【正文】 t0 R(tt0) = 0 t = t0 R(tt0) = t t0 Unit Step Signal 單位階躍信號 ????????02100010)(tttttttt?1 ???????00100)(21 tttt?t 0 t0 1 epsilon 用階躍表示門信號 )2()2()( ????? ???? tttp )2()2()( 000????? ??????? ttttttp2?2?? t t 0t（ 1）突然接入的直流電壓 （ 2）突然接通又馬上斷開電源 K 負載 Signum Function 正負符號函數(shù) Definitions sgn(t) 1 0 t Interpret by Step Signal 1 ?????)0(1)0(1)s gn(ttt1)(2)s gn( ?? tt ?Conclusions 1. We are awash in a sea of signals. 2. Signal categories identity of independent variable, dimensionality, CT or DT, real or plex, periodic or aperiodic, causality, bounded, even amp。 ? Time Shifting f(t) ? f(t?t0) 1t2 4f ( t )??? ????其它 042 2/)2()(tttf??? ???????其它 0422 2/)22()2(tttf??? ????其它 064 2/)4( tt1t4 6??? ???????其它 0422 2/)22()2(tttf??? ???其它 020 2/ tt1t20f ( t? 2 ) f(t?t0)， 表示信號 f(t)右移 t0單位； f(t?t0)， 表示信號 f(t)左移 t0單位。 f ( t )－ 1 t1 2－ 212－ 1－ 200 1 2－ 1－ 21－ 2 － 1 1 2 3123450)()1(tf?)()1(tf( a ) ( b ) ( c )tt(a) f(t)； (b) Differentiation of f(t)； (c) Integration of f(t) . Differentiation and Integration 0 tf ( t )110 t11? ???tfty ?? d)()( Integration 系統(tǒng)描述： 數(shù)學模型：數(shù)學表示式（微分方程，差分方程） 物理模型：用具有理想特性的符號組成圖形來表征系 統(tǒng)的特性。 在光滑平面上 ， 質(zhì)量為 m的鋼性球體在水平外力 f(t)的作用下產(chǎn)生運動 。 tfmt ??圖 力學系統(tǒng) v ( t )f ( t )m 例 : 如圖 ,一個電路系統(tǒng) 。 tuLtutuR L CtiLCtiRCti sssLLL ????? 如果描述連續(xù)系統(tǒng)輸入輸出關(guān)系的數(shù)學模型是 n階微分方程 ， 就稱該系統(tǒng)為 n階連續(xù)系統(tǒng) 。 )()()( tfdtdtf jjj ? )()()( tydtdtyiij ?圖 電路系統(tǒng) ＋－＋－＋－uC( t )iC( t )Ri1( t )us 1( t )LiL( t )us 2( t )alCClassification of systems In the study of systems, certain properties of the system operator T are mon to many different kinds of physical situations. This lead to an attempt to classify systems not according to their physical character ( electrical, mechanical, economic, and the like ) but according to the character of the system operator T. This operator, which defines the model for the system, can be ?Static (instantaneous) and Dynamic systems ?causal or noncausal ?linear or nonlinear ?timeinvariant or timevarying For the most part we will be concerned with dynamic, causal, linear, timeinvariant, deterministic models. Static (instantaneous) and Dynamic systems （ 靜態(tài) (即時 )系統(tǒng)和動態(tài)系統(tǒng) ） A dynamic system is said to possess memory because of this dependence on past history. A static system is said to be memoryless. )(tvi1R2R )(tvo)()(212 tvRRRtvio ??dttdvCti )()( ??? diCtv t? ??? )(1)(Causal and noncausal systems A causal system cannot yield any response until after the excitation is applied. In other words, a causal system is not anticipative, it cannot predict the future behavior of the excitation. Noncausal Causal Example： y(t)=5f(t?2 ) Causal System y(t)=5f(t+2) Noncausal System Linear and nonlinear systems A system is linear if and only if it is both additive and homogeneous. )()()()()()()()( :ad d i t i v i t y ofp r o p er t y t h )()(yh