精品課件大學(xué)物理2(雙語)(文件)
【正文】 tfttfA n a l y s i s ??? ??)()()()0( 39。 dtt?? ??? ?? )0()1()()( )()( nnn fdttft?Unit impulse 單位沖激信號(hào) Minute miniquiz problem Problem Interpret and sketch the generalized function f(t) where )()( 39。 chapter 2 TimeDomain Analysis of Continuous Time Signals And Systems Definition 的物理意義 )(tvc+ )(t?)2()]2()2()[2(1)( ??????????????? tttttv c2??2? t f(t) Unit impulse 單位沖激信號(hào) 2?2?? t )]2()2([)()( ????? ????? ttcdt tdvcti cc2??2? t f(t) 1 t 0 2?2?? t )(t?0 t Unit impulse 單位沖激信號(hào) Unit impulse 單位沖激信號(hào) The unit impulse δ(t), is defined by the integral relation ????????????00)(1)(ttdtt??For CT signal ? 連續(xù)時(shí)間單位沖激信號(hào) ? 持續(xù)時(shí)間無窮小，瞬間幅度無窮大，涵蓋面積恒為1的一種理想信號(hào)，記 ? Dirac’s function )(t?1)(1)( 00 ??? ?? ?????? dttdtt ??Unit impulse 單位沖激信號(hào) Unit impulse narrow pulse approximation To obtain an intuitive feeling for the unit impulse, it is often helpful to imagine a set of rectangular pulses where each pulse has width and height so that its area is 1. The unit impulse is the quintessential(精萃的 ) tall and narrow pulse! )]()([lim)( 2210 ???? ??? ???? ? ttt?1?Unit impulse 單位沖激信號(hào) Unit impulse —— the shape does not matter There is nothing special about the rectangular pulse approximation to the unit impulse. A triangular pulse approximation is just as good. As far as our definition is concerned both the rectangular and triangular pulse are equally good approximations. Both act as impulses. ?? ??21?21 ?21?21?? ?? ??2?? 2?Unit impulse 單位沖激信號(hào) Unit impulse —— properties 1. 抽樣性 由定義有 we will use a tall rectangular pulse of unit area as an approximation to the unit impulse. As the rectangular pulse gets taller and narrower, .)0()()()(l i m 0 ? ???? ??? ftfdttptf ????? ??? ? )0()()( fdtttf ?可得 )()0()()( tfttf ?? ?)( tf)1(t0t))((0tft0t)()(0tttf ??)()0()()( tfttf ?? ?0 )()( ttf ?)()()()( 000 tttftttf ??? ??Unit impulse 單位沖激信號(hào) Unit impulse —— properties ??????????????????)0()()0()0()()()(fdttfdtftdttft???t )0(f0 )()()()()(0000tfdttttfdttftt?????????????????)( 0tf0 t Unit impulse 單位沖激信號(hào) Unit impulse —— properties Sampling of CT signals ???????kkTttfkTf )()()( ?)(tf)(kTft k . ? ?? ?????????????????????????????302302552)2()4)2()3)]()([s i n)2)()12()1ktktdtktedtktetttdtttt??????1 0 41 ?? e4?eUnit impulse 單位沖激信號(hào) Unit impulse —— properties 2. 尺度變換特性 )(1)( taat ?? ?dtattg )()( ?????adxxaxgxat )()/( ??? ????ag )0(?dtattg )()( ????? ag )0(?Unit impulse 單位沖激信號(hào) Unit impulse —— properties 3. 偶函數(shù)性 )()( tt ?? ??If a= ?1,
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