منابع مشابه
Wavelets, Fourier Transform, and Fractals
Wavelets and Fourier analysis in digital signal processing are comparatively discussed. In data processing, the fundamental idea behind wavelets is to analyze according to scale, with the advantage over Fourier methods in terms of optimally processing signals that contain discontinuities and sharp spikes. Apart from the two major characteristics of wavelet analysis multiresolution and adaptivit...
متن کاملWavelets, fractals, and radial basis functions
Wavelets and radial basis functions (RBFs) lead to two distinct ways of representing signals in terms of shifted basis functions. RBFs, unlike wavelets, are nonlocal and do not involve any scaling, which makes them applicable to nonuniform grids. Despite these fundamental differences, we show that the two types of representation are closely linked together . . . through fractals. First, we iden...
متن کاملMultiscale representations: fractals, self-similar random processes and wavelets
2 Principles 4 2.1 Fractals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Definition and history . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Fractal dimension . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Hölder exponent and singularity spectrum . . . . . . . . . . . . . 6 2.2 Self-similar random processes . . . . . . . . . . . . . . ....
متن کاملWavelets and differential operators: from fractals to Marr’s primal sketch
Invariance is an attractive principle for specifying image processing algorithms. In this presentation, we promote affine invariance—more precisely, invariance with respect to translation, scaling and rotation. As starting point, we identify the corresponding class of invariant 2D operators: these are combinations of the (fractional) Laplacian and the complex gradient (or Wirtinger operator). W...
متن کاملNotes on Rauzy Fractals
An alphabet A is a finite set of letters. A word is a finite sequence of letters. Denote the set of words by A+. For a word u = u1u2 · · ·un ∈ A+, |u| is called the length of u. For each letter a, we denote by |u|a the number of occurrence of a in u. Full Shifts. Let AZ be the set of all biinfinite sequences of alphabets from A, i.e. AZ = {x = (xi)i∈Z : xi ∈ A, ∀i ∈ Z}. Consider a shifting oper...
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2006
ISSN: 0213-2230
DOI: 10.4171/rmi/452