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# 物理代写|传感器代写Sensor代考|IELEG2214 Signal Characterization

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## 物理代写|传感器代写Sensor代考|Signal Characterization

Signals are functions describing the variation of states in physical or technology domains.

A first classification could be drawn between deterministic and random signals.

A deterministic signal is described by a mathematical function or rule that uniquely determines any past and any future state. The knowledge of a deterministic signal corresponds to the identification of the related function or rule model. An example is illustrated in Fig. 2.6A with a sinusoidal function.

A random signal is a signal in which future values are known only under the concept of probability. These signals can be described using the mathematical tool of random variables. The knowledge of stochastic signals corresponds to the identification of the random variable model characteristics, such as (among many others) its probability density function (PDF). An example is shown in Fig. 2.6C.
For a correct framework, it is better to focus on two distinct viewpoints in sensor design.

Characterization mode. We can characterize the system from a theoretical point of view, based on known physical models used in the design. Furthermore, from the experimental point of view, a known signal could be fed into the input, either deterministic (analytical function) or stochastic (by means of a known random variable), and the output is recorded. The experimental test could validate the theoretical model, if present, or be used to characterize an experimental model in the absence of a theoretical one.

Operating mode. The sensor, once characterized, monitors the environment to extract the information. In this case, the input is fed by an unknown signal whose knowledge will be determined on the basis of the sensor models.

## 物理代写|传感器代写Sensor代考|Limits of the Quasistatic Characteristic and Frequency Domain Representation

The input-output relationship determined by the static characteristic, as shown in Fig. 2.7, should be taken with great caution since it is valid when signal time variations are much lower than any time constant of the sensor system. If time constants of the sensor come into play, the input-output cross-point no longer follows the quasistatic characteristic due to the role of gain and phase shift operated by the system

If the system behaves as linear time-invariant (LTI), the gain and phase relationships between input and output are described by a complex function of the frequency $H(f)$ referred to as the transfer function. From now on, we will primarily refer to low-pass transfer functions so that the gain $S$, identified by the quasistatic characteristic, is equal to $H(0)$.

As shown in Fig. 2.8A, if we excite a first-order low-pass system with a sinusoidal signal having frequency components greater than the reciprocal of its characteristic time constant, we have that the static characteristic could not determine the phase shift and the amplitude of the output signal components. The input-output relationship might be described by a closed trajectory or limit cycle or orbit in the input-output space whose shape is determined by the system time-response description (e.g., poles and zeros) transfer function for small signals) in the bias point. In the case of a linear system, single time-constant and low-pass behavior with respect to a small sinusoidal excitation, as shown in Fig. 2.8B, the phase and amplitude scale could be described by an ellipse trajectory. ${ }^2$ For very low frequency, the ellipse is squeezed on the ideal static curve; then, for increasing frequency, the phase lag increases the ellipse’s minor axis. Finally, the amplitude scale is the determinant effect for very high frequency by squeezing the ellipse on a horizontal line. The previous observation on the static characteristic’s role points out that a frequency-domain representation is necessary when time variations come into play.

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## 物理代写|传感器代写传感器代考|准静态特性和频域表示的极限

. 如图2.7所示，由静态特性决定的输入输出关系应该非常谨慎，因为当信号时变化远远低于传感器系统的任何时间常数时，它是有效的。当传感器的时间常数起作用时，由于系统操作的增益和相移的作用，输入输出交叉点不再遵循准静态特性 如果系统表现为线性时不变(LTI)，则输入和输出之间的增益和相位关系用频率$H(f)$的复函数描述，称为传递函数。从现在开始，我们将主要参考低通传递函数，使由准静态特性识别的增益$S$等于$H(0)$ .

## 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。