章兼容保存-信息与通信工程.pptx

Chapter7

AlgorithmsandStructuresforOptimumLinearFiltersmadebyFHY1

AlgorithmsandStructuresforOptimumLinearFilters2Thedesignandapplicationofoptimumfiltersinvolves:Thesolutionofthenormalequationstodeterminetheoptimumsetofcoefficients;Theevaluationofthecostfunctiontodeterminewhethertheobtainedparameterssatisfythedesignrequirements;Theimplementationoftheoptimumfilter,thatis,thecomputationofitsoutputthatprovidestheestimateofthedesiredresponse.[1]ManolakisDG,IngleVK,KogonSM.Statisticalandadaptivesignalprocessing:spectralestimation,signalmodeling,adaptivefiltering,andarrayprocessing[M].Norwood:ArtechHouse,2005.Inthischapter,wepresentdifferentalgorithmsforthesolutionofthenormalequations,thecomputationoftheminimummeansquareerror(MMSE),andtheimplementationoftheoptimumfilter.Preface

3[1]ManolakisDG,IngleVK,KogonSM.Statisticalandadaptivesignalprocessing:spectralestimation,signalmodeling,adaptivefiltering,andarrayprocessing[M].Norwood:ArtechHouse,2005.InSection6.3,weintroducedamethodtosolvethenormalequationsandcomputetheMMSEusingtheposition.Theoptimumestimateiscomputedasasumofproductsusingalinearcombinersuppliedwiththeoptimumcoefficientsandtheinputdata.Thekeycharacteristicofthisapproachisthattheorderoftheestimatorshouldbefixedinitially,andincasewechooseadifferentorder,wehavetorepeatallthecomputations.Suchcomputationalmethodsareknownasfixed-orderalgorithms.7.1FUNDAMENTALSOFORDER-RECURSIVEALGORITHMSAlgorithmsandStructuresforOptimumLinearFilters

4[1]ManolakisDG,IngleVK,KogonSM.Statisticalandadaptivesignalprocessing:spectralestimation,signalmodeling,adaptivefiltering,andarrayprocessing[M].Norwood:ArtechHouse,2005.Whentheorderoftheestimatoresadesignvariable,weneedtomodifyournota