the manifold joys of conformal mapping外语英文电子书

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1、ManifoldJoysofConformalMappingJamesA.MoorerTheManifoldJoysofConformalMapping:ApplicationstoDigitalFilteringinthendStudio–2TryJamesA.MoorerThisisaneditedversionofapaperthatappearedintheJournaloftheAudioEngineeringSociety[1].Manytyposhavebeencorrected,andsomesupplementarymate

2、rialhasbeenadded.IthasalsobeencombinedwithanIEEEarticle[2]thatalsoinvolvesconformalmapping.Abstract:Conformalmappingisawell-knowntechniqueformodifyingthecut-offorresonantfrequenciesoffilters.Conformalmappingisappliedtotheproblemofdigitalfiltersforprofessionalaudioproduction

3、.Methodsareexaminedforcomputingthecoefficientsofpresencefilters,suchasparametricequalizerswithorwithoutshelving,andofband-passorband-rejectfilters.Formulasaregivenforthecoefficientsofthesefiltersintermsofthespecifications(centerfrequency,boost/cut,andsoon),whichareexactandr

4、elativelystraightforwardtocompute.Anewkindofshelvingfilterisintroducedthatisequirippleinthepassbandsandcanhaveanarbitrarilynarrowtransitionband(withincreasingfilterorder).IntroductionEverystudiomixingdeskhasafiltersectionforeachandeverychannel.Thesegofromthesimplestbass-tre

5、blecontrolstosophisticatedparametricboost/cutfilters.Alsoquitepopularas“outboard”equipmentaregraphicequalizersandhigh-orderband-stopandnotchfilters.Withthecomingofdigitalaudioitseemscertainthatthemixingdesksofthefuturewillhavetorealizeallthesefunctionsentirelyinthedigitaldo

6、main.Torealizesomeoftherealadvantagesofdigitalcontrol(precisionandrepeatability),thecharacteristicsofsuchfiltersmustbeverywellunderstood,andtheirdesignformulasmustbeexactandexplicit.Inthispaper,wegooversomeofthemostcommonstudiofilters(andsomeratheruncommonones)anddevelopdes

7、ignequationsforeachofthem.Theseequationswillallowtheimplementertocalculateexactlythefiltercoefficientsforthedesiredcharacteristics.Asecondrunningthemeinthepaperisconformalmapping.Weusethismappingasatoolfordecomposingtheproblemoffilterdesignintoindividualstagesofwhicheachone

8、istractable.Sincemanyofthereaderswillnotbefamiliarwiththistechnique,itisexploredin