信號與系統(tǒng) 9

1、School of Computer Science and Information School of Computer Science and Information A system is composed with many components which are relation with one another.A system means a special function.A system can be represent by mathematic formulas.ConceptsSchool of Computer Science and Information 5.

2、1 System Properties1. Causality A system is causal if the output does not anticipate future values of the input, i.e., if the output at any time depends only on values of the input up to that time. All real-time physical systems are causal, because time only moves forward. Effect occurs after cause.

3、School of Computer Science and Information :if causal is SystemA )()(tytx0210212211)()()()()()()()(tttytytttxtxtytxtytx all for Then all for and Whencausal. is system The on depends )4()5()1()(2xytxtySchool of Computer Science and Information noncausal. is system The future the on depends xyxytxty)6

4、()5()1()(noncausal. is system The future the on depends but ok, is xyxyxynxny)5()5()5()5()()(causal. is system The on depends )4()5()1()()(3121xynxnynSchool of Computer Science and Information 2. Time-Invariance (TI)A system is time-invariant (TI) if its behavior does not depend on what time it is.

5、School of Computer Science and Information School of Computer Science and Information 3. LinearityA continuous-time system is linear if it has the superposition property:School of Computer Science and Information 5.2 Analyzing CT System In Time DomainThe method can not be involved with any mathemati

6、c transform. Only to find solution for differential equations or integral equations. The method shows clear concept.The method needs complex calculation.We do not discuss the method in the course.School of Computer Science and Information ).()(?)(. 2)0(, 1)0(),()()(3)()(2)(3)(22trtrtrrrtutetetedtdtr

7、trdtdtrdtdzsziresponse state-zero , response input-zero itsout point and response entire its determine To asdescribed condition initial the input the if:equationaldifferenti theby described system LTI the Consider School of Computer Science and Information :Soultionresponse input-zero the determine

8、To )1( 1)0()0(2)0()0(0)(2)(3)(zizizizizizizirrrrtrtrtr2, 1023212 )()()(221tueAeAtrttzi 342)2()0(1)()0(212121AAAArAArzizi)()34()(2tueetrttzi School of Computer Science and Information response state-zero the determine To )2()(3)()(2)(3)()()(tuttrtrtrtutezizizi :Suppose1 a )()()()()()()(tuattrtuatrtub

9、tatrzszszs 0)0()0(, 11)0()0( zszszszsrrrrSchool of Computer Science and Information )()()(221tueBeBtrttzsh :Suppose23)()( CtCutrzsp)()23()()()(221tueBeBtrtrtrttzspzsh 2121)2()0(0)23()0(212121BBBBrBBrzszs)()23212()(2tueetrttzs )()23252()()()(2tueetrtrtrttzszi School of Computer Science and Informatio

10、n 5.3 Analyzing CT System With Convolutionimpulses. ofseries a into decomposed be can signal Input tx )( ttxdtxtxt)()()()()(0 )()(thtx If:is system of response state-zero the then thtxty)()()( School of Computer Science and Information 123A System as the picture shows:if( )( ),( )(1),( )( ). then(1)

11、The unit impulse response( )?(2)When( )( )(1),then( )?h tu th tth tth tx tu tu ty t School of Computer Science and Information 1213Soultion:(1)( )( )( )( )( )( )( )When( )( ),then( )( )( )( )(1)( ) ( )( )(1)(2)( )( )( ) ( )(1) ()(1).( )2(1)y tx th tx th th th tx tth ttu tttu ttu tu ty tx th tuuu tu tdt u ttu (1)(2)(2)ttu tSchool of Computer Science and Information . ?)()()(3)(),(2)()()(23thtuetrtedtdHtueteteHtrtt response impulse-unit its determine To ,kn