Daubechies wavelets

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  • These are not the same as the orthogonal Daubechies wavelets, and also not very similar in shape and properties.
  • They are a modified version of Daubechies wavelets with increased symmetry.
  • This is usually a poor approximation, whereas Daubechies wavelets are among the simplest but most important families of wavelets.
  • The Daubechies wavelets are not defined in terms of the resulting scaling and wavelet functions; in fact, they are not possible to write down in closed form.
  • Daubechies wavelets are widely used in solving a broad range of problems, e.g. self-similarity properties of a signal or fractal problems, signal discontinuities, etc.
  • While software such as Mathematica supports Daubechies wavelets directly a basic implementation is simple in MATLAB (in this case, Daubechies 4).
  • Because the Daubechies wavelets have a compact support, the Hamiltonian application can be done locally which permits to have a linear scaling in function of the number of atoms instead of a cubic scaling for traditional DFT software.
  • The Daubechies wavelets, based on the work of Ingrid Daubechies, are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support.
  • Orthogonal wavelets -- the Haar wavelets and related Daubechies wavelets, Coiflets, and some developed by Mallat, are generated by scaling functions which, with the wavelet, satisfy a quadrature mirror filter relationship.