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# 信号处理代写signal processing代考|Spectrogram for time-frequency analysis: dial tone pad

##### 代写数字信号处理signal processing

In comparison, the output viewpoint examines how a single point in the output signal is determined by the various values from the input signal. Just as with discrete signals, each instantaneous value in the output signal is affected by a section of the input signal, weighted by the impulse response flipped left-for-right. In the discrete case, the signals are multiplied and summed. In the continuous case, the signals are multiplied and integrated. In equation form:

$$y(t)=\int_{-\infty}^{+\infty} x(\tau) h(t-\tau) d \tau$$

The convolution integral. This equation defines the meaning of: $y(t)=x(t) * h(t)$.

This equation is called the convolution integral, and is the twin of the convolution sum ) used with discrete signals.shows how this equation can be understood. The goal is to find an expression for calculating the value of the output signal at an arbitrary time, $t$. The first step is to change the independent variable used to move through the input signal and the impulse response. That is, we replace $t$ with $\tau$ (a lower case Greek tau). This makes $x(t)$ and $h(t)$ become $x(\tau)$ and $h(\tau)$, respectively. This change of variable names is needed because $t$ is already being used to represent the point in the output signal being calculated. The next step is to flip the impulse response left-for-right, turning it into $h(-\tau)$. Shifting the flipped impulse response to the location $t$, results in the expression becoming $h(t-\tau)$. The input signal is then weighted by the flipped and shifted impulse response by multiplying the two, i.e., $x(\tau) h(t-\tau)$. The value of the output signal is then found by integrating this weighted input signal from negative to positive infinity.

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• 微分方程 Differential equations
• 递归关系 Recurrence relations
• 变换理论 Time-frequency analysis – for dealing with non-stationary signals [14]
• 时频分析 Transformation theory Time-frequency analysis – for dealing with non-stationary signals
• 频谱估计 Spectral estimation – for determining the spectral content
• 统计信号处理 Statistical signal processing – for analyzing and extracting information based on the stochastic properties of signals and noise
• 线性时不变系统理论和变换理论 Linear time-invariant systems theory and transformation theory
• 多项式信号处理 Polynomial signal processing – analysis of systems related to inputs and outputs using polynomials

## 信号处理代写signal processing代考|Dual Tone Multi-Frequency (DTMF)

The underlying concept of touch-tone telephone dialling is the Dual Tone Multi-Frequency (DTMF) system, which assigns a signal composed of two sinusoids to each button of the keypad, that is
$$y[n]=\sin \left(2 \pi f_{1} n\right)+\sin \left(2 \pi f_{2} n\right),$$
where $f_{1}, f_{2}$ are the frequencies in $\mathrm{Hz}$, and $n$ is the time index.
The pairs of frequencies corresponding to each key are shown in Table 1 and an example of the signal corresponding to the digit 0 is shown

## 信号处理代写SIGNAL PROCESSING代考|MATLAB documentation

1. Generate a random London landline number, i.e. a sequence of the form: $020 \times X X X X X X X$, where the last eight digits are drawn from the set ${0,1,2,3,4,5,6,7,8,9}$ (with uniform probability). Compute the discrete time sequence $\mathbf{y}$ according to Eq. (34) and Table 1 using the sampling rate of $32768[\mathrm{~Hz}]$, assume that each digit is pressed for $0.25$ [s] followed by an idle time of $0.25$ [s] so that your dialled sequence lasts for $0.25 * 21=5.25$ [s]. Explain why the proposed sampling rate is appropriate and plot the signal $\mathbf{y}$ for any two different keys and the idle sequence, adjust zoom and axis parameters to show the difference between the tones.
2. Familiarise yourself with the function spectrogram within the MATLAB documentation, and use it to analyse the spectral components of the sequence $y$. Choose the parameters of the function carefully so that the FFT is computed for non-overlapping segments containing touch-tone information corresponding to either a single key, or to the idle time in between pressed keys (it might be useful to consider a Hanning window in this part). Analyse the results and plot the corresponding FFT segments.
3. Explain, using Table 1 and your spectrum estimates, whether it is possible to identify the sequence generated by a key press, and elaborate on how you would perform key classification.
4. In real-world conditions, the signal is corrupted by channel noise. Repeat Parts $1-3$ while adding white noise to the sequence $\mathbf{y}$. Consider three cases, starting from low-variance noise until the original signal is, at least visually, completely immersed in noise. Explain both analytically and from simulations how the noise affects the tone identification.

## 信号处理代写SIGNAL PROCESSING代考|MATLAB DOCUMENTATION

1. 生成一个随机的伦敦固定电话号码，即以下形式的序列：020×XXXXXXX，其中最后八位数字是从集合中提取的0,1,2,3,4,5,6,7,8,9 在一世吨H你n一世F○r米pr○b一种b一世一世一世吨和. 计算离散时间序列和根据方程式。34和表1使用的采样率32768[ H和], 假设每个数字都被按下0.25s其次是空闲时间0.25s这样您的拨号序列将持续0.25∗21=5.25s. 解释为什么建议的采样率是合适的并绘制信号和对于任意两个不同的键和空闲序列，调整缩放和轴参数以显示音调之间的差异。
2. 熟悉 MATLAB 文档中的函数 spectrogram，并使用它来分析序列的频谱分量和. 仔细选择函数的参数，以便为包含与单个按键或按键之间的空闲时间相对应的按键信息的非重叠段计算 FFT一世吨米一世GH吨b和你s和F你一世吨○C○ns一世d和r一种H一种nn一世nG在一世nd○在一世n吨H一世sp一种r吨. 分析结果并绘制相应的 FFT 段。
3. 使用表 1 和您的频谱估计解释是否可以识别按键生成的序列，并详细说明您将如何执行按键分类。
4. 在现实条件下，信号会被信道噪声破坏。重复部分1−3同时为序列添加白噪声和. 考虑三种情况，从低方差噪声开始，直到原始信号至少在视觉上完全沉浸在噪声中。通过分析和模拟解释噪声如何影响音调识别。

## 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。