信号与系统信号与系统信号与系统 (18).ppt

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1、BEIJING JIAOTONG UNIVERSITYThe Course Group of Signals and Systems,Beijing Jiaotong University.P.R.CHINA.Copyright 2020Signals and Systems Example of C-T LTI System Response(2)The impulse response h(t);(4)The full response y(t);(1)The ZI response ;(3)The ZS response ;(5)Determine the systems stabili

2、ty.Example 1:The DE of a C-T LTI system isGiven the input x(t)=u(t),initial state y(0-)=1,y(0-)=2,Please answer below questions.Solutions:characteristic roots ,，With initial stateK1=6,K2=5 characteristic equation Example of C-T LTI System ResponseExample 1:The DE of a C-T LTI system isGiven the inpu

3、t x(t)=u(t),initial state y(0-)=1,y(0-)=2,(1)The ZI response Find the undetermined coefficients:A=1,B=1Therefore,Solutions:(2)Impulse response h(t)With the impulse balance method,Example of C-T LTI System ResponseExample 1:The DE of a C-T LTI system isGiven the input x(t)=u(t),initial state y(0-)=1,

4、y(0-)=2,Solutions:(3)The ZS response Example of C-T LTI System ResponseThe convolution of the input and the impulse responseExample 1:The DE of a C-T LTI system isGiven the input x(t)=u(t),initial state y(0-)=1,y(0-)=2,Solutions:(4)The full responseThe waveforms of the responsesExample of C-T LTI Sy

5、stem ResponseExample 1:The DE of a C-T LTI system isGiven the input x(t)=u(t),initial state y(0-)=1,y(0-)=2,Solutions:(4)The full responseExample of C-T LTI System ResponseThe full response can also be decomposed ton Natural response yh(t)and forced response yp(t)n Transient response yt(t)and steady

6、-state response ys(t)Example 1:The DE of a C-T LTI system isGiven the input x(t)=u(t),initial state y(0-)=1,y(0-)=2,Example of C-T LTI System ResponseNatural response yh(t):terms related with the characteristic rootsForced response yp(t):terms related with the input signalTransient response yt(t):te

7、rms approaching to zero as time increasesSteady-state response ys(t):terms do not belong to transient responseExample of C-T LTI System ResponseSolutions:(4)The full responseExample 1:The DE of a C-T LTI system isGiven the input x(t)=u(t),initial state y(0-)=1,y(0-)=2,Solutions:(5)Determine the syst

8、ems stabilityThe impulse response of the C-T LTI system isExample of C-T LTI System ResponseTherefore,the C-T LTI system is stable.Example 1:The DE of a C-T LTI system isGiven the input x(t)=u(t),initial state y(0-)=1,y(0-)=2,Please re-evaluate ,and the full responseSolutions:Example 2:if the input

9、signal is changed to x1(t)=0.5u(t1)y(t).Since the initial state is the same,the ZI response does not change.Input signalFrom the linearity and time invariance properties,The ZS response isExample of C-T LTI System ResponseExample of C-T LTI System ResponseSolutions:Please re-evaluate ,and the full r

10、esponse Example 2:if the input signal is changed to x1(t)=0.5u(t1)y(t).AcknowledgmentsMaterials used here are accumulated by authors for years with help from colleagues,media or other sources,which,unfortunately,cannot be noted specifically.We gratefully acknowledge those contributors.Example of C-T LTI System Response