### 数学代写|信息论作业代写information theory代考|CSYS5030

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|信息论作业代写information theory代考|The Dimensionality of the Space

To quantify the amount of information carried by electromagnetic waves of finite energy, we represent the possible messages that the transmitter may send by an ensemble of waveforms, and then attempt to quantify the amount of information transferred by the correct selection at the receiver of one element from this ensemble, according to Shannon’s theory. This selection implies that a certain amount of information has been transported between the two. To realize this program, we are faced with a first fundamental question:
How many distinct waveforms can we possibly select from?
The answer depends on the size of the signals’ space, or the number of degrees of freedom, available for communication and on the resolution at which each degree of freedom can be observed. The number of degrees of freedom is limited by the nature of the wave propagation process, while the resolution is limited by the uncertainty associated with the observation process.

## 数学代写|信息论作业代写information theory代考|Bandlimitation Filtering

Any radiated waveform has an essentially finite bandwidth. Due to the interaction with the propagation medium and with the measurement apparatus used to detect the signal, the high-frequency components are cut off, and any signal appears as the output of a linear filter. Typically this filter also shapes the frequency profile, distorting the transmitted waveform. A simple example of this phenomenon occurs in a scattering environment. Due to multiple scattering, multiple copies of the transmitted waveform, carrying different delays and attenuations while traveling on different paths, may overlap at the receiver, creating interference and distorting the original signal – see Figure 1.3. While in ideal free space the magnitude of the frequency response of the propagation environment would be flat across all frequencies, and the phase of the response would be proportional to the distance between transmitter and receiver, in the presence of a large amount of scattering the response is a highly varying signal, due to the interference over the multiple scattered paths.

An analogous effect occurs in the spatial domain. The signal observed along any spatial cut-set that separates transmitters and receivers is the image of all the elements radiating from one side of the cut to the other. These radiating waveforms may interfere along the cut, leading to spatial filtering – see Figure 1.4.

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。