Radix-4 FFT versus Radix-2

a simple way of looking at a radix-4 FFT is to think of one radix-4 butterfly as containing 4 radix-2 butterflies; 2 butterflies in one pass ... SignalProcessingStackExchangeisaquestionandanswersiteforpractitionersoftheartandscienceofsignal,imageandvideoprocessing.Itonlytakesaminutetosignup. Signuptojointhiscommunity Anybodycanaskaquestion Anybodycananswer Thebestanswersarevotedupandrisetothetop Home Public Questions Tags Users Companies Unanswered Teams StackOverflowforTeams –Startcollaboratingandsharingorganizationalknowledge. CreateafreeTeam WhyTeams? Teams CreatefreeTeam Teams Q&Aforwork Connectandshareknowledgewithinasinglelocationthatisstructuredandeasytosearch. LearnmoreaboutTeams Radix-4FFTversusRadix-2 AskQuestion Asked 9years,2monthsago Modified 4years,2monthsago Viewed 14ktimes 10 $\begingroup$ Isaradix-4implementationfasterthanaequivalentlywellcodedradix-2FFT?Andifso,whywoulditbefaster? fft Share Improvethisquestion Follow askedJul15,2013at5:44 hotpaw2hotpaw2 34k77goldbadges4444silverbadges8888bronzebadges $\endgroup$ Addacomment  |  4Answers 4 Sortedby: Resettodefault Highestscore(default) Datemodified(newestfirst) Datecreated(oldestfirst) 6 $\begingroup$ Itdepends.Theoreticallyyoucansaveafewmultiplieswitharadix-4asradix-4hasa1/4ththenumberofbutterfliesand3mpy+8addsperbutterfly(ifproperlystructured)andtheradix2has1mpy+2addsperbutterfly. Sointermsofmultipliesit'sabitbetter,howeverthereishighercomplexityintermsofcodestructure,exceptionhandling,coefficientmanagement,registermanagement,digit-reverseaddressing,etc. Soit'sonlyanadvantageifthenumberofmpyisthelimitingfactorwhichformosthardwarethesedaysisnotthecase. Share Improvethisanswer Follow answeredJul15,2013at13:09 HilmarHilmar 33.7k11goldbadge2323silverbadges5353bronzebadges $\endgroup$ Addacomment  |  2 $\begingroup$ here!youcanfindanexplanationofthemaindifferencesbetweenthetwoalgorithmsfortheFFT. Attheendofthedocumenttherearesometablesinwhichisitpossibletonotethat,ifthesizeofthedataincreases,theperformanceoftheradix-4fftarebetterthantheradix-2. Share Improvethisanswer Follow answeredApr11,2016at10:33 Leos313Leos313 12133bronzebadges $\endgroup$ Addacomment  |  2 $\begingroup$ asimplewayoflookingataradix-4FFTistothinkofoneradix-4butterflyascontaining4radix-2butterflies;2butterfliesinonepassand2butterfliesinthefollowingpass.andthetwiddlefactorsarethesameexceptthecomplextwiddlefactorforthethebutterfliesareoffbyaphasedifferenceof$\frac{\pi}{2}$.butallthatmeansisswapping$\sin(\cdot)$with$\cos(\cdot)$andswappingsomeplusandminussigns.soyourradix-4FFTalgonlyneedstoreadinthe4complexvaluesonce,loadinthecomplextwiddleonce,doabunchofarithmetic,andstorethe4resultsonce.youdooneradix-4passandyouaccomplishthesametaskastworadix-2passes. thenetnumberofmultiplicationsandadditionsithinkarethesame,buttheradix-4butterflycanbealldoneintheprocessorregisterbank(ithinkthereareabout16differentfloating-pointregistersandyouneed8fortherealandimagpartsofthe4values,2registersforthesinandcosinetwiddles,andmaybesomeotherregisterortwoforscratch).thisisfasterthandoingitinmemory. Share Improvethisanswer Follow editedJun28,2018at17:49 answeredJun27,2018at0:01 robertbristow-johnsonrobertbristow-johnson 17.1k44goldbadges3030silverbadges6868bronzebadges $\endgroup$ Addacomment  |  -2 $\begingroup$ Inradix2,thenumberofsampleisintermsofpowerof2powerbutinradix4thenumberofsamplesbelongisapowerof4. Share Improvethisanswer Follow editedJun26,2018at11:04 tobassist 80655silverbadges1818bronzebadges answeredJun22,2018at23:11 user36410user36410 1 $\endgroup$ 1 1 $\begingroup$ Iwouldsuggestexplainingwhythathasaneffectonalgorithmspeed,whichisnotobviousfromtheexponentvalue. $\endgroup$ – MBaz Jun23,2018at0:12 Addacomment  |  YourAnswer ThanksforcontributingananswertoSignalProcessingStackExchange!Pleasebesuretoanswerthequestion.Providedetailsandshareyourresearch!Butavoid…Askingforhelp,clarification,orrespondingtootheranswers.Makingstatementsbasedonopinion;backthemupwithreferencesorpersonalexperience.UseMathJaxtoformatequations.MathJaxreference.Tolearnmore,seeourtipsonwritinggreatanswers. Draftsaved Draftdiscarded Signuporlogin SignupusingGoogle SignupusingFacebook SignupusingEmailandPassword Submit Postasaguest Name Email Required,butnevershown PostYourAnswer Discard Byclicking“PostYourAnswer”,youagreetoourtermsofservice,privacypolicyandcookiepolicy Nottheansweryou'relookingfor?Browseotherquestionstaggedfftoraskyourownquestion. TheOverflowBlog IspenttwoyearstryingtodowhatBackstagedoesforfree Aserialentrepreneurfinallyembracesopensource(Ep.486) FeaturedonMeta PlannedmaintenancescheduledforWednesday,21September,00:30-03:00UTC... RecentColorContrastChangesandAccessibilityUpdates Linked 4 Radix-2vsRadix-4FFT Related 9 radix-4FFTimplementation 3 Whyexactlyisabit/radixreverserequiredwhencalculatingthefft? 2 Logicforbitgrowthinradix-2fft 1 HowRadix-8andRadix-2^3arerelated 0 FFTAlgorithm:SplitRadixvsRadix-4 1 Bit-reversalequivalenceonIFFT(radix-2Cooley-Tukey) 0 FFT-mixedradix-bitreversal 0 Nonradix-2FFThardwareimplementation:zero-paddingvscustomalgorithms 4 Radix-2vsRadix-4FFT 0 Whynotuse'higherpowerof2'radixFFT? HotNetworkQuestions CanTempleoftheGodsbecastonasmallfloatingareaatsea? Cananyonetellmethenameofabookaboutaboywithanamberringwhoaccidentallykillsaboywithitandeventuallyturnsouttobeachaosgod Whyisthe-eoptionnotinthebashcommandmanual? IsEPSGdefinedseparatelyforeachgeometrycolumn? Roadsiderepair:howtouseascrew-onPrestapumponatubewitharemovablevalvecore Dobasiclandcardsenterthebattlefieldtapped? Weredoctorswhoweredraftedinthe1950/1960years,compelledtotakeanofficer'soathofallegiance? LTspicecapacitorbug? Isitacrimeto"steal"yourownmoneyfromabank? Whatisthisdiskettedrive? Notesnotaddinguptotimesignature,withweirdwhiteovalnote IsitachievabletokeepallofHalacha? InwhichtournamentdidKarpovplayhisfirstmovewithwhitepiecesandofferadraw? Scholarshipsbyemailingprofessors SelectiveCaesarCipher Howtogetsharperedgesinrenderings? RemedyforElectriciansLargeHolesinStuds Whendoesthe'duration'ofadelayedspellbegin? CurrencyexchangerateinParis AsaPhDstudentintheoreticalphysics,whatfractionofmytime(ifany)shouldIspendonbackgroundmaterialratherthanmyresearchproblem? PhDinaprobablyhopelessresearchproject Possibleexplanationsforabnormalday/nightcycle? CanmyUKcompanyordermetojoinasocialevent? Canameteorshowerhaveaintervalgreaterthan1year? morehotquestions Questionfeed SubscribetoRSS Questionfeed TosubscribetothisRSSfeed,copyandpastethisURLintoyourRSSreader. Yourprivacy Byclicking“Acceptallcookies”,youagreeStackExchangecanstorecookiesonyourdeviceanddiscloseinformationinaccordancewithourCookiePolicy. Acceptallcookies Customizesettings