数字信号处理B[双语].ppt

DigitalSignalProcessing数字信号处理B[双语]AboutOurCourseGeneralInformationReferences1INTRODUCTION不需要看书2Discrete-timesignalsandsystems离散时间信号与系统2Discrete-timesignalsandsystems离散时间信号与系统[续]Homework2.0Introduction1WhatisaSignal?2typesofsignals信号类型3Discrete-timeSystems离散时间系统4typesofsystems5What’sDigitalSignalProcessing?什么是数字信号处理？2.1Discrete-timesignals:sequences序列Xa(nT)orx[n]2.1.1BasicSequencesandSequenceOperations基本序列和序列的运算BasicOperationonSequencesp11UnitSampleSequence(Impulsesequence)RepresentationofArbitrarySequences任意序列的表示page11Example2.1.1:generatethesignalwithimpulsesequence.UnitStepSequence单位阶跃序列ExponentialSequence指数序列p13Exmaple2.1.3CombingBasicSequenceSinusoidalSequence正弦序列p13UnitRampSequence单位斜坡序列2.1.2PeriodicityofSequences序列的周期性p15ANIMPORTANTCONCLUSION2.2Discrete-timesystems离散时间系统p16Example2.2.1Anidealdelaysystemp17

Example2.2.2AnMovingAverageSystem2.2.1MemorylessSystems无记忆系统p182.2.2LinearSystem线性系统p18Example2.2.4Considerthesystemgivenbyy[n]=3x[n]+4andthesystemgivenbyy[n]=|x[n]|2asbeinglinearornonlinear.
Solution：
forsystemT{x[n]}=y[n]=3x[n]+4,
wehavey1[n]=T{x1[n]}=3x1[n]+4
andy2[n]=T{x2[n]}=3x2[n]+4.
theny3[n]=T{x3[n]}=T{x1[n]+x2[n]}=3(x1[n]+x2[n])+4
=3x1[n]+3x2[n]+4.
Buty1[n]+y2[n]=3x1[n]+3x2[n]+8,
hence，y3[n]≠y1[n]+y2[n].
thereforeSystemy[n]=3x[n]+4isnonlinear.
Similarly,wecouldverifythatsystemdescribedbyformulaT{x[n]}=y[n]=|x[n]|2isnonlinear,too.2.2.3Timeinvariantsystem时不变系统Example2.2.5characterizethesystemy[n]=nx[n]asbeingtimeinvariantortimevarying2.2.4Causality因果性Example2.2.6Considerthesystemgivenbyy[n]=|x[n+1]|2asbeingcausalornoncausal.
Solution：fory[n]=T{x[n]}=|x[n+1]|2
wehaveT{x1[n]}=|x1[n+1]|2
andT{x2[n]}=|x2[n+1]|2,
therefore,ifx1[n]=x2[n],forn<n0,
butx1[n0]≠x2[n0]
then,fork=n0-1<n0,asaninstantbeforen0,
T{x1[k]}=T{x1[n0-1]}=|x1[n0]|2
andT{x2[k]}=T{x2[n0-1]}=|x2[n0]|2
hence，wehavethatT{x1[k]}≠T{x2[k]},andthesystemisnoncausal.Example2.2.7Otherexamples:
systemy[n]=nx[n]iscausal
thefollowingsystemsarenoncausal：
y[n]=x[n+3]+ax[n]
y[n]=x[n3]
y