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# 物理代写|连续时间信号和系统代写Continuous Time Signals and Systems代考|ELEE10020 Amplitude modulator

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## 物理代写|连续时间信号和系统代写Continuous Time Signals and Systems代考|Amplitude modulator

Modulation is the process used to shift the frequency content of an informationbearing signal such that the resulting modulated signal occupies a higher frequency range. Modulation is the key component in modern-day communication systems for two main reasons. One reason is that the frequency components of the human voice are limited to a range of around $4 \mathrm{kHz}$. If a human voice signal is transmitted directly by propagating electromagnetic radio waves, the communication antennas required to transmit and receive these radio signals would be impractically long. A second reason for modulation is to allow for simultaneous transmission of several voice signals within the same geographic region. If two signals within the same frequency range are transmitted together, they will interfere with each other. Modulation provides us with the means of separating the voice signals in the frequency domain by shifting each voice signal to a different frequency band. There are different techniques used to modulate a signal. Here we introduce the simplest form of modulation referred to as amplitude modulation (AM).

Consider an information-bearing signal $m(t)$ applied as an input to an AM system, referred to as an amplitude modulator. In communications, the input $m(t)$ to a modulator is called the modulating signal, while its output $s(t)$ is called the modulated signal. The steps involved in an amplitude modulator are illustrated in Fig. 2.5, where the modulating signal $m(t)$ is first processed by attenuating it by a factor $k$ and adding a dc offset such that the resulting signal $(1+k m(t))$ is positive for all time $t$. The modulated signal is produced by multiplying the processed input signal $(1+k m(t))$ with a high-frequency carrier $c(t)=A \cos \left(2 \pi f_{\mathrm{c}} t\right)$. Multiplication by a sinusoidal wave of frequency $f_{\mathrm{c}}$ shifts the frequency content of the modulating signal $m(t)$ by an additive factor of $f_{\mathrm{c}}$. Mathematically, the amplitude modulated $\operatorname{signal} s(t)$ is expressed as follows:
$$s(t)=A[1+k m(t)] \cos \left(2 \pi f_{\mathrm{c}} t\right),$$
where $A$ and $f_{\mathrm{c}}$ are, respectively, the amplitude and the fundamental frequency of the sinusoidal carrier.

## 物理代写|连续时间信号和系统代写Continuous Time Signals and Systems代考|Mechanical water pump

The mechanical pump shown in Fig. $2.6$ is another example of a linear CT system. Water flows into the pump through a valve $\mathrm{V} 1$ controlled by an electrical circuit. A second valve V2 works mechanically as the outlet. The rate of the outlet flow depends on the height of the water in the mechanical pump. A higher level of water exerts more pressure on the mechanical valve V2, creating a wider opening in the valve, thus releasing water at a faster rate. As the level of water drops, the opening of the valve narrows, and the outlet flow of water is reduced.

A mathematical model for the mechanical pump is derived by assuming that the rate of flow $F_{\text {in }}$ of water at the input of the pump is a function of the input voltage $x(t)$ :
$$F_{\text {in }}=k x(t),$$
where $k$ is the linearity constant. Valve $\mathrm{V} 2$ is designed such that the outlet flow rate $F_{\text {out }}$ is given by
$$F_{\text {out }}=c h(t),$$
where $c$ denotes the outlet flow constant and $h(t)$ is the height of the water level. Denoting the total volume of the water inside the tank by $V(t)$, the rate of change in the volume of the stored water is $\mathrm{d} V / \mathrm{d} t$, which must be equal to the difference between the input flow rate, Eq. (2.11), and the outlet flow rate, Eq. (2.12). The resulting equation is as follows:
$$\frac{\mathrm{d} V}{\mathrm{~d} t}=F_{\text {in }}-F_{\text {out }}=k x(t)-c h(t) .$$

## 物理代写|连续时间信号和系统代写Continuous Time Signals and Systems代写|Amplitude modulator

$$s(t)=A[1+k m(t)] \cos \left(2 \pi f_c t\right),$$

## 物理代写|连续时间信号和系统代写Continuous Time Signals and Systems代 考|Mechanical water pump

$$F_{\text {in }}=k x(t),$$

$$F_{\text {out }}=\operatorname{ch}(t),$$

$$\frac{\mathrm{d} V}{\mathrm{~d} t}=F_{\text {in }}-F_{\text {out }}=k x(t)-c h(t)$$

## 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。