




版權(quán)說明: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)
文檔簡介
1、,2 Linear Time-Invariant Systems,2.1 Discrete-time LTI system: The convolution sum,2.1.1 The Representation of Discrete-time Signals in Terms of Impulses,2. Linear Time-Invariant Systems,If xn=un, then,2 Linear Time-Invariant Systems,2 Linear Time-Invariant Systems,2.1.2 The Discrete-time Unit Impul
2、se Response and the Convolution Sum Representation of LTI Systems,(1) Unit Impulse(Sample) Response,Unit Impulse Response: hn,2 Linear Time-Invariant Systems,(2) Convolution Sum of LTI System,Solution:,Question:,n hn n-k hn-k xkn-k xk hn-k,2 Linear Time-Invariant Systems,2 Linear Time-Invariant Syst
3、ems,2 Linear Time-Invariant Systems,( Convolution Sum ),So,or yn = xn * hn,(3) Calculation of Convolution Sum,Time Inversal: hk h-k Time Shift: h-k hn-k Multiplication: xkhn-k Summing:,Example 2.1 2.2 2.3 2.4 2.5,2 Linear Time-Invariant Systems,2.2 Continuous-time LTI system: The convolution integra
4、l,2.2.1 The Representation of Continuous-time Signals in Terms of Impulses,Define,We have the expression:,Therefore:,2 Linear Time-Invariant Systems,2 Linear Time-Invariant Systems,or,2 Linear Time-Invariant Systems,2.2.2 The Continuous-time Unit impulse Response and the convolution Integral Represe
5、ntation of LTI Systems,(1) Unit Impulse Response,(2) The Convolution of LTI System,2 Linear Time-Invariant Systems,A.,Because of,So,we can get,( Convolution Integral ),or y(t) = x(t) * h(t),2 Linear Time-Invariant Systems,B.,or y(t) = x(t) * h(t),( Convolution Integral ),2 Linear Time-Invariant Syst
6、ems,2 Linear Time-Invariant Systems,(3) Computation of Convolution Integral,Time Inversal: h() h(- ) Time Shift: h(-) h(t- ) Multiplication: x()h(t- ) Integrating:,Example 2.6 2.8,2 Linear Time-Invariant Systems,2.3 Properties of Linear Time Invariant System,Convolution formula:,2 Linear Time-Invari
7、ant Systems,2.3.1 The Commutative Property,Discrete time: xn*hn=hn*xn Continuous time: x(t)*h(t)=h(t)*x(t),2 Linear Time-Invariant Systems,2.3.2 The Distributive Property,Discrete time: xn*h1n+h2n=xn*h1n+xn*h2n Continuous time: x(t)*h1(t)+h2(t)=x(t)*h1(t)+x(t)*h2(t),Example 2.10,2 Linear Time-Invari
8、ant Systems,2.3.3 The Associative Property,Discrete time: xn*h1n*h2n=xn*h1n*h2n Continuous time: x(t)*h1(t)*h2(t)=x(t)*h1(t)*h2(t),2 Linear Time-Invariant Systems,2.3.4 LTI system with and without Memory,Memoryless system: Discrete time: yn=kxn, hn=kn Continuous time: y(t)=kx(t), h(t)=k (t),Imply th
9、at: x(t)* (t)=x(t) and xn* n=xn,2 Linear Time-Invariant Systems,2.3.5 Invertibility of LTI system,Original system: h(t) Reverse system: h1(t),So, for the invertible system: h(t)*h1(t)=(t) or hn*h1n=n,Example 2.11 2.12,2 Linear Time-Invariant Systems,2.3.6 Causality for LTI system,Discrete time syste
10、m satisfy the condition: hn=0 for n0 Continuous time system satisfy the condition: h(t)=0 for t0,2 Linear Time-Invariant Systems,2.3.7 Stability for LTI system,Definition of stability: Every bounded input produces a bounded output. Discrete time system:,If |xn|B, the condition for |yn|A is,2 Linear
11、Time-Invariant Systems,Continuous time system:,If |x(t)|B, the condition for |y(t)|A is,Example 2.13,2 Linear Time-Invariant Systems,2.3.8 The Unit Step Response of LTI system,Discrete time system:,Continuous time system:,2 Linear Time-Invariant Systems,2.4 Causal LTI Systems Described by Differenti
12、al and Difference Equation,Discrete time system: Differential Equation Continuous time system: Difference Equation,2 Linear Time-Invariant Systems,2.4.1 Linear Constant-Coefficient Differential Equation,A general Nth-order linear constant-coefficient differential equation:,or,and initial condition:
13、y(t0), y(t0), , y(N-1)(t0) ( N values ),2 Linear Time-Invariant Systems,2.4.2 Linear Constant-Coefficient Difference Equation,A general Nth-order linear constant-coefficient difference equation:,or,and initial condition: y0, y-1, , y-(N-1) ( N values ),Example 2.15,2 Linear Time-Invariant Systems,2.
14、4.3 Block Diagram Representations of First-order Systems Described by Differential and Difference Equation,(1) Dicrete time system Basic elements: A. An adder B. Multiplication by a coefficient C. An unit delay,2 Linear Time-Invariant Systems,Basic elements:,2 Linear Time-Invariant Systems,Example: yn+ayn-1=bxn,2 Linear Time-Invariant Systems,(2) Continuous time system Basic elements: A. An adder B. Multiplication by a coefficient C. An (differentiator) integrator,2 Linear Time-Invariant Systems,Basic elements:,2 Linear Time-Invariant Systems,Example: y(t)+ay(t)=bx(t),2 Linear Time
溫馨提示
- 1. 本站所有資源如無特殊說明,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)頁內(nèi)容里面會(huì)有圖紙預(yù)覽,若沒有圖紙預(yù)覽就沒有圖紙。
- 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
- 【正版授權(quán)】 ISO 17201-2:2025 EN Acoustics - Noise from shooting ranges - Part 2: Calculation of muzzle blast
- 2025至2030中國男士鉆石戒指行業(yè)深度研究及發(fā)展前景投資評(píng)估分析
- 2025至2030中國電子書閱讀器行業(yè)發(fā)展研究與產(chǎn)業(yè)戰(zhàn)略規(guī)劃分析評(píng)估報(bào)告
- 2025至2030中國生態(tài)度假農(nóng)莊行業(yè)市場發(fā)展現(xiàn)狀及發(fā)展趨勢與投資報(bào)告
- 2025至2030中國玉石行業(yè)市場占有率及投資前景評(píng)估規(guī)劃報(bào)告
- 2025至2030中國特種紙漿行業(yè)市場占有率及投資前景評(píng)估規(guī)劃報(bào)告
- 百日培訓(xùn)課件
- 培養(yǎng)孩子良好學(xué)習(xí)習(xí)慣的數(shù)字策略研究
- ICU護(hù)理文件書寫培訓(xùn)
- 維修拆卸技能培訓(xùn)課件
- 科創(chuàng)板開戶測試題及答案
- 內(nèi)科護(hù)理學(xué)消化性潰瘍
- 北京市第一零一中學(xué)2023-2024學(xué)年高一下學(xué)期期末考試地理試題(解析版)
- 中小學(xué)暑期安全教育班會(huì)課件
- DB43-T 2988-2024 再生稻高產(chǎn)栽培技術(shù)規(guī)程
- 2024年荊州市荊發(fā)控股集團(tuán)招聘考試真題
- 慢病智能監(jiān)測-洞察及研究
- 部門預(yù)算支出經(jīng)濟(jì)分類科目
- 2025年內(nèi)蒙古呼倫貝爾農(nóng)墾集團(tuán)有限公司招聘筆試沖刺題(帶答案解析)
- 《健康管理師》職業(yè)技能競賽考試題(附答案)
- 在非到發(fā)線上接發(fā)列車站內(nèi)無空閑線路時(shí)的接發(fā)列車39課件
評(píng)論
0/150
提交評(píng)論