A procedure to Estimate the Fractal Dimension of Waveforms
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AbstractIderivedamethodforcalculatingtheapproximatefractaldimension(D)fromasetofN valuesy sampledfromawaveformbetweentimezeroandt max withsamplinginterval. Thewaveformwassubjectedtoadoublelineartransformationthatmapsitintoaunitsquare. Thenormalizedabscissaofthesquareisx *i andthenormalizedordinateisy *i ,bothofthemdefinedasx *i =x i x max y *i =y i y min y max y min wherex max isthemaximumx i andy min andy max aretheminimumandmaximumy i . Thefractaldimensionofthewaveform( )isthenapproximatedbyD as ˇ D= 1 +ln(L)ln(2 N')whereL isthelengthofthecurveintheunitsquareandN 0 = N 1. * ThisworkwasoriginallypublishedinComplexityInternational,anon-linejournal. Sinceitspublication,thejournalbecameinactive, andseveralsymbolsbecamecorruptedon-line. AccordingtoComplexityInternational, theauthorisalwaystheownerofthearticle’scopyrightaslongastheidentificationofComplexityInternationalappearsinthecopies.SeveraltyposarecorrectedinthisversionuploadedtoarXiv. ** Email: csevcik@ivic.gob.ve 1 arXiv:1003.5266v1 [nlin.CD] 27 Mar 2010
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C. Sevcik
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