## 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。

## 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|Network Architecture of Cognitive Radio Networks

This subsection describes the network architecture and components of a CRN. Figure 1 depicts the whole network system. User devices, primary base stations, and CR base stations are the components of a basic CRN. In Fig. 1, there are two channels: channel 1 and channel 2. One primary base station operates in channel 1 and another in channel 2. Transmissions with the primary base station are done through licensed channels by mobile users, and the transmissions are called primary transmissions (denoted by solid lines). Transmissions with the CR base station can be done through either licensed or unlicensed channels and these transmissions are called secondary transmissions (marked by dotted lines). There is also another kind of trañsmission in which any usēr devicee can transmit directly to anothèr userr device.. Therefore, transmissions in a CRN can be grouped into three classes:

• Primary transmissions: Primary transmissions are most prioritized transmissions and cannot be compromised by other transmissions. These transmissions are done in a licensed channel between primary base stations and PUs. Primary transmissions are denoted by solid lines in Fig. 1.
• Secondary transmissions: Secondary transmissions are done in the absence of primary transmissions. Transmissions between the CR base station and the $\mathrm{CR}$ user are usually secondary transmissions.
• Secondary ad hoc transmissions: User-to-user communications are called ad hoc transmissions. These transmissions can continue without base stations or other components of the network architecture. Users create their own network topology and adapt any routing protocols of ad hoc networks. Users in the gray area form an ad hoc network in Fig. 1. There are a lot of routing protocols for mobile ad hoc networks. For example, the proposed routing algorithm in [1], which ensures a fair amount of communications among nodes and improves the load concentration problem, can be used in secondary ad hoc networks. The on-demand cluster-based hybrid routing protocol proposed in [2] is also applicable here.

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

Secondary transmissions depend on spectrum sensing information, so this step should be done very accurately. Inaccurate sensing detection can lead to interferences with the PU that are highly unexpected. Though false alarms (in which channel is not occupied, but is detected as occupied) do not create interferences with the primary transmissions, it makes the CR user choose a channel from a narrower range of channels. As a result, a channel must be shared with many CR users and there would be increased competition among $\mathrm{CR}$ users to access the channel. The authors of [3] present a classification of spectrum sensing techniques. First, they classify sensing techniques into three groups: noncooperative sensing, cooperative sensing, and interference-based sensing. Noncooperative sensing is again classified into three groups: energy detection, matched filter detection, and cyclostationary feature detection. The classification is depicted in Fig. 2.

In noncooperative sensing, CR users do not share sensing information with one another. A CR user makes a decision about the PU’s presence using its own sensing information. We discuss primary transmitter detection and primary receiver detection, which are presented in $[4,5]$, in the following subsection.

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 $\mathrm{CR}$ 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 CR user. We discuss some primary transmitter detection techniques including energy detection, coherent detection, and matched filter detection.

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Network Architecture of Cognitive Radio Networks

• 主传输：主传输是最优先的传输，不能被其他传输影响。这些传输是在主基站和 PU 之间的许可信道中完成的。初级传输在图 1 中用实线表示。
• 二次传播：二次传播是在没有一次传播的情况下进行的。CR基站与CR用户通常是二次传输。

## 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|Need for Advancement in Wireless Technologies

The performance metrics such as packet loss, throughput and delay of WiMAX are measured on the basis of optimal boundary per WiMAX cell under different WiMAX network models. The performance metrics considered are spectral efficiency, throughput, transmit power, percentage of successful links, PAPR, BER.

SNR and CINR. This chapter mainly focusses on spectrum sensing techniques to achieve better spectral efficiency [5].

Recently, there is a lot of demand for tremendous technologies such as 3G, 4G and $5 \mathrm{G}$, where voice-only communications are transitioned into multimedia type applications $[6,7]$. These applications may be mobile TV, mobile P2P, streaming multimedia, video games, video monitors, interactive video, 3D services and video sharing. These high data rate applications consume more and more energy to guarantee quality of service [8]. However, the current frequency allocation schemes are unable to handle the requirements of recent higher data rate systems due to the limitations of the frequency spectrum.

Therefore, more efforts are kept on efficient frequency spectrum usage, and then a solution is found by Joseph Mittola [9], in the name of cognitive radio. The basic definition given by him is that cognitive radio (CR) is a type of a transceiver which can intelligently sense or detect unusable communication channel, and instantly allocate those channels to the unlicensed users without disturbing occupied channels [10]. Though there is no formal meaning of cognitive radio, various definitions can be seen in several contexts. A cognitive radio is, as defined by the researchers at Virginia Tech, ‘A software defined radio with a cognitive engine brain’ [11, 12]. The evolution of SDR in current technologies is provided in Fig. 2. The physical, data link and network layers of OSI model can be implemented by using SDR as shown in Fig. 3. The SDR Forum proposed a multi-tiered definition of SDR by providing the use of open architectures for advanced wireless systems and supports deployment and development [13-15]. An abstraction of the five-tier definition is illustrated in Fig. 4, where the length of the arrow represents the distribution of the software content within the radio [16].

Software-defined radio architecture comprises three sections such as radio frequency (RF), intermediate frequency (IF) and baseband section [17, 18]. It is observed from Fig. 5 that an RF signal received by smart antenna is sent to the hardware (here USRP) in which various components are inbuilt such as daughterboard, ADC/DAC, FPGAs, DSPs and ASICs. This hardware converts RF signal to IF signal and then to low-frequency baseband signal (digitized) and that will be sent to a personal computer (PC) for baseband signal processing in the transmitter (Tx) path. In this experimentation, an open-source software, GNU Radio, is employed as a software to perform baseband processing in which most of the signal processing blocks are inbuilt. All the reverse operations are performed in receiver (Rx) path such that baseband signal is converted to analogue by DAC and then sent into the air by RF hardware.

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

Generally, energy detection performance is measured in terms of probability of false alarm $P_{f a}$ (detection algorithm falsely decides that $\mathrm{PU}$ is present when it actually is absent) and probability of detection $P_d$ (correctly detecting the PU signal). Mathematically, $P_{f a}$ and $P_d$ can be expressed as [16]:
\begin{aligned} &P_{f a}=P_r\left(\text { signal is detectedl } H_0=P_r\left(u>\lambda \mid H_0\right)=\int_\lambda^{\infty} f\left(u \mid H_0\right) d u\right. \ &P_d=P_r \text { (signal is detected } H_1=P_r\left(u>\lambda \mid H_1\right)=\int_\lambda^{\infty} f\left(u \mid H_1\right) d u \end{aligned}
where $f\left(u \mid H_i\right.$ ) denotes the probability density function (pdf) of test statistic under hypothesis $H_i$ with $i=0,1$.

Thus, we target at maximizing $P_d$ while minimizing $P_{f a} . P_d$ versus $P_{f a}$ plot depicts receiver operating characteristics (ROC) and is considered as an important performance indicator. The receiver operating characteristics $(\mathrm{ROC})$ for various number of sensing samples, such as 10,50, 100 and 200, are presented in Fig. 7a, b, c and d, respectively [16]. It can be observed from Fig. 7 that the probability of detection $\left(p_d\right)$ is increased with the number of sensing samples. In our simulations, some assumptions are made such as the primary signal is deterministic, and noise is real Gaussian with mean 0 and variance 1 [17]. The probability of detection for Rayleigh channel is calculated by the averaging the probability of detection for AWGN channel [18].

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Need for Advancement in Wireless Technologies

WiMAX 的丢包率、吞吐量和延迟等性能指标是在不同WiMAX 网络模型下每个WiMAX 小区的最佳边界的基础上测量的。考虑的性能指标是频谱效率、吞吐量、发射功率、成功链接的百分比、PAPR、BER。

SNR 和 CINR。本章主要关注频谱感知技术，以实现更好的频谱效率[5]。

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

$P_{f a}=P_r\left(\right.$ signal is detectedl $H_0=P_r\left(u>\lambda \mid H_0\right)=\int_\lambda^{\infty} f\left(u \mid H_0\right) d u \quad P_d=P_r$ (signal is

## 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|The Basic Network

Consider the simplest configuration for impedance matching, namely, the L-network shown in Fig. 3.1. $Z_{\mathrm{s}}$ is an $L C$ impedance and $Y_{p}$ is an $L C$ admittance such that when the network is terminated in $R_{L}$, the input impedance is $R_{S}$ at the frequencies of interest. Let, at $s=j \omega, Z_{s}=j X_{s}$ and $Y_{P}=j B_{P}$, where $X$ denotes reactance and $B$ denotes susceptance. Then, at the frequencies of interest, we should have
$$R_{S}=j X_{s}+1 /\left(j B_{p}+G_{L}\right)$$
where $G_{L}=1 / R_{L}$. Cross multiplying, simplifying, and equating the real and imaginary parts on both sides give the two equations
$$X_{S} B_{p}=1-R_{S} G_{L} \text { and } R_{S} B_{p}=X_{S} G_{L}$$
The second equation shows that $X_{s}$ and $B_{p}$ must be of the same sign, both positive or both negative. Combining this fact with the first Equation in (3.2), we note that $R_{S} G_{L}$ must be less than unity, i.e. $R_{S}$ must be less than $R_{L}$. However, this is no restriction because the other situation, i.e. $R_{S}>R_{L}$, can be taken care of by simply interchanging the positions of $R_{S}$ and $R_{L}$ in Fig. 3.1. Eliminating $B_{p}$ from the two Equations in (3.2), we get
$$X_{s}^{2}=R_{S}\left(R_{L}-R_{S}\right)=R_{1}^{2}, \text { say }$$

Or,
$$X_{\mathrm{s}}=\pm R_{1}$$
Combining this with the second Equation in (3.2) gives
$$B_{p}=\pm R_{1} /\left(R_{L} R_{S}\right)=\pm G_{2} \text {, say }$$
As already stated, the signs in Eqs. (3.4) and (3.5) should be either both positive or both negative.

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Impedance Matching at a Single Frequency

For matching $R_{L}$ to $R_{S}$ at a single frequency $\omega_{0}$, we can choose either an inductance $L_{s}$ for $X_{s}$ and a capacitance $C_{p}$ for $B_{p}$, or a capacitance $C_{s}$ for $X_{s}$ and an inductance $L_{p}$ for $B_{p}$. In the first case, to be referred to as Design 1 (D1)
$$L_{s}=R_{1} / \omega_{0} \text { and } C_{p}=G_{2} / \omega_{0}$$
while for the alternative design, to be called Design 2 (D2),
$$C_{s}=1 /\left(R_{1} \omega_{0}\right) \text { and } L_{p}=1 /\left(G_{2} \omega_{0}\right)$$
We shall mostly use D1 in our further discussions, it is being implied that D2 is equally applicable, giving another set of solutions.

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

$$R_{S}=j X_{s}+1 /\left(j B_{p}+G_{L}\right)$$

$$X_{S} B_{p}=1-R_{S} G_{L} \text { and } R_{S} B_{p}=X_{S} G_{L}$$

$$X_{s}^{2}=R_{S}\left(R_{L}-R_{S}\right)=R_{1}^{2} \text {, say }$$

$$X_{\mathrm{s}}=\pm R_{1}$$

$$B_{p}=\pm R_{1} /\left(R_{L} R_{S}\right)=\pm G_{2}, \text { say }$$

## 电子工程代写|数字信号处理代写Digital Signal Processing代考|Impedance Matching at a Single Frequency

$$L_{s}=R_{1} / \omega_{0} \text { and } C_{p}=G_{2} / \omega_{0}$$

$$C_{s}=1 /\left(R_{1} \omega_{0}\right) \text { and } L_{p}=1 /\left(G_{2} \omega_{0}\right)$$

## 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。