Transcription of Wavelet Transforms in Time Series Analysis - UMD
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Wavelet Transforms in Time Series Analysis - UMD
Wavelet Transforms in Time SeriesAnalysisAndrew TangbornGlobal Modeling and Assimilation Office, Goddard Space Flight Fourier What is a Wavelet ?3. Continuous and Discrete Wavelet Transforms4. Construction of Wavelets through dilation Example - Haar wavelets6. Daubechies Compactly Supported Data compression, efficient Soft Continuous Transform - Morlet Wavelet10. Applications to approximating error correlationsFourier Transforms A good way to understand how wavelets work and why they are useful is bycomparing them with Fourier Transforms . The Fourier Transform converts a time Series into the frequency domain:Continuous Transformof a function f(x): f( ) = Z f(x)e i xdxwhere f( ) represents thestrengthof the function at frequency , where Transformof a function f(x): f(k) = Z f(x)e ikxdxwherekis a discrete discrete dataf(xj),j= 1,..,N fk=NXj=1fje( i2 (k 1)(j 1)/N) The Fast Fourier Transform (FFT) iso(NlogN) : Single Frequency Signalf(t) = sin(2 t)012345678910 1 Coefficient Imaginary CoefficientFourier Transform Discrete Fourier Transform (DFT) locates the single frequency and re-flection.
Wavelet Transforms in Time Series Analysis Andrew Tangborn Global Modeling and Assimilation Office, Goddard Space Flight Center Andrew.V.Tangborn@nasa.gov
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