信號(hào)與系統(tǒng)課件2013-13-2

1、Chapter 10 Discrete-time Linear Time-invariant SystemIntroductionRecall two important properties:Why do we research LTI systems?Test for time invariance00 n ndx n ny ny nSystemDelay n0 xnynyn-n0SystemDelay n0 xnxn-n0ydnLinearity11221122 a x na xna y na ynWhy emphasizing LTI systems?離散LTI系統(tǒng)占有十分重要的地位，

2、這是因?yàn)?許多的物理系統(tǒng)都可按照LTI系統(tǒng)建模。例如，大多數(shù)數(shù)字濾波器。我們可以解出描寫(xiě)連續(xù)和離散的LTI模型的方程解。通過(guò)LTI系統(tǒng)的分析和設(shè)計(jì)，可以得到很多關(guān)于系統(tǒng)的信息。10 discrete-time linear time-invariant systemlImpulse representation of discrete-time signals;lConvolution for discrete-time LTI System;lProperties of DT LTI systems;lDifference equation models;lTerms in the natu

3、ral response;lBlock diagramslSystem response for complex-exponential inputs.10.1 Impulse representation of discrete-time signalsRecall impulse function;Relationship between common signal and impulse function.Discrete-time signalslReview of unit impulse function) 0(0) 0(1nnn)(0)(1000nnnnnnn0n0nn0n0nR

4、elationship for common signal and impulse function000nnnxnnnxkknkxnxelseknkxknnx0,10 discrete-time linear time-invariant systemlImpulse representation of discrete-time signals;lConvolution for discrete-time LTI System;lProperties of DT LTI systems;lDifference equation models;lTerms in the natural re

5、sponse;lBlock diagramslSystem response for complex-exponential inputs.10.2 Convolution for discrete-time LTI Systemx n ynUnit impulse response, figure 10.2; n hn.Sum of impulse Sum of impulse response; Convolution sum;LTISum of impulse responsekknkxnxkknhkxnyconvolutionDefinition of Convolution Suml

6、卷積和揭示，一個(gè)LTI離散系統(tǒng)的沖激響應(yīng)沖激響應(yīng)hn，可以完整地描述了系統(tǒng)的輸入輸出關(guān)系。如果沖激響應(yīng)已知，就可以利用卷積和求取任意輸入信號(hào)作用下的系統(tǒng)響應(yīng)。 *nhnxknhkxnykAdditional properties of convolution sum Convolution for unit impulse:yn=n*hn=hn;yn-n0=n -n0*hn=n*hn-n0=hn-n0;gn=n*gn;gn-n0 = n -n0*gn=n*gn-n0;Difference between convolution and multiplication!kxkhkhExample

7、10.2:兩個(gè)序列的卷積和兩個(gè)序列的卷積和kknhkxnyknx0kx0 yk1 0 1 2 3 4 5 60n Example 10.2 (continued)kh（3）1 kxkh2kx 1 yk1 0 1 2 3 4 5 62 yk1 0 1 2 3 4 5 61n 2n 卷積和的另外一個(gè)例子0,04ny1,1 15ny2,2 19ny y n總結(jié)：卷積和計(jì)算步驟FIR and IIR systemlFIR system, finite impulse response;lIIR system, infinite impulse response;lExample 10.3;lExamp

8、le 10.4. 1 y nay nx n ?h n kknhkxny x nu n10.2 Convolution for discrete-time LTI Systemx n ynProperties of convolution sum;Relationship of response and input;Evaluation of convolution, examples.How to calculate the impulse response of a discrete system?LTIProperties of convolutionThree properties of

9、 convolutionvCommutative property, figure 10.7;vAssociative property, figure 10.8;vDistributive property, figure 10.9. * * x nh nh nx n1212 * *( ) * * x nh nhnx nh nh n1212 * *( ) * x nh nx nhnx nh nh nExample 10.5xnh3nh4nynh1n* h2nh1nh2nhn=(h1n*h2n+h3n)*(h4nxnyn10.3 Properties of discrete-time LTI

10、systems無(wú)記憶系統(tǒng)(Memoryless Systems)可逆性(Invertibility)因果性 (Causality)穩(wěn)定性 (Stability)單位階躍響應(yīng)(Unit Step Response)kknhkxnyCausalityl判斷判斷:根據(jù)根據(jù)h(t) (It must be a causal signal);l對(duì)于一個(gè)滿足因果律的線性時(shí)不變系統(tǒng)來(lái)對(duì)于一個(gè)滿足因果律的線性時(shí)不變系統(tǒng)來(lái)說(shuō)，如何確定卷積和求和區(qū)間。說(shuō)，如何確定卷積和求和區(qū)間。0 nkky nx k h nkx k h nkStabilityl對(duì)于一個(gè)對(duì)于一個(gè)LTILTI系統(tǒng)而言，系統(tǒng)穩(wěn)定的條系統(tǒng)而言，系統(tǒng)穩(wěn)定的條件是其沖激響應(yīng)絕對(duì)可積的。件是其沖激響應(yīng)絕對(duì)可積的。lExample 10.6Example 10.60 kh