數(shù)字信號(hào)處理英文版課件：3-4,3-5 All-pass Systems

§3.4All-passSystems一、DefinitionAll-passExample:First-orderall-passsystemzero:pole:conjugatereciprocalpair二、Generalformofanall-passsystemRealsystem三、Property1.Thenumberofpolesissameaszerosandeachpoleispairedwithaconjugatereciprocalzero.3.isanIIRsystem.2.Forastableandcausalall-pallsystem,thegroupdelayisalwayspositive,andthecontinuousphaseisalwaysnonpositivefor.ProofProof：1)Toacausalandstableall-passsystem,allpolesareinsidetheunitcircleandallzerosareoutsidethiscircle.afirst-orderall-passsys.2)四、Application1.Anyrationalsystemcanbeexpressedas:2.Theycanbeusedasacompensatorforphasedistortion

example3.Improvetheperformanceofsystembycascadinganall-passsystem.exampleExample:DesignalinearphasefilterwithIIR

--compensatingforphasedistortion

Example:Improvetheperformanceofsystem

cascadeaall-passsystem:stableReview--All-passSystemsProperty1.Thenumberofpolesissameaszerosandeachpoleispairedwithaconjugatereciprocalzero.3.isanIIRsystem.2.Forastableandcausalall-pallsystem,thegroupdelayisalwayspositive,andthecontinuousphaseisalwaysnonpositivefor.Application1.Anyrationalsystemcanbeexpressedas:2.Theycanbeusedasacompensatorforphasedistortion

3.Improvetheperformanceofsystembycascadinganall-passsystem.§3.5Minimum-Phasesystems一、Definition

AllzerosinsidetheunitcircleAllzerosoutsidetheunitcircleMaximum-phasesys.

Minimum-phasesys.

AllzerosandpolesinsidetheunitcircleMinimum-phase-lagsys.二、Minimum-phaseandall-passdecomposition

Anyrationalsystemfunctioncanbeexpressedas:Proof:SupposeH(z)isarationalsystem

system

conjugatereciprocal

Example5.14p281Example:acausaldiscretetimeLTIsys.1)Findtheexpressionofforand

2)Sketchthefrequencyresponseof,where

Solution:1）2）zeropolepole三、Appliccation（frequency-responsecompensation）

(inversesys.)

Ifasignalisdistortedbyacausalandstableminimum-phasesystem,itcanbecompensatedbyacascadecausalstablesys.

2.Toanyrationalsystem,themagnitudecanbecompensatedexactly,butthephasecan’t.Example5.15CompensationofanFIRsystem

p283四、Properties(tocausalstablesys.)1.Theminimumphase-lagpropertyProof

Theminimum-phasesystemhastheminimumphaselagamongthesecausalstablesystemswhichhavethesamemagnitude——theminimum-phase-lagproperty()2.Theminimumgroup-delaypropertyProof:3.Theminimumenergy-delayproperty4.Theinversesystemofacausalstableminimum-phasesystemiscausalstable.5.Themagnitude-frequencyresponseofacausalstableminimum-phasesystemspecifi