快速抗混叠傅立叶变换方法的误差分析(英文)

作者:刘开培;李俊娥;黄天戍;何承波 刊名:仪器仪表学报 上传者:纪艳

【摘要】本文对快速抗混叠傅立叶变换算法 (FAFT)进行了误差分析 ,给出了它的误差估计。当用二次多项式分段逼近时 ,其频谱误差估计结果为 M2 4(TN) 3,其中 M为变换区间内被变换函数的三阶导数的最大值 ,N为样本数 ,T为变换区间

全文阅读

1IntroductionWhenananalogsignalissampledandtransformedtodigitalsignals,errorswillresultsuchastruncatederrors,leakageerrorsandaliasingerrors.TheseerrorscanbecontributedtotheviolationofShannonsamplingtheoremofband-limitedsignal.Thesamplingtheoremforpolynomialinterpolation[4,5]turnsouttobeequivalenttoShannonsamplingtheoremwhensamplingrateisinfinite.Obviously,itisimpossibleforpolynomialInterpolationtoeliminateabsolutelytheerrorsmentionedabove.IfthefunctionisexpandedorinterpolatedbyLagrangepolynomialorTaylorpolynomial,itdoesn'tmeanthattheexpandedformswouldbeconvergenttotheprimaryfunction.Tosatisfytheconvergentcondition,theinterpolationmustobeysomerules[58].FromtheerrorsofLagrangepolynomialorTaylorpolynomial,thehighertheorderofthepolynomialis,thefewertheerrorswillbe.Ingeneral,highorderinterpolationandexpandedformareseldomused.Increasingsamplingpointscanmaketheinterpolationfunctionapproachtheinterpolatedfunctionininterpolationpoint,butthevaluesofthefunctionbetweentwoadjacentpointsmaynotapproachtheprimaryfunctionaccurately,andthedifferencecanevenbeverylargesometimes.Fromtheroundingerrorsalittlevarietyofthefunction'svalueswillleadtogreatchangesinthehighorderdifferenceequationforequalintervalpoints.Oneusedtodividethefunctioninseveralintervalstointerpolatesothattheinterpolationerrorsarelessthandesiredone[7,8].TheFastAnti-aliasFourierTransform(FAFT)[1,2,3]employsthismethodtoapproachtheintegratefunctionanddealswithitinFouriertransform.Thepracticalapplicationsshowthatthisapproachcanmakethe

参考文献

引证文献

问答

我要提问