简介:ThispaperpresentsamethodforthecomputationoftheStokesfor-mulausingtheFastHartleyTransform(FHT)techniques.Thealgorithmismostsuitableforthecomputationofrealsequencetransform,whiletheFastFourierTransform(FFT)techniquesaremoresuitableforthecomputatonofcomplexse-quencetransform.Amethodofsphericalcoordinatetransformationispresentedinthispaper.Bythismethodtheerrors,whichareduetotheapproximatetermintheconvolutionofStokesformula,canbeeffectivelyeliminated.Somenumericaltestsaregiven.ByacomparisonwithbothFFTtechniquesandnumericalintegra-tionmethod,theresultsshowthattheresultingvaluesofgeoidalundulationsbyFHTtechniquesarealmostthesameasbyFFTtechniques,andthecomputation-alspeedofFHTtechniquesisabouttwotimesfasterthanthatofFFTtechniques.
简介:DHToflengthplq(pisoddandqisarbitrary)isturnedintoplDHTsoflengthqandsomeadditionaloperations,whiletheadditionaloperationsonlyinvolvesthecomputationofcos-DFTandsin-DFTwithlengthp.IfthelengthofaDHTisp1l1…PNlN2l(P1…,PNareoddprimes),afastalgorithmisobtainedbythesimilarrecursivetechnique.Therefore,thealgorithmcancomputeDHTofarbitrarylength.ThepaperalsoProvesthatoperationsforcomputingDHToflengthNbythealgorithmarenomorethanO(Nlog2N),whenthelengthisN=pl,operationsofthealgorithmarefewerthanthatofotherknownalgorithms.