## 计算机代写|计算机视觉代写Computer Vision代考|CS763

statistics-lab™ 为您的留学生涯保驾护航 在代写计算机视觉Computer Vision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。我们的专家在代写计算机视觉Computer Vision方面经验极为丰富，各种代写计算机视觉Computer Vision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

## 计算机代写|计算机视觉代写Computer Vision代考|Geometric primitives and transformations

In this section, we introduce the basic 2D and 3D primitives used in this textbook, namely points, lines, and planes. We also describe how 3D features are projected into 2D features. More detailed descriptions of these topics (along with a gentler and more intuitive introduction) can be found in textbooks on multiple-view geometry (Hartley and Zisserman 2004; Faugeras and Luong 2001).
Geometric primitives form the basic building blocks used to describe three-dimensional shapes. In this section, we introduce points, lines, and planes. Later sections of the book discuss curves (Sections $7.3$ and 12.2), surfaces (Section 13.3), and volumes (Section 13.5).
2D points. 2D points (pixel coordinates in an image) can be denoted using a pair of values, $\mathbf{x}=(x, y) \in \mathcal{R}^2$, or alternatively,
$$\mathbf{x}=\left[\begin{array}{l} x \ y \end{array}\right]$$
(As stated in the introduction, we use the $\left(x_1, x_2, \ldots\right)$ notation to denote column vectors.)

2D points can also be represented using homogeneous coordinates, $\tilde{\mathbf{x}}=(\tilde{x}, \tilde{y}, \tilde{w}) \in \mathcal{P}^2$, where vectors that differ only by scale are considered to be equivalent. $\mathcal{P}^2=\mathcal{R}^3-(0,0,0)$ is called the 2D projective space.

A homogeneous vector $\tilde{\mathbf{x}}$ can be converted back into an inhomogeneous vector $\mathbf{x}$ by dividing through by the last element $\tilde{w}$, i.e.,
$$\tilde{\mathbf{x}}=(\tilde{x}, \tilde{y}, \tilde{w})=\tilde{w}(x, y, 1)=\tilde{w} \overline{\mathbf{x}},$$
where $\overline{\mathbf{x}}=(x, y, 1)$ is the augmented vector. Homogeneous points whose last element is $\tilde{w}=0$ are called ideal points or points at infinity and do not have an equivalent inhomogeneous representation.
2D lines. 2D lines can also be represented using homogeneous coordinates $\tilde{\mathbf{I}}=(a, b, c)$. The corresponding line equation is
$$\overline{\mathbf{x}} \cdot \tilde{\mathbf{l}}=a x+b y+c=0 .$$
We can normalize the line equation vector so that $\mathbf{l}=\left(\hat{n}_x, \hat{n}_y, d\right)=(\hat{\mathbf{n}}, d)$ with $|\hat{\mathbf{n}}|=1$. In this case, $\hat{\mathbf{n}}$ is the normal vector perpendicular to the line and $d$ is its distance to the origin (Figure 2.2). (The one exception to this normalization is the line at infinity $\tilde{\mathbf{l}}=(0,0,1)$, which includes all (ideal) points at infinity.)

We can also express $\hat{\mathbf{n}}$ as a function of rotation angle $\theta, \hat{\mathbf{n}}=\left(\hat{n}_x, \hat{n}_y\right)=(\cos \theta, \sin \theta)$ (Figure 2.2a). This representation is commonly used in the Hough transform line-finding algorithm, which is discussed in Section 7.4.2. The combination $(\theta, d)$ is also known as polar coordinates.
When using homogeneous coordinates, we can compute the intersection of two lines as
$$\tilde{\mathbf{x}}=\tilde{\mathbf{l}}_1 \times \tilde{\mathbf{l}}_2,$$
where $\times$ is the cross product operator. Similarly, the line joining two points can be written as
$$\tilde{\mathbf{l}}=\tilde{\mathbf{x}}_1 \times \tilde{\mathbf{x}}_2 .$$
When trying to fit an intersection point to multiple lines or, conversely, a line to multiple points, least squares techniques (Section 8.1.1 and Appendix A.2) can be used, as discussed in Exercise 2.1.

## 计算机代写|计算机视觉代写Computer Vision代考|2D transformations

Having defined our basic primitives, we can now turn our attention to how they can be transformed. The simplest transformations occur in the 2D plane are illustrated in Figure 2.4.
Translation. $2 \mathrm{D}$ translations can be written as $\mathbf{x}^{\prime}=\mathrm{x}+\mathbf{t}$ or
$$\mathbf{x}^{\prime}=\left[\begin{array}{ll} \mathbf{l} & \mathbf{t} \end{array}\right] \overline{\mathbf{x}},$$
where $I$ is the $(2 \times 2)$ identity matrix or
$$\overline{\mathbf{x}}^{\prime}=\left[\begin{array}{cc} \mathbf{I} & \mathbf{t} \ \mathbf{0}^T & 1 \end{array}\right] \overline{\mathbf{x}},$$
where $\mathbf{0}$ is the zero vector. Using a $2 \times 3$ matrix results in a more compact notation, whereas using a full-rank $3 \times 3$ matrix (which can be obtained from the $2 \times 3$ matrix by appending a [0 $\left.0^T 1\right]$ row) makes it possible to chain transformations using matrix multiplication as well as to compute inverse transforms. Note that in any equation where an augmented vector such as $\overline{\mathbf{x}}$ appears on both sides, it can always be replaced with a full homogeneous vector $\tilde{\mathbf{x}}$.

# 计算机视觉代考

## 计算机代写|计算机视觉代写Computer Vision代考|Geometric primitives and transformations

$$\mathbf{x}=\left[\begin{array}{ll} x & y \end{array}\right]$$
（如介绍中所述，我们使用 $\left(x_1, x_2, \ldots\right)$ 表示列向量的符号。)

$$\tilde{\mathbf{x}}=(\tilde{x}, \tilde{y}, \tilde{w})=\tilde{w}(x, y, 1)=\tilde{w} \overline{\mathbf{x}},$$

$$\overline{\mathbf{x}} \cdot \tilde{\mathbf{l}}=a x+b y+c=0 .$$

$$\tilde{\mathbf{x}}=\tilde{\mathbf{l}}_1 \times \tilde{\mathbf{l}}_2$$

$$\tilde{\mathbf{1}}=\tilde{\mathbf{x}}_1 \times \tilde{\mathbf{x}}_2 .$$

## 计算机代写|计算机视觉代写Computer Vision代考|2D transformations

$$\mathbf{x}^{\prime}=\left[\begin{array}{ll} \mathbf{1} & \mathbf{t} \end{array}\right] \overline{\mathbf{x}}$$

$$\overline{\mathbf{x}}^{\prime}=\left[\begin{array}{lll} \mathbf{I} & \mathbf{t} \mathbf{0}^T & 1 \end{array}\right] \overline{\mathbf{x}}$$

## 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。

## 计算机代写|计算机视觉代写Computer Vision代考|CPS843

statistics-lab™ 为您的留学生涯保驾护航 在代写计算机视觉Computer Vision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。我们的专家在代写计算机视觉Computer Vision方面经验极为丰富，各种代写计算机视觉Computer Vision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

## 计算机代写|计算机视觉代写Computer Vision代考|Book overview

In the final part of this introduction, I give a brief tour of the material in this book, as well as a few notes on notation and some additional general references. Since computer vision is such a broad field, it is possible to study certain aspects of it, e.g., geometric image formation and 3D structure recovery, without requiring other parts, e.g., the modeling of reflectance and shading. Some of the chapters in this book are only loosely coupled with others, and it is not strictly necessary to read all of the material in sequence.

Figure $1.12$ shows a rough layout of the contents of this book. Since computer vision involves going from images to both a semantic understanding as well as a 3D structural description of the scene, I have positioned the chapters horizontally in terms of where in this spectrum they land, in addition to vertically according to their dependence. ${ }^9$

Interspersed throughout the book are sample applications, which relate the algorithms and mathematical material being presented in various chapters to useful, real-world applications. Many of these applications are also presented in the exercises sections, so that students can write their own.
At the end of each section, I provide a set of exercises that the students can use to implement, test, and refine the algorithms and techniques presented in each section. Some of the exercises are suitable as written homework assignments, others as shorter one-week projects, and still others as

open-ended research problems that make for challenging final projects. Motivated students who implement a reasonable subset of these exercises will, by the end of the book, have a computer vision software library that can be used for a variety of interesting tasks and projects.

If the students or curriculum do not have a strong preference for programming languages, Python, with the NumPy scientific and array arithmetic library plus the OpenCV vision library, are a good environment to develop algorithms and learn about vision. Not only will the students learn how to program using array/tensor notation and linear/matrix algebra (which is a good foundation for later use of PyTorch for deep learning), you can also prepare classroom assignments using Jupyter notebooks, giving you the option to combine descriptive tutorials, sample code, and code to be extended/modified in one convenient location. ${ }^{10}$

As this is a reference book, I try wherever possible to discuss which techniques and algorithms work well in practice, as well as provide up-to-date pointers to the latest research results in the areas that I cover. The exercises can be used to build up your own personal library of self-tested and validated vision algorithms, which is more worthwhile in the long term (assuming you have the time) than simply pulling algorithms out of a library whose performance you do not really understand.
The book begins in Chapter 2 with a review of the image formation processes that create the images that we see and capture. Understanding this process is fundamental if you want to take a scientific (model-based) approach to computer vision. Students who are eager to just start implementing algorithms (or courses that have limited time) can skip ahead to the next chapter and dip into this material later. In Chapter 2, we break down image formation into three major components. Geometric image formation (Section 2.1) deals with points, lines, and planes, and how these are mapped onto images using projective geometry and other models (including radial lens distortion). Photometric image formation (Section 2.2) covers radiometry, which describes how light interacts with surfaces in the world, and optics, which projects light onto the sensor plane. Finally, Section $2.3$ covers how sensors work, including topics such as sampling and aliasing, color sensing, and in-camera compression.

## 计算机代写|计算机视觉代写Computer Vision代考|Sample syllabus

Teaching all of the material covered in this book in a single quarter or semester course is a Herculean task and likely one not worth attempting. ${ }^{11}$ It is better to simply pick and choose topics related to the lecturer’s preferred emphasis and tailored to the set of mini-projects envisioned for the students.
Steve Seitz and I have successfully used a 10-week syllabus similar to the one shown in Table $1.1$ as both an undergraduate and a graduate-level course in computer vision. The undergraduate course $^{12}$ tends to go lighter on the mathematics and takes more time reviewing basics, while the graduate-level course ${ }^{13}$ dives more deeply into techniques and assumes the students already have a decent grounding in either vision or related mathematical techniques. Related courses have also been taught on the topics of 3D photography and computational photography. Appendix C.3 and the book’s website list other courses that use this book to teach a similar curriculum.

When Steve and I teach the course, we prefer to give the students several small programming assignments early in the course rather than focusing on written homework or quizzes. With a suitable choice of topics, it is possible for these projects to build on each other. For example, introducing feature matching early on can be used in a second assignment to do image alignment and stitching. Alternatively, direct (optical flow) techniques can be used to do the alignment and more focus can be put on either graph cut seam selection or multi-resolution blending techniques.

In the past, we have also asked the students to propose a final project (we provide a set of suggested topics for those who need ideas) by the middle of the course and reserved the last week of the class for student presentations. Sometimes, a few of these projects have actually turned into conference submissions!

No matter how you decide to structure the course or how you choose to use this book, I encourage you to try at least a few small programming tasks to get a feel for how vision techniques work and how they fail. Better yet, pick topics that are fun and can be used on your own photographs, and try to push your creative boundaries to come up with surprising results.

# 计算机视觉代考

## 计算机代写|计算机视觉代写Computer Vision代考|Sample syllabus

Steve Seitz 和我成功地使用了类似于表中所示的为期 10 周的教学大纲1.1作为计算机视觉的本科和研究生课程。本科课程12倾向于在数学上变得更轻松，并且需要更多时间复习基础知识，而研究生水平的课程13更深入地研究技术，并假设学生已经在视觉或相关数学技术方面有良好的基础。还教授了有关 3D 摄影和计算摄影主题的相关课程。附录 C.3 和本书的网站列出了使用本书教授类似课程的其他课程。

## 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。

## 计算机代写|计算机视觉代写Computer Vision代考|CMSC426

statistics-lab™ 为您的留学生涯保驾护航 在代写计算机视觉Computer Vision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。我们的专家在代写计算机视觉Computer Vision方面经验极为丰富，各种代写计算机视觉Computer Vision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

## 计算机代写|计算机视觉代写Computer Vision代考|What is computer vision

As humans, we perceive the three-dimensional structure of the world around us with apparent ease. Think of how vivid the three-dimensional percept is when you look at a vase of flowers sitting on the table next to you. You can tell the shape and translucency of each petal through the subtle patterns of light and shading that play across its surface and effortlessly segment each flower from the background of the scene (Figure 1.1). Looking at a framed group portrait, you can easily count and name all of the people in the picture and even guess at their emotions from their facial expressions (Figure 1.2a). Perceptual psychologists have spent decades trying to understand how the visual system works and, even though they can devise optical illusions ${ }^1$ to tease apart some of its principles (Figure 1.3), a complete solution to this puzzle remains elusive (Marr 1982; Wandell 1995; Palmer 1999; Livingstone 2008; Frisby and Stone 2010).

Researchers in computer vision have been developing, in parallel, mathematical techniques for recovering the three-dimensional shape and appearance of objects in imagery. Here, the progress in the last two decades has been rapid. We now have reliable techniques for accurately computing a 3D model of an environment from thousands of partially overlapping photographs (Figure 1.2c). Given a large enough set of views of a particular object or façade, we can create accurate dense 3D surface models using stereo matching (Figure 1.2d). We can even, with moderate success, delineate most of the people and objects in a photograph (Figure 1.2a). However, despite all of these advances, the dream of having a computer explain an image at the same level of detail and causality as a two-year old remains elusive.

Why is vision so difficult? In part, it is because it is an inverse problem, in which we seek to recover some unknowns given insufficient information to fully specify the solution. We must therefore resort to physics-based and probabilistic models, or machine learning from large sets of examples, to disambiguate between potential solutions. However, modeling the visual world in all of its rich complexity is far more difficult than, say, modeling the vocal tract that produces spoken sounds.

The forward models that we use in computer vision are usually developed in physics (radiometry, optics, and sensor design) and in computer graphics. Both of these fields model how objects move and animate, how light reflects off their surfaces, is scattered by the atmosphere, refracted through camera lenses (or human eyes), and finally projected onto a flat (or curved) image plane. While computer graphics are not yet perfect, in many domains, such as rendering a still scene composed of everyday objects or animating extinct creatures such as dinosaurs, the illusion of reality is essentially there.

In computer vision, we are trying to do the inverse, i.e., to describe the world that we see in one or more images and to reconstruct its properties, such as shape, illumination, and color distributions. It is amazing that humans and animals do this so effortlessly, while computer vision algorithms are so error prone. People who have not worked in the field often underestimate the difficulty of the problem. This misperception that vision should be easy dates back to the early days of artificial intelligence (see Section 1.2), when it was initially believed that the cognitive (logic proving and planning) parts of intelligence were intrinsically more difficult than the perceptual components (Boden 2006).

## 计算机代写|计算机视觉代写Computer Vision代考|A brief history

In this section, I provide a brief personal synopsis of the main developments in computer vision over the last fifty years (Figure 1.6) with a focus on advances I find personally interesting and that have stood the test of time. Readers not interested in the provenance of various ideas and the evolution of this field should skip ahead to the book overview in Section 1.3.
1970s. When computer vision first started out in the early $1970 \mathrm{~s}$, it was viewed as the visual perception component of an ambitious agenda to mimic human intelligence and to endow robots with intelligent behavior. At the time, it was believed by some of the early pioneers of artificial intelligence and robotics (at places such as MIT, Stanford, and CMU) that solving the “visual input” problem would be an easy step along the path to solving more difficult problems such as higher-level reasoning and planning. According to one well-known story, in 1966, Marvin Minsky at MIT asked his undergraduate student Gerald Jay Sussman to “spend the summer linking a camera to a computer and getting the computer to describe what it saw” (Boden 2006, p. 781). ${ }^5$ We now know that the problem is slightly more difficult than that. ${ }^6$

What distinguished computer vision from the already existing field of digital image processing (Rosenfeld and Pfaltz 1966; Rosenfeld and Kak 1976) was a desire to recover the three-dimensional

structure of the world from images and to use this as a stepping stone towards full scene understanding. Winston (1975) and Hanson and Riseman (1978) provide two nice collections of classic papers from this early period.

Early attempts at scene understanding involved extracting edges and then inferring the 3D structure of an object or a “blocks world” from the topological structure of the 2D lines (Roberts 1965). Several line labeling algorithms (Figure 1.7a) were developed at that time (Huffman 1971; Clowes 1971; Waltz 1975; Rosenfeld, Hummel, and Zucker 1976; Kanade 1980). Nalwa (1993) gives a nice review of this area. The topic of edge detection was also an active area of research; a nice survey of contemporaneous work can be found in (Davis 1975).

Three-dimensional modeling of non-polyhedral objects was also being studied (Baumgart 1974; Baker 1977). One popular approach used generalized cylinders, i.e., solids of revolution and swept closed curves (Agin and Binford 1976; Nevatia and Binford 1977), often arranged into parts relationships ${ }^7$ (Hinton 1977; Marr 1982) (Figure 1.7c). Fischler and Elschlager (1973) called such elastic arrangements of parts pictorial structures (Figure 1.7b).

A qualitative approach to understanding intensities and shading variations and explaining them by the effects of image formation phenomena, such as surface orientation and shadows, was championed by Barrow and Tenenbaum (1981) in their paper on intrinsic images (Figure 1.7d), along with the related $21 / 2$-D sketch ideas of Marr (1982). This approach has seen periodic revivals, e.g., in the work of Tappen, Freeman, and Adelson (2005) and Barron and Malik (2012).

More quantitative approaches to computer vision were also developed at the time, including the first of many feature-based stereo correspondence algorithms (Figure 1.7e) (Dev 1974; Marr and Poggio 1976, 1979; Barnard and Fischler 1982; Ohta and Kanade 1985; Grimson 1985; Pollard, Mayhew, and Frisby 1985) and intensity-based optical flow algorithms (Figure 1.7f) (Horn and Schunck 1981; Huang 1981; Lucas and Kanade 1981; Nagel 1986). The early work in simultaneously recovering $3 \mathrm{D}$ structure and camera motion (see Chapter 11) also began around this time (Ullman 1979; Longuet-Higgins 1981).

## 计算机代写|计算机视觉代写Computer Vision代考|A brief history

70 年代。当计算机视觉在早期开始时1970 秒，它被视为模仿人类智能并赋予机器人智能行为的雄心勃勃议程的视觉感知组成部分。当时，人工智能和机器人技术的一些早期先驱（在麻省理工学院、斯坦福大学和卡内基梅隆大学）认为，解决“视觉输入”问题将是解决更困难的道路上的一个简单步骤高级推理和规划等问题。根据一个众所周知的故事，1966 年，麻省理工学院的马文·明斯基 (Marvin Minsky) 要求他的本科生杰拉尔德·杰伊·萨斯曼 (Gerald Jay Sussman) “用整个夏天将相机连接到计算机，并让计算机描述它所看到的内容”（Boden 2006，第 781 页） ).5我们现在知道这个问题比那个稍微难一点。6

Barrow 和 Tenenbaum (1981) 在他们关于固有图像的论文（图 1.7d）中提倡采用定性方法来理解强度和阴影变化并通过图像形成现象（例如表面方向和阴影）的影响来解释它们，以及相关的21/2-D 素描 Marr (1982) 的想法。这种方法已经周期性地复兴，例如，在 Tappen、Freeman 和 Adelson（2005 年）以及 Barron 和 Malik（2012 年）的工作中。

## 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
• (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
• (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
• (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
• (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
• (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
• (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。

## 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
• (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|Primary Transmitter Detection

Transmitter detection techniques emphasize detecting low power signals from any PU. Low power signals mix with noise from the environment and make it hard for the CR user to detect primary signals. A low signal-to-noise ratio, multipath fading effects, and time depression make primary transmissions detection very difficult for the $\mathrm{CR}$ user. We discuss some primary transmitter detection techniques including energy detection, coherent detection, and matched filter detection.

This technique does not require CR users to have knowledge of PU signal characteristics, and it is easy to implement. Because of this, it is widely used to detect primary transmissions. Let us assume $S(n)$ is the signal received by the CR user, $W(n)$ is white Gaussian noise, and $P(n)$ is the original signal from the PU.
$$\begin{gathered} H_0: S(n)=W(n) \ H_1: S(n)=W(n)+h P(n) \end{gathered}$$
Hypothesis $H_0$ indicates the absence of a PU and hypothesis $H_1$ indicates the presence of PU transmissions. $h$ denotes the channel gain between the primary and secondary transmissions. Then, the average energy $S$ of $N$ samples is
$$S=1 / N \sum_{n=1}^N S(n)^2$$
The CR user collects $N$ samples, calculates the average energy, and compares it with a threshold $\lambda$. If the average energy is greater than the threshold, $\lambda$, then the CR user concludes that primary transmissions are present. To measure the performance, we denote the probability of the false positive (CR detects the presence of PU transmissions when there is no PU transmission) as $P_f$ and probability of the detection as $P_d$
\begin{aligned} &P_f=P\left(S>\lambda \mid H_0\right) \ &P_d=P\left(S>\lambda \mid H_1\right) \end{aligned}
To improve the performance, we need to keep the PU’s transmission secured. Therefore, the false positive probability should be less than $0.1$ and the detection probability should be greater than $0.9$.

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

The most effective way to detect PU transmissions is to detect the primary receivers who are receiving from the primary channel. The circuit in Fig. 5 shows a simple RF receiver. It has a local oscillator that emits a very low power signal for its leakage current in the circuit. A CR user can detect the leakage signals from the RF receiver circuit and identify the presence of primary transmissions. This detection technique solves both the hidden terminal and shadowing effect problems. Since the signal power is very low, it is very challenging and costly to implement the circuit for primary receiver detection.

When primary signal features like modulation type, pulse shape, operating frequency, packet format, noise statistics, etc., are known, matched filter detection can be an optimal detection technique. If these parameters are known, the CR user only needs to calculate a small number of samples. As the signal-to-noise ratio decreases, the $\mathrm{CR}$ user needs to calculate a greater number of samples. The disadvantages of this technique are the complexities in low signal-to-noise ratio, the high cost of implementation, and the very poor performance if the features are incorrect.

In a broader sense, a signal can be called a cyclostationary process if its statistical properties vary cyclically with time. In [6], the authors presented a signal classification procedure that extracts cyclic frequency domain profiles and classifies them by comparing their log-likelihood with the signal type in the database. This technique can work very well in a low SNR. The drawback of this technique is that it needs a huge amount of computation and thus, a high-speed sensing is hard to achieve [7].

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

$$H_0: S(n)=W(n) H_1: S(n)=W(n)+h P(n)$$

$$S=1 / N \sum_{n=1}^N S(n)^2$$
CR用户收藏 $N$ 采样，计算平均能量，并将其与阈值进行比较 $\lambda$. 如果平均能量大于阈值， $\lambda$ ，则 CR 用户断定存在 主要传输。为了衡量性能，我们将误报的概率表示为 (CR 在没有 $\mathrm{PU}$ 传输时检测到 $\mathrm{PU}$ 传输的存在) 为 $P_f$ 和检 测概率为 $P_d$
$$P_f=P\left(S>\lambda \mid H_0\right) \quad P_d=P\left(S>\lambda \mid H_1\right)$$

## 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。