高级变换方法小波andy watson 14 wavelets arw compatibility mode14.pdfVIP

TheWaveletTransform

Whatisa“Wavelet”?

••aa“smallsmallwavewave”ororaa

“wavepacket”.

Wecanmakeafamilyof

waveletsby:

•scalingandshiftinga

baseormotherwavelet

••totocreatecreatedaughterdaughter

wavelets(sometimes

calledbabywavelets)Samewavelet,

jjustscaledandtime-shifted

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WaveletsinApplication

•Newwayofevaluatingandprocessingsignals

•Worksonnonstationarydata

•Usefulinmanytypesofapplications

–Patternrecognition

•Biotech:Biotech:distinguishdistinguishnormalnormalfromfrompathologicalpathologicalmembranesmranes

•Biometrics:facial/corneal/fingerprintrecognition

–Featureextraction

•Metallurgy:characterizationofroughsurfaces

–Trenddetection:

•Finance:Finance:exploringexploringvariationvariationofofstockstockpricesprices

–Perfectreconstruction

•Communications:wirelesschannelsignals

–compression–JPEG2000

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TheWavelet

•Considerscalingandtranslatingthefunctionψ

⎛t−b⎞

ψψ(())ψψ

t→⎜⎜⎟⎟

⎝⎝a⎠⎠

•adeterminesthecentrefrequency.

•bbdeterminesdeterminesthethetranslationtranslation.

•Timefrequencycentreofψ(t−b)/a()

areb(timecentre)

ω/aωismeanfreqofψ

and(frequencycentre)

1tb−