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一种基于全相位预处理的PMF-FFT改进算法.docx

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一种基于全相位预处理的PMF-FFT改进算法 Title:AnImprovedPMF-FFTAlgorithmbasedonFullPhasePreprocessing Abstract: ThePrincipalCascadeFactor-MultiplyFastFourierTransform(PMF-FFT)algorithmhasshowngreatpotentialinvariousdigitalsignalprocessingapplicationsduetoitsefficientrepresentationofdiscreteFouriertransform(DFT).However,thetraditionalPMF-FFTalgorithmsuffersfromphasedistortionsthataffecttheaccuracyofsignalprocessingtasks.ThispaperproposesanimprovedPMF-FFTalgorithmbyintroducingfullphasepreprocessingtechniques.ThealgorithmenhancesthetraditionalPMF-FFTalgorithmbycompensatingforphasedistortionsinthefrequencydomain,leadingtoimprovedsignalqualityandhigheraccuracyinsignalanalysisandsynthesis. 1.Introduction TheFourierTransform(FT)iswidelyusedinvariousscientificandengineeringapplications,suchasimageandsignalprocessing,communications,andaudiosynthesis.ThetraditionalPMF-FFTalgorithmoffersanefficientsolutionforcomputingDFT,butitdoesnotconsiderthephasecomponents,resultinginphasedistortionsthatimpacttheaccuracyofsignalanalysisandsynthesis.Inthispaper,weproposeanimprovedPMF-FFTalgorithmthatincorporatesfullphasepreprocessingtechniquestomitigatethesedistortions. 2.Background 2.1PrincipalCascadeFactor-MultiplyFastFourierTransform(PMF-FFT)Algorithm ThePMF-FFTalgorithmisavariantoftheCooley-TukeyFFTandisknownforitsreducedmultiplicationsandadditionscomparedtothetraditionalFFTalgorithm.ThePMF-FFTalgorithmcomputestheDFTofasequencebydecomposingitintotwosmallersubsequencesanditerativelycombiningtheirDFTsusingtheprincipalcascadefactor. 3.TheImprovedPMF-FFTAlgorithm 3.1FullPhasePreprocessing InthetraditionalPMF-FFTalgorithm,thephaseinformationisdisregardedduringthecomputation,leadingtophasedistortions.Theimprovedalgorithmincorporatesfullphasepreprocessingtechniquestocompensateforthesedistortions.Itanalyzesthephaseinformationoftheinputsignalbyapplyingaphaseshiftingmethodtoeachfrequencybininthefrequencydomain.Bycapturingandcorrectingthesephasedistortions,theimprovedalgorithmensuresmoreaccuratesignalanalysisandrec