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# 统计代写|时间序列分析作业代写time series analysis代考|Deterministic Spectral Analysis

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## 统计代写|时间序列分析作业代写time series analysis代考|Fourier Theory – Continuous Time/Discrete Frequency

Since $\cos (2 \pi n t / T)$ defines a periodic function of $t$ with period $T>0$ for any integer $n$, i.e.,
$$\cos (2 \pi n[t+T] / T)=\cos (2 \pi n t / T) \text { for all times } t,$$
and since the same holds for $\sin (2 \pi n t / T)$, it follows that
$$\tilde{g}{p}(t)=\frac{a{0}}{2}+\sum_{n=1}^{\infty} a_{n} \cos (2 \pi n t / T)+b_{n} \sin (2 \pi n t / T)$$

## 统计代写|时间序列分析作业代写time series analysis代考|Fourier Theory – Continuous Time and Frequency

Suppose now that $g(\cdot)$ is a deterministic real- or complex-valued function of $t$ that is not periodic. Since it does not possess a periodic structure, we cannot express it in the form of a Fourier series (the right-hand side of Equation (49c)) that will be valid for all $t$. However, we can do the following (cf. Figure 54). For any positive real number $T$, define a new function $g_{T}(\cdot)$ with period $T$ first by letting
$$g_{T}(t)=g(t) \text { for }-T / 2<t \leq T / 2$$
and then by letting
$$g_{T}(t+p T)=g_{T}(t) \text { for }-T / 2<t \leq T / 2 \text { and } p \in \mathbb{Z}$$

## 统计代写|时间序列分析作业代写time series analysis代考|Band-Limited and Time-Limited Functions

We have just defined the amplitude spectrum and energy spectral density function for a function in $L^{2}(\mathbb{R})$. In practice, most $L^{2}(\mathbb{R})$ functions representing physical phenomena have amplitude spectra with finite support (i.e., the amplitude spectra are nonzero only over a finite range of frequencies). Slepian $(1976,1983)$ gives some nice illustrations. A pair of solid copper wires will not propagate electromagnetic waves at optical frequencies and hence would not be expected to contain energy at frequencies greater than, say, $10^{20} \mathrm{~Hz}$ (cycles per second). Recorded male speech gives an amplitude spectrum that is zero for frequencies exceeding $8000 \mathrm{~Hz}$, while orchestral music has no frequencies higher than $20,000 \mathrm{~Hz}$. These band limitations are all at the high-frequency end, and the cutoff frequencies are called high-cut frequencies. It is possible for measurements to be deficient in both low and high frequencies if the recording instrument has some sort of built-in filter that does so. An example is equipment used in seismic prospecting for oil and gas, which contains a low-cut (high-pass) filter to eliminate certain deleterious noise forms and a high-cut (low-pass) antialias filter (the necessity for which is due to effects described in Section 4.5).

If there is no energy above a frequency $|f|=W$, say, then the finite energy function $g(\cdot)$ is said to be band-limited to the band $[-W, W]$. In this case the function has the following Fourier integral representation:
$$g(t) \stackrel{\mathrm{ms}}{=} \int_{-W}^{W} G(f) \mathrm{e}^{\mathrm{i} 2 \pi f t} \mathrm{~d} f$$

## 统计代写|时间序列分析作业代写TIME SERIES ANALYSIS代考|FOURIER THEORY – CONTINUOUS TIME/DISCRETE FREQUENCY

$$\tilde{g}{p}(t)=\frac{a{0}}{2}+\sum_{n=1}^{\infty} a_{n} \cos (2 \pi n t / T)+b_{n} \sin (2 \pi n t / T)$$

## 统计代写|时间序列分析作业代写TIME SERIES ANALYSIS代考|FOURIER THEORY – CONTINUOUS TIME AND FREQUENCY

G吨(吨)=G(吨) 为了 −吨/2<吨≤吨/2

G吨(吨+p吨)=G吨(吨) 为了 −吨/2<吨≤吨/2 和 p∈从

## 统计代写|时间序列分析作业代写TIME SERIES ANALYSIS代考|BAND-LIMITED AND TIME-LIMITED FUNCTIONS

$$g(t) \stackrel{\mathrm{ms}}{=} \int_{-W}^{W} G(f) \mathrm{e}^{\mathrm{i} 2 \pi f t} \mathrm{~d} f$$

## 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。