assignmentutor-lab™ 为您的留学生涯保驾护航 在代写信息论information theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写信息论information theory代写方面经验极为丰富，各种代写信息论information theory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

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

By identifying the sequence of random variables $\left{\mathrm{X}{n}\right}$ with the coefficients representing a given waveform, we can view each possible waveform as a random point in a space of $N{0}$ dimensions. It follows that a large typical volume corresponds to signals that are widely dispersed, while a small typical volume means that most signals are concentrated in a small portion of the space and asymptotic equipartition can be expressed by the statement:
Almost all observed signals are almost equally probable.
To obtain an information-theoretic description of the typical waveforms, we proceed in an analogous way to the one followed in the deterministic setting: to bound the size of the typical volume we introduce an energy constraint that restricts the possible signal’s configurations. Then, in order to obtain a bit representation, we introduce a resolution limit at which each waveform can be observed.
To realize this program, we consider random waveforms of the form
$$f(t)=\sum_{n=1}^{N_{0}} a_{n} \psi_{n}(t)$$
where $\left{a_{n}\right}$ are realizations of an independent and identically distributed (i.i.d.) real-valued random process $\left{\mathrm{A}{n}\right}$, and $\psi{n}$ are deterministic, orthonormal, real basis functions. Each random variable in the process is distributed as $\mathrm{A}$ and satisfies the expected squared norm per degree of freedom constraint,
$$\mathbb{E}\left(\mathrm{A}^{2}\right) \leq P$$

## 数学代写|信息论作业代写information theory代考|Quantized Typical Waveforms

The amount of information of our continuum state space of signals depends not only on its statistical dispersion, but also on the level of quantization at which each signal is observed. If we quantize each dimension of the signals’ space at level $\epsilon$, then the number of quantized typical signals is roughly
$$N=\frac{2^{N_{0} h_{\mathrm{A}}}}{\epsilon^{N_{0}}} \leq \frac{(2 \pi e P)^{N_{0} / 2}}{\epsilon^{N_{0}}}=\left(\frac{\sqrt{2 \pi e P}}{\epsilon}\right)^{N_{0}},$$
and since these are roughly equiprobable, the corresponding statistical entropy of the equipartitioned system of quantized signals is
$$H=\log N \leq N_{0} \log \left(\frac{\sqrt{2 \pi e P}}{\epsilon}\right),$$
where the equality is achieved by a zero-mean Gaussian of variance $P$. The statistical entropy in (1.46) also corresponds to the number of bits needed on average to represent any quantized signal in the space. This follows from the observation that there are $N$ quantized typical signals, and each can be identified by a sequence of $H=\log N$ bits.
The bound (1.46) should be compared with (1.24). In the deterministic case the Kolmogorov e-entropy of the signals’ space grows at most linearly with the number of degrees of freedom and at most logarithmically with the signal-to-noise ratio $\sqrt{E} / \epsilon$. In the stochastic case, the Shannon entropy of the space of $\epsilon$-quantized signals grows at most linearly with the number of degrees of freedom and at most logarithmically with the expected signal-to-noise per degree of freedom ratio $\sqrt{P} / \epsilon$. While in the deterministic model we bounded the energy of the signal and introduced quantization in terms of Euclidean distances, in the stochastic model we introduced an average constraint and a quantization on each dimension of the space.

The result (1.46) can be derived by writing the statistical entropy of the space of $\epsilon$-quantized signals in terms of the entropy of a single quantized coefficient. Consider a coefficient $\mathrm{A}$ distributed according to a continuous density $g(a)$. We perform quantization as indicated in Figure 1.17. By continuity, for all $k$ we let $a(k)$ be a value such that
$$g(a(k)) \epsilon=\int_{k \epsilon}^{(k+1) \epsilon} g(a) d a .$$

# 信息论代写

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

$$f(t)=\sum_{n=1}^{N_{0}} a_{n} \psi_{n}(t)$$

$$\mathbb{E}\left(\mathrm{A}^{2}\right) \leq P$$

## 数学代写|信息论作业代写information theory代考|Quantized Typical Waveforms

$$N=\frac{2^{N_{0} h_{\mathrm{A}}}}{\epsilon^{N_{0}}} \leq \frac{(2 \pi e P)^{N_{0} / 2}}{\epsilon^{N_{0}}}=\left(\frac{\sqrt{2 \pi e P}}{\epsilon}\right)^{N_{0}}$$

$$H=\log N \leq N_{0} \log \left(\frac{\sqrt{2 \pi e P}}{\epsilon}\right)$$

$$g(a(k)) \epsilon=\int_{k \epsilon}^{(k+1) \epsilon} g(a) d a .$$

## 有限元方法代写

assignmentutor™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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师