assignmentutor-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|Application of Frequency Transformation

Let $\omega_{0}$ be normalized to $1 \mathrm{rad} / \mathrm{s}$ and let $S$ denote the complex frequency variable in the single-frequency matching network. Then the problem of multiple frequency impedance matching reduces to that of transforming $S=\pm j 1$ to another set of frequencies $s=\pm j \omega_{\mathrm{i}}, i=1$ to $N$, where $s$ denotes the complex frequency variable in the transformed network. It is well known $[1,2]$ that the functional relationship between $S$ and $s$ is an $L C$ impedance or admittance function of the general form
$$S=\left(k_{0} / s\right)+k_{\infty} s+\sum_{i} k_{i} s /\left(s^{2}+q_{i}\right)$$
Using Eq. (3.8) on D2, for example, $C_{s}=1 / R_{1}$ (recall that $\omega_{0}$ has been normalized to unity) transforms to a parallel connection of a capacitance of value $k_{\infty} / R_{1}$, an inductance of value $R_{1} / k_{0}$, and a number of series $L C$ circuits, the number being the same as the upper limit in the summation of Eq. (3.8). The ith series $L C$ circuit will have an inductance of value $R_{1} / k_{i}$ and a capacitance of value $k_{i} /\left(q_{i} R_{1}\right)$. Similarly, the inductance $L_{p}=1 / G_{2}$ transforms to a series connection of an inductance of value $k_{\infty} / G_{2}$, a capacitance of value $G_{2} / k_{0}$ and a number of parallel $L C$ circuits, the number being the same as in the case of $C_{s}$. The $i$ th parallel $L C$ circuit will have an inductance of value $k_{i} /\left(q_{i} G_{2}\right)$ and a capacitance of value $G_{2} / k_{\mathrm{i}}$. Similarly, Eq. (3.8) can be used on D1 to derive another circuit which can be used for the same purpose.

In addition, note that applied to an inductance, Eq. (3.8) results in a Foster $1(\mathrm{~F} 1)$ form of realization, while applied to capacitance, the result is a Foster $2(\mathrm{~F} 2$ ) form of realization. Each of them can be converted to the other Foster form or Cauer 1 (C1) or Cauer 2 (C2) form. By different combinations of these forms for the two $L C$ networks, a large number of competing circuits can be generated. The set can be further expanded by synthesizing each $L C$ impedance by combining two or more of $\mathrm{F} 1, \mathrm{~F} 2, \mathrm{C} 1$ and $\mathrm{C} 2$ forms to generate more circuits having the same impedancematching properties.

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

Let the frequencies at which matching is needed be $\omega_{1}$ and $\omega_{2}$. We use the transformation
$$S=\left(k_{0} / s\right)+k_{\infty} s$$
As mentioned in the previous section, using this on D1 and D2 suffices to find the only possible competing networks. Note, in passing, that Eq. (3.9) is the well-known low-pass to bandpass transformation. By putting $S=+j 1$ and $s=j \omega$ in Eq. (3.9) and simplifying, we get the following quadratic equation in $\omega$ :
$$\omega^{2}-\left(1 / k_{\infty}\right) \omega-\left(k_{0} / k_{\infty}\right)=0$$
Since $S$ has a pole at $s=0$, the roots of this equation are $-\omega_{1}$ and $\omega_{2}$, so that Eq. (3.10) should be identical to the following:
$$\omega^{2}-\left(\omega_{2}-\omega_{1}\right) \omega-\omega_{1} \omega_{2}=0$$
Comparing coefficients, we get
$$k_{\infty}=1 /\left(\omega_{2}-\omega_{1}\right) \text { and } k_{0}=\omega_{1} \omega_{2} /\left(\omega_{2}-\omega_{1}\right)$$
The networks obtained by using Eq. (3.9) on D1 and D2 are shown in Fig. 3.2a and b, respectively.

We shall now compare the two designs with the help of a numerical example. Let $\omega_{1}=0.5 \mathrm{rad} / \mathrm{s}$ and $\omega_{2}=0.7 \mathrm{rad} / \mathrm{s}$; these are normalized frequencies and the results can be applied to any situation where $\omega_{1}: \omega_{2}=5: 7$ by appropriate frequency scaling. Also, let $R_{L}=2$ Ohms and $R_{S}=1$ Ohms; again, the results can be applied to any situation where $R_{L}: R_{S}=2: 1$ by impedance scaling. Calculation gives $k_{\infty}=$ $5, k_{0}=1.75, R_{1}=1$ Ohms, and $G_{2}=0.5 \mathrm{mho}$. The element values, from left to right, are calculated as $5 \mathrm{H}, 0.5714 \mathrm{~F}, 2.5 \mathrm{H}$ and $1.1428 \mathrm{~F}$ for Fig. $3.2 \mathrm{a}$ and $0.5714 \mathrm{H}$, $5 \mathrm{~F}, 10 \mathrm{H}$ and $0.2857 \mathrm{~F}$ for Fig. $3.2 \mathrm{~b}$. Table $3.1$ shows a comparison of the two circuits for some relevant implementation parameters. Clearly, the circuit of Fig. 3.2a would be a better choice from all considerations. Note that the inductance and capacitance spreads are the same in each circuit; this is expected from the general values given in Fig. 3.2.

# 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|Application of Frequency Transformation

$$S=\left(k_{0} / s\right)+k_{\infty} s+\sum_{i} k_{i} s /\left(s^{2}+q_{i}\right)$$

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

$$S=\left(k_{0} / s\right)+k_{\infty} s$$

$$\omega^{2}-\left(1 / k_{\infty}\right) \omega-\left(k_{0} / k_{\infty}\right)=0$$

$$\omega^{2}-\left(\omega_{2}-\omega_{1}\right) \omega-\omega_{1} \omega_{2}=0$$

$$k_{\infty}=1 /\left(\omega_{2}-\omega_{1}\right) \text { and } k_{0}=\omega_{1} \omega_{2} /\left(\omega_{2}-\omega_{1}\right)$$

## 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