Posted on Categories:Digital Signal Processing, 数字信号处理, 电子代写

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 电子代写|数字信号处理代写Digital Signal Processing代考|The Frequency Sampling Method of FIR Filter Design

The frequency sampling method $[10,11]$ of FIR filter design consists of the following steps.
$1 \rightarrow$ Specify the desired frequency response, $H[m]$.
$2 \rightarrow$ Take the inverse discrete Fourier transform that yields the impulse response, $h[n]$.
$3 \rightarrow$ Multiply this impulse response by one of many possible windowing functions.
$4 \rightarrow$ Normalize the magnitude of the impulse response to the overall desired DC gain.
$5 \rightarrow$ Compare the results with the specified frequency response using the discrete time FT and if desired pass a test signal through a filter with the final coefficients using convolution.
Defining the Frequency Response of the FIR Filter
In order to correctly define the frequency response, there are three separate vectors that we must set. We need a vector indicating the independent variable, which is the normalized frequency. Further, we require a vector specifying the magnitude response at the given frequencies and another specifying the phase response. Clearly, the vector specifying the frequencies at which we will define our response must be formatted such that the IDFT can correctly compute the impulse response. The vector defining normalized frequency obeys the format $m / N$ where $m=0,1 \ldots N-1$, and $N$ represents the tap length of the FIR filter.

Example 2.27: (Part 1) Defining the Frequency Response, $H[m]$, of a Low Pass FIR Filter
Assume a low pass FIR filter of tap length $N=13$ running at a sample rate of $20 \mathrm{MHz}$. It is our goal to force a response that passes frequency content below $3.5 \mathrm{MHz}$ (normalized frequency $=$ $3.5 / 20 \mathrm{MHz}=0.175 \mathrm{~Hz}$ ) and blocks it everywhere else. According to the rule regarding frequency assignments above, we set the frequency vector as follows.

## 电子代写|数字信号处理代写Digital Signal Processing代考|Understanding the Phase and Group Delay

The phase and group delays are two common metrics that illustrate phase distortion in linear systems such as filters. These metrics calculate the transit time that a sinusoid at a particular frequency or groups of sinusoids at different but close frequencies experience as they traverse a filter. In communication systems, a great number of filters are tasked to attenuate interference and noise outside the bandwidth of the signal of interest. The time that it takes each frequency to traverse these filters should be the same. If this is not the case, then the different frequency components of the signal in the pass band will reassemble out of phase at the output, causing linear distortion. The phase and group delay function are tools that allow us to easily visualize the presence of phase distortion. The phase response of a linear system that does not introduce phase distortion and thus delays all frequency components equally is a straight line as is suggested by the time shifting property of the Fourier transform (see Section 3.1 of this chapter.)
$$\begin{array}{ll} x(t) \quad \stackrel{F T}{\rightarrow} X(f) \ x\left(t-t_0\right) & \stackrel{F T}{\rightarrow} X(f) \cdot e^{-j 2 \pi f t_o} \end{array}$$
Phase and group delay are functions of frequency and can be calculated directly from the phase response of the linear time invariant system.
Phase Delay
The phase delay is a measure of transit time, $t_0$, experienced by a complex sinusoid, $\exp (j 2 \pi f t)$, as it travels through a linear time-invariant system such as a filter. The transit time is calculated by comparing the input and output phases of the complex sinusoid.
$$\begin{gathered} \theta(f)=\angle \text { Output }(f)-\angle \operatorname{Input}(f)=2 \pi f\left(t-t_o\right)-2 \pi f t \ \theta(f)=-2 \pi f t_o \ \text { PhaseDelay }(f)=t_o=-\frac{\theta(f)}{2 \pi f} \text { seconds } \end{gathered}$$

## 电子代写|数字信号处理代写Digital Signal Processing代考|The Frequency Sampling Method of FIR Filter Design

FIR滤波器设计的频率采样方法$[10,11]$包括以下步骤。
$1 \rightarrow$指定所需的频率响应，$H[m]$。
$2 \rightarrow$求离散傅里叶反变换得到脉冲响应$h[n]$。
$3 \rightarrow$将这个脉冲响应乘以许多可能的窗口函数之一。
$4 \rightarrow$将脉冲响应的幅度归一化到所需的总体直流增益。
$5 \rightarrow$使用离散时间傅里叶变换将结果与指定的频率响应进行比较，如果需要的话，可以使用卷积将测试信号通过带有最终系数的滤波器。

$$\sin \left(2 \pi f_o t=\frac{1}{2 j}\left(e^{j 2 \pi f_o t}-e^{-j 2 \pi f_o t}\right) \quad=-j \frac{1}{2}\left(e^{j 2 \pi f_o t}+e^{-j 2 \ pi }\right) =e^{-j \frac{pi }{2}}. \frac{1}{2}\left(e^{j 2\pi f_d t}+e^{-j 2 \pi f_{f_t} e^{j \pi}\right)\quad=frac{1}{2}\left(e^{j 2\pi f_d t}) \cdot e^{-j frac{{pi}{2}}+e^{-j 2pi f_d t}. \cdot e^{j frac{pi}{2}}}\right）\right。$$

## 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。

Posted on Categories:Digital Signal Processing, 数字信号处理, 电子代写

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 电子代写|数字信号处理代写Digital Signal Processing代考|The LTI Model

The model that we will use to express LTI systems needs to include three central features that make it suitable for our purposes.

1. Memory
The model used to approximate linear time-invariant systems must be able to represent processes that are differential / discrete in nature. Systems described by differential or discrete equations are unique in that they remember and use past inputs to produce current outputs. In electrical engineering, we may think of a lumped element circuit featuring capacitors and inductors whose voltages and currents depend on circuit conditions in the past. The model that we use must therefore have memory.
2. Time Invariance
To keep our model simple enough, we assume that the coefficients describing the differential / discrete equations do not change with time. The assumption that the capacitance, inductance, and resistance values of a circuit remain constant during operation is entirely reasonable. A system whose characteristics remain constant over time is called time-invariant. Systems whose characteristics change over time will be addressed in the section on adaptive signal processing.
3. Linearity
Our system model must be linear in order to keep the mathematical rigor involved in analyzing such systems at a level that is reasonable. Although virtually all systems become non-linear when their inputs are excessively large, many systems act linearly over their useful range of operation.
The structure we use to model a discrete LTI system is the transversal filter, shown next. It features time delays marked $D$ (or $z^I$ ), which are arranged serially and delay their input values by one sample period. The terminals of these delays, also called taps, are multiplied by constants $h_0$ through $h_{N-1}$ and summed to yield the output $y[n]$. It is these delay elements that provide the model with the required memory. Further, the model is time-invariant if factors $h_0$ through $h_{N-1}$ remain constant.

## 电子代写|数字信号处理代写Digital Signal Processing代考|Convolution in Matrix Form

In later chapters, we will work with the convolution operation in matrix form, so let us reformulate our equation for $N$ model coefficients accordingly. As done in the MatLab code, $X$ and $H$ are both defined as column vectors.
\begin{aligned} & y[n]=X^T[n] \cdot H \ & y[n]=[x[n] \quad x[n-1] \quad \cdots \quad x[n-(N-1)]] \cdot\left[\begin{array}{c} h[0] \ h[1] \ \vdots \ h[N-1] \end{array}\right] \ & \end{aligned}
Expanding our formulation for $M$ outputs at time indices $n=0,1 \ldots M$-1 changes the expression by expanding the number of columns of $X$ from one to $M$. The matrix expression below computes all $M$ outputs from $n=0,1 \ldots M-1$.

## 电子代写|数字信号处理代写Digital Signal Processing代考|LTI模型

1. 1.记忆
用来近似线性时变系统的模型必须能够表示微分/离散性质的过程。由微分或离散方程描述的系统是独特的，因为它们记得并使用过去的输入来产生当前的输出。在电气工程中，我们可以想到一个以电容和电感为特征的块状元素电路，其电压和电流取决于过去的电路条件。因此，我们使用的模型必须有记忆。
2. 时间不变性
为了使我们的模型足够简单，我们假设描述微分/离散方程的系数不随时间变化。一个电路的电容、电感和电阻值在运行期间保持不变的假设是完全合理的。一个特性随时间保持不变的系统被称为时间不变的。特性随时间变化的系统将在自适应信号处理的章节中讨论。
3. 线性化
我们的系统模型必须是线性的，以便将分析这类系统所涉及的数学严谨性保持在一个合理的水平。尽管几乎所有的系统在其输入过大时都会变成非线性，但许多系统在其有用的操作范围内都是线性的。
我们用来模拟离散LTI系统的结构是横向滤波器，下图所示。它的特点是标有$D$（或$z^I$）的时间延迟，这些延迟是连续排列的，并将其输入值延迟一个采样周期。这些延迟的终端，也叫抽头，与常数$h_0$到$h_{N-1}$相乘，然后相加，得到输出$y[n]$。正是这些延迟元素为模型提供了所需的记忆。此外，如果因子$h_0$到$h_{N-1}$保持恒定，该模型是时间不变的。

## 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。