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Introduction to Wavelet - Computer Science

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Workshop 118 on Wavelet Application in Transportation Engineering, Sunday, January 09, 2005Fengxiang Qiao, Texas Southern UniversitySSA1D1A2D2A3D3Introduction to Wavelet A TutorialTABLE OF CONTENTTABLE OF CONTENTOverviewHistorical DevelopmentTime vs Frequency Domain Analysis Fourier Analysis Fourier vs Wavelet TransformsWavelet Analysis Tools and SoftwareTypical ApplicationsSummary ReferencesOVERVIEWOVERVIEWWavelet A small waveWavelet Transforms Convert a signal into a series of wavelets Provide a way for analyzing waveforms, bounded in both frequency and duration Allow signals to be stored more efficiently than by Fourier transform Be able to better approximate real-world signals Well-suited for approximating data with sharp discontinuities The Forest & the Trees Notice gross features

♥Main branch leading to wavelets ♥By Joseph Fourier (born in France, 1768-1830) with frequency analysis theories (1807) From the Notion of Frequency Analysis to Scale Analysis ♥Analyzing f(x) by creating mathematical structures that vary in scale Ø Construct a function, shift it by some amount, change its scale, apply that

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