ELEM018 Advanced Transform MethodsLab 2: The Wavelet Transform (2 w eeks)Name:SuiLuyiQMNumber:jp0927921.1.ObjectivesObjectives2.2.IntroductionIntroduction3.3.ExercisesExercises3.1DiscreteWavelet Transform FilterBankQuestion:Explainhow thisMatlab functionw orks and check that itimplementsthe recursionformulassimilar∑−=−iimnmcnihc,0,1]2[2to∑−=−ijmnmcnihd,1,1]2[2and (Arethe filtersh0 and h1 inthe Matlab code exactlythe same filtersas h0 and h1 inthese formulas?Explainanydifference(s)youdiscover).Answ er:The functionisiterationfunction.At firstthe functionw illcheck validationof theinput.Then the functionw illgenerate tw o sequences low pass_c=conv(h0,c)andhipass_c=conv(h1,c),theyare convolutionof the inputsequencec w ithhigh-passfilterh1 and low -passfilterh0.Then itw illsubsamplethe sequences w ithfactor of 2 w ithacoefficient2astheformulad1=sqrt(2)*hipass_c(2:2:end)andc1=sqrt(2)*low pass_c(2:2:end).The resultd1 ishighfrequencypart,itw illbe putback inthe outputsequence.The resultc1 islow frequencypart,itw illbe took as inputsequenceof the nest iteration.Forthe formularh0 =[1/21/2]and h1 =[1/2-1/2].Inthe codeh0 isthe same,h1 isinversed.Sciencethe functionneeds to do the convolutionineach iteration,itw illgetthe same resultas the formulasdo .3.2InverseDWTFilterBankQuestion:Explainhow thisMatlab functionw orks,and check that itimplementsa recursionformulasimilarto:⎟⎠⎞⎜⎝⎛−+−∑∑−−=iiimimnmdinhcinhc,11,10,]2[]2[2Answ er:Atfirst,it shou ldmakesu rewhetherthe inpu tsequ enceis validandwhetherthe iterationat the endstep.Accordingto the formu lar,itwillgeneratethe filterkernelandprocessthefirsthalfin the nextiteration.Andthen ,it willu p-samplethe twopartsofthe sequ encewithzero.Bycalcu latingthe convolu tionofthe filterkernel,itcanfilterthe signal.Finally,itwilltakethe twopartstogetherwiththe coefficientof 2 andtake...
