聲音信號中的分形及混沌特征研究.pdf

1、山東大學碩士學位論文聲音信號中的分形及混沌特征研究姓名：耿淑娟申請學位級別：碩士專業(yè)：信號與信息處理指導教師：劉孝賢20040422山東大學碩士學位論文ABSTRACTn圮chaosandfractaltheoryhavebeenusedtoanalyzethecharactedsticofmusicsignalandexplorethemelodyofitThefracudtheoryisanactivefieldofnonlinea

2、rmathematics，withitsmainobjectthenonsmoothandnondifferentiablearisinginnonlinearsystemsandthemainconstant蠹actaldimensionnlechaosandfractaltheorybelongtononlinearscienceNonlinearscienceisaimingatdiscoveringthecommonproper

3、tybasiccharacteristicandlawsinthisarea，anditiscrossdisciplineTheresearchofnonlinearscienceusuallyinvolvedeepeningoftheconceptsofcertaintyandstochastic，orderanddisordersimplicityandcomplexityquantitativechangeandqualitati

4、vechange，integerandlocal，andthishasgreatlyinfluencedthedevelopmentofnaturalscienceTheprecisedefmifionofchaosishardtomake，sincedifferentsubjecttendtohayedifferentunderstandingIt’Susuallyholdthatchaosbehaviorissomewhatpred

5、icable，andiSthecombinationofcertaintyandstochasticacdonThishasmadechaosphenomenonsensibletotheinitialconditionandveryhardtopredictThoughchaosandfractalarcdifferentinappearance，nleyarebothnonlinearphenomenonandarecloselyr

6、elatedTheybotharisesformPoincarcdynamicalsystemsThechaoticattractorisinessgncefractalset，andthefracta]setisthesetofthosestartingpointsoftheunstableorbitsindynamicalsystemsBesides，thefocusofchaosresearchisthecomplexityapp

7、earingindynamicalsystems，whileinfractalresearch，moreattentionispaidtothestrangeattractorInthispapertheauthorhasanextensiveanddeepstudyaboutchaosandfractaltheoryandtheUSeofwhichintheanalysisofacousticsignalARerbrieflyintr

8、oducedthedefinitionendbasictheoryoffractalandchaoshowtodiscriminatefractaltimeseriesfromnonfractaltimeseriesisdiscussedSeveralparameterssuchasLyapunovexponent，correlationdimension，Poincarcmap，powerspectrumdensityprincipa

9、lcomponentanalysisareusedtecognizeifthetimeseriesarefractalsThereliabilitiesoftheparametersusedabovearccomparedThentheacousticsignalgenemtedbychaoscircuitiSanalyzedFinallythemusicisanalyzedtofindthechaosandfractalinitInt