代写|数字信号过程代写digital signal process代考|Orthogonal Vectors and Matrices

$$\sum_{n=0}^{N-1} v_1[n] \cdot v_2[n]=0$$

## 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。

## 电气工程代写|数字信号过程代写digital signal process代考|ENEE425

statistics-lab™ 为您的留学生涯保驾护航 在代写数字信号过程digital signal process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过程digital signal process代写方面经验极为丰富，各种代写数字信号过程digital signal process相关的作业也就用不着说。

• 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

## 电气工程代写|数字信号过程代写digital signal process代考|Roots of Polynomials

The two expressions below show a quadratic (degree 2 ) and a cubic (degree 3 ) polynomial function. The roots or solutions to these expressions may be found by setting them to zero and solving for the dependent variable $x$, or by plotting them and observing where $f(x)$ crosses zero.
$$\begin{array}{llrl} f(x) & =a \cdot x^2+b \cdot x+c & & \leftarrow \text { quadratic } \ f(x) & =a \cdot x^3+b \cdot x^2+c \cdot x+d & & \leftarrow \text { cubic } \end{array}$$
In the examples below we factor two polynomials thus revealing the roots algebraically and then verify those results graphically.

The roots, which are clearly revealed when we factor the polynomials, naturally fall at the zero crossings of the curves. While the above quadratic is easy to factor using mental math, more sophisticated expressions require the use of the well-known quadratic formula.
$$a z^2+b z+c=0 \quad \rightarrow \quad \text { Roots }=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$$
All was well in the world of mathematics until someone tried to apply the equation above to an innocuous expression like $f(x)=s^2-4 s+8$. The initial curiosity was to fathom why the curve never crosses zero; moreover, applying the coefficients $a=1, b=-4$, and $c=8$ to our quadratic equation forces us to take the square root of a negative number.
$$\text { Roots }=\frac{+4 \pm \sqrt{-16}}{2}=\frac{+4 \pm 4 \sqrt{-1}}{2}=2 \pm j 2$$
Given what we have learned so far, accepting the fact that roots can be complex is no longer an obstacle, but the fact that the curve does not cross zero remains confusing.

## 电气工程代写|数字信号过程代写digital signal process代考|Complex Exponentials and Euler’s Formulas

In the study of communication systems and digital signal processing, few equations are as mysterious and useful as Euler’s formula, which establishes a relationship between trigonometric and complex exponential functions. His formula states the following.
\begin{aligned} e^{j \theta} &=\cos (\theta)+j \sin (\theta) \ & \text { and therefore } \ \operatorname{Mag} \cdot e^{j \theta}=& \text { Mag } \cdot(\cos (\theta)+j \sin (\theta)) \end{aligned}
This formula allows us to express a complex number in polar format, $\operatorname{Mag} \angle \theta$, as a value, Mag $\cdot e^{\prime \theta}$, that can be easily manipulated in equations. It simplifies complex multiplication, since multiplying exponential functions of the form $e^{j a \cdot} e^{j b}=e^{j(a+b)}$ involves the mere addition of exponents.

How an exponentially increasing function can be linked to trigonometric expressions (sine and cosine) that are oscillatory in nature is mysterious indeed. Although we won’t recreate his approach used to arrive at the formula, we will show that it is true.

Leonhard Euler not only introduced the formula, for which he is now famous but also established the number $e$, which he defined as a series [3].
$$e=1+\frac{1}{1}+\frac{1}{1 \cdot 2}+\frac{1}{1 \cdot 2 \cdot 3}+\frac{1}{1 \cdot 2 \cdot 3 \cdot 4} \cdots=\sum_{n=0}^{\infty} \frac{1}{n !}=2.7182818$$
The Taylor series expansions for the more general case of $e^\theta$, as well as for $\sin (\theta)$ and $\cos (\theta)$ are shown next and can be looked up in any calculus text book [3].

## 电气工程代写|数字信号过程代写digital signal process代考|Roots of Polynomials

$f(x)=a \cdot x^2+b \cdot x+c \quad \leftarrow$ quadratic $f(x)=a \cdot x^3+b \cdot x^2+c \cdot x+d \leftarrow$ cubic

$$a z^2+b z+c=0 \rightarrow \text { Roots }=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$$

$$\text { Roots }=\frac{+4 \pm \sqrt{-16}}{2}=\frac{+4 \pm 4 \sqrt{-1}}{2}=2 \pm j 2$$

## 电气工程代写|数字信号过程代写digital signal process代考|Complex Exponentials and Euler’s Formulas

$$e^{j \theta}=\cos (\theta)+j \sin (\theta) \quad \text { and therefore } \operatorname{Mag} \cdot e^{j \theta}=\mathrm{Mag} \cdot(\cos (\theta)+j \sin (\theta))$$

$$e=1+\frac{1}{1}+\frac{1}{1 \cdot 2}+\frac{1}{1 \cdot 2 \cdot 3}+\frac{1}{1 \cdot 2 \cdot 3 \cdot 4} \cdots=\sum_{n=0}^{\infty} \frac{1}{n !}=2.7182818$$

## 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。

## 电气工程代写|数字信号过程代写digital signal process代考|ECE714

statistics-lab™ 为您的留学生涯保驾护航 在代写数字信号过程digital signal process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过程digital signal process代写方面经验极为丰富，各种代写数字信号过程digital signal process相关的作业也就用不着说。

• 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

## 电气工程代写|数字信号过程代写digital signal process代考|The Development of Numbers

Complex numbers have confounded the greatest minds in the history of mathematics for the very same reason they confound us today. It is difficult to picture a complex amount of stuff. In our mind we can imagine 4 potatoes and $21 / 2$ oranges, but $2+j$ lemons just doesn’t make much sense. Even the idea of zero lemons becomes awkward. After all, numbers were invented to express the amount of something that we can see, touch, or otherwise appreciate.

Mathematicians brought complex numbers to life in their quest to find solutions to algebraic equations. To be more specific, they tried to find solutions to polynomial equations of the following form.
$$a_n x^n+a_{n-1} x^{n-1}+\ldots+a_1 x^1+a_0=0$$
In the expression above, $x$ represents the variable that we wish to find, while the quantities $a_0$ through $a_n$ are constants. The degree, or order, of the polynomial is defined as the highest exponent, $n$, in the expression. For lower orders, polynomials reduce to simple algebraic expressions used for everyday calculations. Here are examples of first and second order polynomial equations.
$$\begin{gathered} x+4=0 \ x^2+2 x+1=0 \end{gathered}$$
To get a better appreciation of numbers in general and complex numbers in particular, let’s examine how their use evolved over time and how they helped find the solution for polynomial equations with which mathematicians seemed to be so enamored.

## 电气工程代写|数字信号过程代写digital signal process代考|Expanding Our Concept of Numbers as Mere Quantities

The fact that complex numbers have given closure to the task of finding all roots of polynomials may be reassuring to a whole host of long-dead mathematicians, but it still doesn’t help us appreciate the meaning of negative two sacks of grain or $2+j$ dollars. Luckily, the work of English mathematician John Wallis (1616-1703) paved the way for the use of the number line, which provides numbers with geometric meaning that had not previously been available to the layperson.

The number lines $a$ through $c$ above take us from the original counting or whole numbers through integers and finally to real numbers. While we still can’t put a concrete meaning to negative numbers, as the integers and real number lines seem to allow, we have nevertheless seen and dealt with these lines often enough to feel comfortable handling the numbers that lie on them.

To better understand positive and negative numbers, we think of them as vectors, which feature two separate parameters: a magnitude and a direction. The two vectors lying on number line $d$ represent numbers $1.5$ and $-3$. Their magnitudes, $1.5$ and 3 , are quantities that have a direct and palpable meaning that we as human beings can understand. Their direction conveys a quality about the object that is abstract in nature. The direction in the case-of minus 2 sacks of grain could indicate their state of ownership. The positive sign means that you own it, while the negative sign indicates that you owe it. Just take a look at the negative sign of your bank account balance after you’ve spent more money than you should have. Clearly, in the realm of integers and real numbers there are only two directions, featuring opposite bearings. Since a direction in 2D space is equivalent to an angle, we assign 0 degrees to the positive sign and $180 /-180$ degrees to the negative sign. Let’s reformulate the two numbers $1.5$ and $-3$ in terms of magnitude and direction (angle).
$$+1.5=1.5 \angle 0^{\circ} \quad-3.0=3.0 \angle 180^{\circ}$$

## 电气工程代写|数字信号过程代写digital signal process代考|The Development of Numbers

$$a_n x^n+a_{n-1} x^{n-1}+\ldots+a_1 x^1+a_0=0$$

$$x+4=0 x^2+2 x+1=0$$

## 电气工程代写|数字信号过程代写digital signal process代考|Expanding Our Concept of Numbers as Mere Quantities

+1.5=1.5∠0∘−3.0=3.0∠180∘

## 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。

## 电气工程代写|信号和系统代写signals and systems代考|ECE3101

statistics-lab™ 为您的留学生涯保驾护航 在代写信号和系统signals and systems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。我们的专家在代写信号和系统signals and systems代写方面经验极为丰富，各种代写信号和系统signals and systems相关的作业也就用不着说。

• 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

## 电气工程代写|信号和系统代写signals and systems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.
$\sum_{n=0}^{N-1} a^n=\frac{\left(1-a^n\right)}{(1-a)} \quad a \neq 1$
$-N \quad a-1$
2.
$$\sum_{n=0}^{\infty} a^n=\frac{1}{(1-a)} \quad a<1$$

## 电气工程代写|信号和系统代写signals and systems代考|Linear and Nonlinear Systems

A linear discrete time system obeys the property of superposition. As discussed for $\mathrm{CT}$ 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 $y_3[n]=y_4[n]$, then given DT system is linear. Otherwise it is nonlinear.

## 电气工程代写|信号和系统代写signals and systems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. 周期信号是功率信号，反之则不成立。这里，每个周期的信号能量是有限的。
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.
$\sum_{n=0}^{N-1} a^n=\frac{\left(1-a^n\right)}{(1-a)} \quad a \neq 1$
$-N \quad a-1$
2.
$$\sum_{n=0}^{\infty} a^n=\frac{1}{(1-a)} \quad a<1$$

## 电气工程代写|信号和系统代写signals and systems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. 求输出的加权和为
$$y_3[n]=a_1 y_1[n]+a_2 y_2[n]$$
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 $y_3[n]=y_4[n]$ ，则给定DT系统是线性的。否则是非线性的。

## 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。