Wavelets, Fractals, and Fourier TransformsM. Farge, Julian C. R. Hunt, J. C. Vassilicos Many of the recently developed mathematical techniques used to describe complex algebraic functions and analyze empirical continuous data have been derived from a wide range of signal data from such sources as turbulent flows and oil well logs. Probably the most important and rapidly developing of these techniques involve Fourier methods, fractals, and wavelets. This important collection of essays provides a useful introduction to the mathematics of wavelets, fractals, and Fourier transforms, and to their many applications. The book emphasizes throughout how the different methods of analysis expose very different aspects of complex signals and surfaces, and that the most suitable method of analysis often depends on the application under consideration. It will be of significant interest to researchers, teachers, and students involved in pure and applied mathematics. |
Contents
Section | 1 |
Wavelets Fractals and OrderTwo Densities by K J Falconer | 39 |
Algorithms and Applications | 47 |
Copyright | |
19 other sections not shown
Common terms and phrases
algorithm amplitude analysing wavelet bandwidth Barnsley bases basis functions behaviour cascade cells computed consider constant continuous wavelet transform convergence correlation curve Daubechies decomposition defined density derived described detection dilated dimensional discrete distribution dynamical energy equation example filter banks finite fluid Fourier transform fractal dimension frequency bands Gabor galaxies Gaussian Gibbs Phenomenon given H-fractal H₁(z Hausdorff Hausdorff dimension Ho(z IFSS increase integral interface Iterated Kolmogorov capacity length linear maps Mathematics measure method Morlet multifractal multiresolution analysis natural scenes neurons noise nonlinear orthogonal overshoot parameters particles phase spectrum pixel power spectrum properties random range receptive field representation sample scale invariant scale space self-similar shown in Figure shows signal singularity space and frequency spatial spectra spiral statistical structure theorem tion two-dimensional Vassilicos velocity visual system vortex vortices waveform wavelet coefficients zero