数字信号处理英文版课件：3-3 Frequency Response for Rational System Function

§3.3FrequencyResponseforRationalSystemFunction一、Frequencyresponseandzero/poleRationalsystemfunction:Frequencyresponse:1.magnituderesponse(orlogmagnituderesponse)magnituderesponse

logmagnituderesponse

GainindBAttenuationindB=-GainindB【Note】toasingle-zero/polesystem(i.e.isnearertounitcircle）,thevalleyissharper.2.When,(i,.e.),then（i.e.,then3.,isnearertounitcircle）,thepeakissharper.When4.Thezerosorpolesattheoriginhasnoeffecton

1.Themagnitudechangewith.When,theisshortest,thengetavalley.whentheisshotest.thengetapeak2.PhaseresponseandgroupdelayContinuousphase:Groupdelay:Example:singlezerosystemM=1,N=0【Note】Ifthezeros(orpoles)occuronunitcircle,thephasejump.

Zero（orpole）,thephasearoundor）hasasteepandpositiveslop.

（orpole）,theslopeissteeper.Example

first-orderdifferenceequationSolution:Example5.8

p2651)magnitude:

2)phase:

ExampleExample

sketchthemagnitudeof

Solution:二、RelationshipbetweenmagnitudeandphaseIngeneral,thereisnoconstraintbetweenmagnitudeandphase.However,forsystemswithrationalsystemfunctions,thereissomeconstraintbetweenmagnitudeandphase.Ifthemagnitudeisgiven,andthenumbersofzerosandpolesareknown,thepossiblechoicesofcorrespondingphasearefinite,andviceversa.(exampleP2715.11)Tolinearconstantcoefficientdifferenceequationandarepolesof,Whereand

Ifandarezerosof,Whereand

conjugatereciprocal共轭倒数

1)AssumeH(z)bereal,zeros(andpoles)eitherarerealoroccurincomplexconjugatepairs.2)Toacausalandstablesystem,allthepolesareintheunitcircle.3)Toaminimum-phasesystem,allthezerosareinsidethe