数字信号处理英文版课件：3-6 Generalized linear phase systems

§3.6Generalizedlinearphasesystems、Linearphase1.DefinitionThen

hasalinearphase.

Note:ExampleIdealdelaysystemExample5.16Ideallowpasswithlinearphasep293cangetazerophasesequenceCannotgetazerophasesequenceIngeneral,foralinear-phasesystem,with

Ifisinteger,thenh[n]hasevensymmetryabout

Ifisnoninteger,thenh[n]willnothavesymmetry.

Definition:2.GeneralizedlinearphaseThen

hasgeneralizedlinearphase

.

Note:3.PropertiesSuppose:

isrealnecessaryconditionofageneralizedlinear-phasesystem

【Discuss:】,

evenfunction

oddfunctionproofa)Proof:二、LinearphaseFIRsystem1.causalsystemIf(a)or(b)issatisfied,then,when.i.e.thissystemisanFIRsystem(length:M+1).

Proofcausal

FIR2.Sufficientcondition

IfanFIRsystemisevenoroddsymmetry,i.e.or,thenthesystemhasageneralizedlinearphase.Proof

evenfunction1)Evensymmetryoddfunction2)Oddsymmetry3.FourtypesFIRsystemswithgeneralizedlinear-phase1)TypeⅠ:Evensymmetry,Miseven(lengthisM+1,odd)

Characteristics:b)CanbeusedasallkindoffrequencyselectiveFIRfilter

2)TypeⅡ:Evensymmetry,Misodd(lengthisM+1,even)Characteristics:c)CannotbeusedasHP,BSFIRfilters3)TypeⅢ:oddsymmetry,Miseven(lengthisM+1,odd)c)CannotbeusedasLP,HP,BSFIRfilter

Characteristics:4)TypeⅣ:Oddsymmetry,Misodd(lengthisM+1,even)c)CannotbeusedasLP,BSFIRfilterCharacteristics:4.PropertyofzerosSoeachzeropairswithaconjugatereciprocalzero.5.Relationshipbetweenminimum-phaseandlinear-phaseTheorderofH(z):

hasallzerosinsidetheunitcircle.

hasallzerosontheunitcircle.conjugatereciprocal

hasallzerosoutsidetheunitcircle.6.Toacausalsystem:Example:Acausallineartime-invariantsystemhassystemfunctionFindexpressionforaminimum-phasesystemandageneralizedlinear-phaseFIRsystem,sothatsolution三、SummaryaboutlinearphaseFIR1.Typic