Nonuniform biorthogonal wavelets on positive half line via Walsh Fourier transform

Wavelets associated with Nonuniform Multiresolution Analysis on positive Half-Line

Gabardo and Nashed have studied nonuniform multiresolution analysis based on the theory of spectral pairs in a series of papers, see Refs. 4 and 5. Farkov,3 has extended the notion of multiresolution analysis on locally compact Abelian groups and constructed the compactly supported orthogonal p-wavelets on L(R+). We have considered the nonuniform multiresolution analysis on positive half-line. ...

Fast Approximate Fourier Transform via Wavelets Transform

We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coeecients are dropped and no approximations are made, the proposed algorithm computes the exact result, and its computational comple...

On Biorthogonal Wavelets Related to the Walsh Functions

In this paper, we describe an algorithm for computing biorthogonal compactly supported dyadic wavelets related to the Walsh functions on the positive half-line R+. It is noted that a similar technique can be applied in very general situations, e.g., in the case of Cantor and Vilenkin groups. Using the feedback-based approach, some numerical experiments comparing orthogonal and biorthogonal dyad...

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...

From Fourier Transform to Wavelets