




下載本文檔
版權(quán)說(shuō)明:本文檔由用戶提供并上傳,收益歸屬內(nèi)容提供方,若內(nèi)容存在侵權(quán),請(qǐng)進(jìn)行舉報(bào)或認(rèn)領(lǐng)
文檔簡(jiǎn)介
1、Blekinge Institute of TechnologySchool of EngineeringDepartment of Mathematics and ScienceExaminationRandom Processes, MS1102/MSA002March 25, 2009, 9 am - 2 pmAllowed means: Calculator (any type).All solutions must be motivated.1. Which of the functions in a)-c) are power density spectra (spectral d
2、ensities) for a wide sense stationary, zero-mean process? The answers must be motivated. Answers without motivation will give 0 points. (0.3 p/each)a)b) c)d) A random process X has the autocorrelation functionwhere a is a positive constant. Is the process X wide sense stationary or not? Motivate! (0
3、.3 p)2. A certain filter has impulse responsewhere u is the Heaviside step function. The input to the filter is a Gaussian wide sense stationary process with mean 0 and autocorrelation functionFind the power density spectrum (spectral density) of the output Y. (0.6 p)3. Consider a stationary random
4、process X(t) with autocorrelation function . Find the power density spectrumof X(t). (0.7 p)b) Is the process differentiable (once) in square mean? Calculations are required. (0.5 p)Hint: Note that it must be checked that the potential autocorrelation function really is an autocorrelation function.4
5、. Let X(t), for integer values of t, be a sequence of independent random variables with mean and variance . Let and let .a. Find the autocorrelation function of Y(t).(0.5 p)b. Find the autocorrelation function of Z(t).(0.6 p)5. A random signal X(t) with autocorrelation function is input to a linear
6、system described by the following differential equation.where Y(t) is the output of the system. Find the power density spectrum of Y(t).(0.8 p)6. Consider a linear system consisting of one resistor and one capacitor which are connected as in the figure below. Let X(t) be the input and let Y(t) be th
7、e output of the system.C=1 FR=1 WY(t)X(t)a. Find the impulse response h(t) of the system.(0.5 p)b. Let X(t) be a stationary random process with power density spectrum .Find the power of the output Y(t).(0.6 p)BTHTEK/AMNSolution to the exam in Random processes, MS1102/MSA002March 25, 20091.a) Yes. It
8、 is obviously even and non-negative and it is integrable since the primitive is , so the integral becomes b) No. It is not an even function.c) Yes. It is obviously even and non-negative since it contains only even powers of It is integrable, since it is less than 1/9 for small values of and less tha
9、n for large values of . Both these functions are integrable in the respective intervals.d) Since, the function depends only on the time difference and the process is stationary.2) The power spectral density of the output equals.Sinceandthe power spectral density of the output equals3.a) Since the Fourier transform of equals and the Fourier transform of equalsit follows that the power density spectrum isb) The process is continuous in mean square if and only if exists and is continuous at The first derivative equalsand thus we
溫馨提示
- 1. 本站所有資源如無(wú)特殊說(shuō)明,都需要本地電腦安裝OFFICE2007和PDF閱讀器。圖紙軟件為CAD,CAXA,PROE,UG,SolidWorks等.壓縮文件請(qǐng)下載最新的WinRAR軟件解壓。
- 2. 本站的文檔不包含任何第三方提供的附件圖紙等,如果需要附件,請(qǐng)聯(lián)系上傳者。文件的所有權(quán)益歸上傳用戶所有。
- 3. 本站RAR壓縮包中若帶圖紙,網(wǎng)頁(yè)內(nèi)容里面會(huì)有圖紙預(yù)覽,若沒(méi)有圖紙預(yù)覽就沒(méi)有圖紙。
- 4. 未經(jīng)權(quán)益所有人同意不得將文件中的內(nèi)容挪作商業(yè)或盈利用途。
- 5. 人人文庫(kù)網(wǎng)僅提供信息存儲(chǔ)空間,僅對(duì)用戶上傳內(nèi)容的表現(xiàn)方式做保護(hù)處理,對(duì)用戶上傳分享的文檔內(nèi)容本身不做任何修改或編輯,并不能對(duì)任何下載內(nèi)容負(fù)責(zé)。
- 6. 下載文件中如有侵權(quán)或不適當(dāng)內(nèi)容,請(qǐng)與我們聯(lián)系,我們立即糾正。
- 7. 本站不保證下載資源的準(zhǔn)確性、安全性和完整性, 同時(shí)也不承擔(dān)用戶因使用這些下載資源對(duì)自己和他人造成任何形式的傷害或損失。
最新文檔
- 防御編程漏洞的動(dòng)態(tài)測(cè)試框架-全面剖析
- 企業(yè)管理-建筑工程合同充裕度標(biāo)準(zhǔn)規(guī)定
- 綠色供應(yīng)鏈在圖書(shū)業(yè)的應(yīng)用-全面剖析
- 跨文化交流中的影視藝術(shù)傳播策略-全面剖析
- 光伏產(chǎn)業(yè)供應(yīng)鏈2025年優(yōu)化與市場(chǎng)競(jìng)爭(zhēng)力前瞻報(bào)告
- 單層裝修租房合同樣本
- 制式綜合市場(chǎng)投資合同標(biāo)準(zhǔn)文本
- 醫(yī)療保健合同樣本
- 使用對(duì)方合同樣本情況說(shuō)明
- 單價(jià)框架類合同標(biāo)準(zhǔn)文本
- 2024年汽車維修案例分析方法試題及答案
- 18 井岡翠竹 課件
- 地質(zhì)災(zāi)害地震課件
- 粵教粵人版初中地理七下知識(shí)梳理
- 共建聯(lián)合實(shí)驗(yàn)室合作合同協(xié)議書(shū)范本模板5篇
- 社會(huì)調(diào)查方法(第3版)課件:資料處理
- 工程簽工單表格范本
- 土壤微生物與重金屬污染-洞察分析
- 《消費(fèi)者心理與行為分析》第五版 課件全套 肖澗松 單元1-10 消費(fèi)者心理與行為概述 - 消費(fèi)者購(gòu)買決策與購(gòu)后行為
- 塑料污染治理-洞察分析
- 反詐知識(shí)競(jìng)賽題庫(kù)及答案(共286題)
評(píng)論
0/150
提交評(píng)論