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基于CORDIC算法的高速ODDFS电路设计.docx

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基于CORDIC算法的高速ODDFS电路设计 Introduction Thehigh-speedODDFS(OddFunctionSynthesis)circuitisdefinedasacircuitthatsynthesizesasignalwhoseFouriercoefficientsareoddfunctionsofthefrequencyindex.TheCORDIC(COordinateRotationDIgitalComputer)algorithmisamethodusedtoefficientlycalculatetrigonometricandhyperbolicfunctions.Thispaperfocusesonthedesignofahigh-speedODDFScircuitbasedontheCORDICalgorithm. CORDICAlgorithm TheCORDICalgorithmisaniterativealgorithmusedtocalculatetrigonometricandhyperbolicfunctions.Itoperatesbyiterativelyrotatingavectortoapproachadesiredangle.Thevectorisinitializedtothedesiredangle,andeachiterationrotatesthevectorbyananglethatisprecomputedbasedonthedesiredangleandthecurrentiteration.Theprecomputedanglesarestoredinalookuptable,andtherotationisperformedusingonlyshiftandaddoperations. TheCORDICalgorithmhasseveraladvantages,includinghighspeed,lowhardwarecomplexity,andflexibilityinthechoiceofalgorithmparameters.Itiscommonlyusedindigitalsignalprocessingapplicationssuchasfilterdesign,signalgeneration,andimageprocessing. High-SpeedODDFSCircuitDesign Thehigh-speedODDFScircuitcanbedesignedusingtheCORDICalgorithmbyutilizingthefactthattheFouriercoefficientsofoddfunctionsarepurelyimaginary.TheimaginarycomponentoftheFouriercoefficientcanbeobtainedbycalculatingthesineofthecorrespondingangle.TheCORDICalgorithmcanbeusedtoefficientlycalculatethesineoftheangle. TheODDFScircuitcanbeimplementedasaseriesofCORDICunits,whereeachunitcalculatesthesineofaspecificangle.TheinputtothecircuitisadigitalsignalthatrepresentsthefrequencyindexofthedesiredFouriercoefficient.TheoutputofthecircuitisadigitalsignalthatrepresentstheimaginarycomponentoftheFouriercoefficient. Thedesignofthehigh-speedODDFScircuitinvolvesseveralconsiderations,includingthechoiceofCORDICalgorithmparameters,theprecisionoftheinputandoutputsignals,andtheoptimizationofhardwareresources.ThechoiceofCORDICalgorithmparametersdependsonthedesiredaccuracyofthecircuitandtheavailablehardwareresources.Theprecisionoftheinputandoutputsigna