【正文】 其中 ， 電壓源 us1(t)和 us2(t)是電路的激勵 。 odd, etc. 3. Building block signals eternal plex exponentials and singularity functions are a rich class of signals and we will show that they can be summed to represent virtually any signal of physical interest. ?Addition ： f(t) = f1(t)+f2(t) f1( t )t? tt1f ( t )Operations on signals ?Multiplication : f(t) = f1(t) f2(t) f1( t )t1? 1 1f 2 ( t )t12? 2t1? 1 1?Time scaling f(t) ? f(at) a0 1t2 4f ( t )??? ????其它 042 2/)2()(tttf??? ???其它 0422 2/)22( tt??? ????其它 021 1 tt1t1 2f (2 t )?)2( tf??? ????其它 042/2 2/)22/()2/(tttf??? ????其它 084 4/)4( tt1t4 8f ( t /2 )尺度變換小結(jié)： 若 0a1，則 f(at)是 f(t)的擴展。Signals amp。 若 a1， 則 f(at)是 f(t)的壓縮。 若設(shè)電感中電流 iL(t)為電路響應(yīng) ， 則由基爾霍夫定律列出節(jié)點 a的支路電流方程為 )(1)]()([1)(1)(1)( 39。 tfmt ??圖 力學(xué)系統(tǒng) v ( t )f ( t )m 例 : 如圖 ,一個電路系統(tǒng) 。 – Ramp Signal 斜變信號 – Unit Step Signal單位階躍信號 – Signum Function符號函數(shù) – Unit Impulse Signals單位沖激 Unit Ramp Signal 單位斜變信號 0 1 t 0 t0 t0+1 t R(t) R(tt0) t =0 R(t) = t t 0 R(t) = 0 t 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。 Systems信 號 與 系 統(tǒng) CHAPTER 1 INTRODUCTION Contents ?Description amp。 例：尺度變換變換后語音信號的變化 f (t) f () f () ? reflection f(t) ? f(?t) 1t2 4f ( t )??? ????其它 042 2/)2()(tttf??? ???????其它 042 2/)2()(tttf??? ???????其它 024 2/)2( tt1t? 4f ( ? t )? 2f(?t)表示將 f(t)以縱軸為中心作 180?翻轉(zhuǎn)。 22139。 根據(jù)牛頓第二定律 ， 有 dttdmtmatf )()()( ???)(1)(39。 ? 例如 : ? x(t)=sint 是確定信號，把帶入可以求出任何一時刻的x(t)值 ? 生活中大多是隨機信號（新信息）： 耗電、打電話等 Deterministic and Stochastic (nondeterministic) Signals 確定性信號隨機信號 (非確定性信號 ) ? Even signal A signal x(t) or x[n] is referred to as an even signal if it is identical to its timereversed counterpart, ., with its reflection about the origin. In continuous time a signal is even if ? ?tftf ee ??)(Odd and Even Signals while a discretetime signal is even if ][][ kfkf ??? Odd signal A signal is said to be odd if ][][ kfkf ???)()( tftf ???In continuous time In discrete time )()()( tftftf eo ??)]()()()([21)( tftftftftf ???????)]()([21)]()([21 tftftftf ??????)()( tftf oe ??Odd and Even Signals In fact, any signal f(t) can be expressed as a sum of its even part and its odd part, that is )]()([21)( txtxtx e ???)]()([21)( txtxtx o ???Even part: Odd part: S