Time-frequency localization of compactly supported wavelets
نویسنده
چکیده
Two items will be presented in the talk. The rst one is modiication of classic Daubechies compactly supported wavelets preserving localization in time with the growth of smoothness. The second one is nonstation-ary wavelets with the use of scaling lters that vary from one scale to the next ner one. Wavelets are a tool for decomposing functions in various applications. It is closely connected with transforms in signal processing subband coding algorithms, multiresolution transform in computer vision. Local-ization in time and frequency of wavelets are of main signiicance for applications. A function 2 L 2 R is called a stationary or-thonormal wavelet if its normalized, translated dilates jk t : = 2 j=2 2 j t , k; j; k 2 Z t 2 R; form an orthonormal basis for L 2 R. In the wavelet theory the localization of ' is characterized by the radius of autocorrelation function t : =
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