(教授、博導(dǎo) 信號(hào)與信號(hào)的描信號(hào)的運(yùn)階躍信號(hào)與沖激信號(hào)的系統(tǒng)模型及其線性時(shí)不變系統(tǒng)分析StateKeyLabofASIC&Systems,FudanUniversity,Jinmei階躍信號(hào)和沖激奇異信號(hào)（函數(shù)要求StateKeyLabofASIC&Systems,FudanUniversity,Jinmei1、單位斜變信號(hào)（斜坡信號(hào)、斜升信號(hào)

ff(t)

t t

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t t t0t0StateKeyLabofASIC&Systems,t0t01、單位斜變信號(hào)（斜坡信號(hào)、斜升信號(hào)KOt Ktf1(t)

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t0 t t0 ,StateKeyLabofASIC&Systems,FudanUniversity,Jinmei,2、單位階躍信 接入時(shí)刻t0StateKeyLabofASIC&Systems,FudanUniversity,Jinmei2、單位階躍信 式描述StateKeyLabofASIC&Systems,FudanUniversity,Jinmei2、用單位階躍信號(hào)描述G(t)utut

Gτ

StateKeyLabofASIC&Systems,FudanUniversity,JinmeisgntOt2、用單位sgntOt tsgn(t)

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u(t)1[sgn(t)2StateKeyLabofASIC&Systems,FudanUniversity,Jinmei3、單位沖激信號(hào)（難點(diǎn)、重點(diǎn)StateKeyLabofASIC&Systems,FudanUniversity,Jinmei定義1:規(guī)則信號(hào)取極 2 2矩形脈沖信號(hào)：f(t1ut 2 2

StateKeyLabofASIC&Systems,FudanUniversity,Jinmei定義1:規(guī)則信號(hào)取極限(續(xù))11fO22 2 2f(t)1ut 2 2 t0面積1保持不變；★面積為 三個(gè)特點(diǎn)：寬度為0★幅度0

ttStateKeyLabofASIC&Systems,FudanUniversity,Jinmei定義1:規(guī)則信號(hào)取極限(續(xù))(t)limf(t)lim1

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2 u 2k k

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StateKeyLabofASIC&Systems,FudanUniversity,Jinmei(a)三角形脈 (b)雙邊指數(shù)脈 niversity,Jinmei (Dirac)給出(t)函數(shù)的定 t函數(shù)值只在t0t=0時(shí)，(t) 函(t)dt0 StateKeyLabofASIC&Systems,FudanUniversity,Jinmei (Dirac)給出(t)函數(shù)定義(續(xù)StateKeyLabofASIC&Systems,FudanUniversity,Jinmei

StateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateKeyLabofASIC&Systems,FudanUniversity,Jinmei沖激函數(shù)的StateKeyLabofASIC&Systems,FudanUniversity,Jinmei如果f(t)在t0ffo篩選特性：(tf(tfffo

(t)f(t)dtf(t)f(tt0)f(t0)(t 篩選特性t0f(t)f(t0(tt0) (tt0)f(t)dtf(t0StateKeyLabofASIC&Systems,FudanUniversity,Jinmei2、尺度變 at

aStateKeyLabofASIC&Systems,FudanUniversity,Jinmei推論1(tf(t)(t)dtf t

f(t)(t)dt f()()(d f()()(df(0)StateKeyLabofASIC&Systems,FudanUniversity,Jinmei3、沖激信號(hào)與階躍信號(hào)tu(t) (t)(t) du(tStateKeyLabofASIC&Systems,FudanUniversity,Jinmei StateKeyLabofASIC&Systems,FudanUniversity,Jinmei沖激

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(t)dt⑤f(t)(t) f(0)(t) f(0)(t

注意：(tf(t)f(0)

StateKeyLabofASIC&Systems,FudanUniversity,Jinmeiu(t(tf(t)，uu(t(tf1O11OO1O11OO StateKeyLabofASIC&Systems,FudanUniversity,Jinmei信號(hào)與信號(hào)的描信號(hào)的運(yùn)階躍信號(hào)與沖激信號(hào)的系統(tǒng)模型及其線性時(shí)不變系統(tǒng)分析StateKeyLabofASIC&Systems,FudanUniversity,Jinmei將信號(hào)分解為一些簡(jiǎn)單(基本)的信號(hào)之和:StateKeyLabofASIC&Systems,FudanUniversity,Jinmei1、直流分量與交流能 E

f(t

2dt(連續(xù)信號(hào) -Ex(n2(離散 功 0Plim1 T信號(hào)T

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N2N1nE；PStateKeyLabofASIC&Systems,FudanUniversity,Jinmei1、直流分量與交流f(t) fA(t) fD(t

T1TfD(t) 1T

ffDt：信號(hào)的直流分即平均值ffAf

T fD 信號(hào)的直流分量：信號(hào)的平信號(hào)的交流分量：從原信號(hào)中去掉StateKeyLabofASIC&Systems,FudanUniversity,Jinmei1、直流分量與交流分量(續(xù)信號(hào)的平均功率StateKeyLabofASIC&Systems,FudanUniversity,Jinmei2、偶分量與奇f(t)f(t)f

f

o:f(t)1f(t)f 2e2Plim

t0

f2(t)dt

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f(t)f2tT1T

2 (2 (t)dt

t

2 2 信號(hào)的平均功率3、脈沖分量ftft1 當(dāng)tt1,脈高：f

存在區(qū)間：u(tt1u(tt1t1StateKeyLabofASIC&Systems,FudanUniversity,Jinmei把所有窄脈沖相加 t1tf(t)limf(t1)[u(tt1)u(tt1t1)].t1/t1t10t1tf(t)limf(t1)(ttt1t

f(t)

f(t1)(t出現(xiàn)在不同時(shí)刻的，不同強(qiáng)度的沖激函數(shù)StateKeyLabofASIC&Systems,FudanUniversity,Jinmei階躍信號(hào)分量的ff(titftii

階躍信號(hào)分量的f(it)f(ti)f(tif(it)u(tit

StateKeyLabofASIC&Systems,FudanUniversity,Jinmei /p-tf(t)f(0)u(t) df(ti)u(ttt dti

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f*(t)f(t)jf(tfr(t)

2

f(t)

*(t)

jf

(t)

2

f(t)

*(t)可借助于復(fù)信號(hào)來研究實(shí)信號(hào)的問題，可以簡(jiǎn)化StateKeyLabofASIC&Systems,FudanUniversity,Jinmei把信號(hào)分解為正交函數(shù)分量的研究方法在信號(hào)與系統(tǒng)理論中占有重要地位，這將是本課程討論的cosnt,sinnt

StateKeyLabofASIC&Systems,FudanUniversity,Jinmei信號(hào)與信號(hào)的描信號(hào)的運(yùn)階躍信號(hào)與沖激信號(hào)的系統(tǒng)線性時(shí)不變系統(tǒng)分析StateKeyLabofASIC&Systems,FudanUniversity,Jinmei1、信號(hào)時(shí)域運(yùn)算的基本單元方框 加法器乘法器微分器積分器延時(shí)器StateKeyLabofASIC&Systems,FudanUniversity,Jinmeie2rte2rt

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