Transcription of Wavelet Transforms in Time Series Analysis - UMD
{{id}} {{{paragraph}}}
Example: bachelor of science
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.
Construction of Wavelets • We consider here only orthogonally/compactly supported wavelets - Orthogonality means: Z∞ −∞ ψj k(x)ψ j′ k′(x)dx= δkk′δjj′ • Wavelets are constructed from scaling functions, φ(x) : φ(x) come from the dilation equation: φ(x) = X k ckφ(2x−k) ck: Finite set of filter coefficients • General ...
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: