数字信号处理英文版课件：3-1,3-2 3.1 Transform Analysis of Linear-Time-Invariant Systems

Chap.3TransformAnalysisofLinear-timeSystems

contents§3.1TransformAnalysisofLinear-Time-InvariantSystems§3.3FrequencyResponseforRationalSystemFunction

§3.2LinearConstant-coefficientDifferenceEquations§3.4All-passSystems

§3.6Generalizedlinearphasesystems§3.5Minimum-Phasesystems

§3.1TransformAnalysisofLinear-Time-InvariantSystems一、Idealfrequency-selectivefilters1.Lowpass2.Highpass3、Bandpass4.Bandstop【note】Idealfrequency-selectivefilters

1)noncausal,IIR,2)notcomputationallyrealizable3)zero-phase二、ThreeparametersofDFfrequencyresponse

1、magnitude-squaredresponseexampleExample2、Phaseresponse1）Principalvalue

2）Continuousphase

01）Definition——Aconvenientmeasureofthelinearityofthephase3、Groupdelay

Example5.1EffectsofAttenuationandGroupDelayP2430.850.250.50.250.50.85delay200samples

delay50samples

Example:1.Idealdelaysystem:2.Ideallowpassfilterwithlinearphase:

Delaydistortionisarathermildformofphasedistortion.Mostofthetime,itisinconsequential,oritcouldeasilybecompensated.（constant-linearphase）§3.2LinearConstant-coefficientDifferenceEquations一、DifferenceEquationsandsystemfunctions

Differenceequation:

LTI:systemfunction

Example：Writedifferenceequationofthegivensystem.Solution:

二、StabilityandcausalityCausalandstable:Stablesys：

Causalsys.ROC:

Allpolesareinsidetheunitcircle三、Inversesystem逆系统inverse2)Notallsystemshaveaninversesysteme.g.Ideallowpassfilter.3)Multiinversesystemmayexistforasystem,【Note】1）TheROCof

andmustoverlap.4）IfROCofis,theinversesystemmustbecausal.5)TheinversesystemofacausalandstablesystemH(z)iscausalandstableiff.allpolesandzerosofH(z)isinsidetheunitcircle.i.e.theROCofmustincludetheunitcircle,andallzerosandpolesareinsidetheunitcircle.(因果稳定的最小相位系统）exampleExample5.5Findtheinverseofthegivensystemp250——bothcausalandstable

——causalandunstable——stableandnoncausal四、Impulseresponseforrationalsystemfunction

1.Infiniteimpulseresponsesystem(IIR)2）Necessaryconditions:thestructureofsystemisrecursivestructures(递归结构）(orhavefeedbackloops)

3）isinfinitelength1)hasonepoleatleastexceptExample:ARsystem(Auto-Regressive

自回归系统)——nozeroAR-MA（Auto-Regressive

and

Moving

Average

Model自回归滑动平均系统）2.Finiteimpulseresponsesystem(FIR)2）Sufficientconditions:ifasystemhasnonrecursivestructure(orhasnoloops),itmustbeanFIRsystem.3）isfinitelength1)has