信號與系統(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 x na y na y nWhy emphasizing LTI systems?離散LTI系統(tǒng)占有十分重要的地

2、位，這是因為: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。我們可以解出描寫連續(xù)和離散的LTI模型的方程解。通過LTI系統(tǒng)的分析和設計，可以得到很多關于系統(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 na

3、tural 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)(1000nnnnnnn0n0nn0n0

4、nRelationship 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

5、response;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 Su

6、ml卷積和揭示，一個LTI離散系統(tǒng)的沖激響應沖激響應hn，可以完整地描述了系統(tǒng)的輸入輸出關系。如果沖激響應已知，就可以利用卷積和求取任意輸入信號作用下的系統(tǒng)響應。 *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!kxkhkhExampl

7、e 10.2:兩個序列的卷積和兩個序列的卷積和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 卷積和的另外一個例子0,04ny1,1 15ny2,2 19ny y n總結：卷積和計算步驟FIR and IIR systemlFIR system, finite impulse response;lIIR system, infinite impulse response;lExample 10.3;lExa

8、mple 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

9、of 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 LT

10、I systemsl無記憶系統(tǒng)(Memoryless Systems)l可逆性(Invertibility)l因果性 (Causality)l穩(wěn)定性 (Stability)l單位階躍響應(Unit Step Response)kknhkxnyCausalityl判斷判斷:根據(jù)根據(jù)h(t) (It must be a causal signal);l對于一個滿足因果律的線性時不變系統(tǒng)來對于一個滿足因果律的線性時不變系統(tǒng)來說，如何確定卷積和求和區(qū)間。說，如何確定卷積和求和區(qū)間。0 nkky nx k h nkx k h nkStabilityl對于一個對于一個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絕對可積的。件是其沖激響應絕對可積的。lExample 10.6Example 10.60 kh