Fractal signals

Pence, D.V. and Beasley, D.E. 1995. Multi-fractal signal simulation of pressure fluctuations in a bubbling gas-flu-idized bed. Proceedings of the Sixth International Symposium on Gas-Solid Flows, Hilton Head, SC, August... 

J. Muzy, E. Bacry, Multifractal formalism for fractal signals The structure-function approach versus the wavelet-transform modulus-maxima method, Phys. Rev. E 47 (1993) 875-884. 

A number of promising metal structures for fluorescence signal enhancement have been proposed silver island films (SIFs) that provide about 5-15-fold enhancement [89], fractal-like structures that resulted in stronger enhancements at specific hot spots [90-92], and SIFs deposited on silver or gold films with about 50-fold enhancement [93, 94], Recently, it was found that strong enhancement on a gold film based plasmonic platform may change even the shape of the emission spectrum [95],... 

Figure 7.5 Pb (A) and U (B) background/baseline maps compiled using spatial and spectral analysis (S—A method). The values have been obtained by decomposition of the Pb and U geochemical maps (Fig. 7.1A and B, respectively) into separate components using the fractal filters selected on the S—A plot. Pb background/baseline map is generated only with signals with power spectrum (E) >15,713 (selected cutoff in Fig. 7.6A). U background/baseline map is generated only with signals with power spectrum (E)>706 (selected cutoff in Fig. 7.6B). For both maps pixel values have been reclassified by fractal C—A plot (see text).

Xia et al. (1992) applied this signal analysis method to study the oscillatory behavior of light output signals in a fast fluidized bed. Figure 4-23 shows the typical power spectral density of optic output signals in the fast fluidized bed. The oscillatory behavior of the optic output signals has no characteristic time scale, or a deterministic frequency response, but forms fractal time characteristics. 

G.W. Wornell, A.V. Oppenheim, Wavelet-based representations for a class of selfsimilar signals with application to fractal modulation, IEEE Transformation and Information Theory. 38 (1992). 785. 

Goldberger, A.L. D.R. Rigney. 1989. On the non-linear motions of the heart Fractals, chaos and cardiac dynamics. In Cell to Cell Signalling From Experiments to Theoretical Models, A. Goldbeter, ed. Academic Press, London, pp. 541-50. 

The spatial spectrum of frequencies, F(u,v) is the two-dimensional system consisting of the amplitude signal and the time along each direction. If the surface topography is fi ctal, its spatial spectrum of frequencies shows a linear distribution in the doubly logarithmic system and the surface fractal dimension can be expressed as ... 

Like the sine wave containing only one frequency, white noise signal is the other extreme containing all frequencies of equal amplitudes. As with file sine wave or unit impulse, white noise is an ideal concept. It is a fractal curve any enlargement will just bring up similar curves. It is an interesting excitation waveform, because file system is examined at all... 

The theory of fractal dimension may be used in bioimpedance signal analysis, for example, for studying time series. Such analysis is often done by means of Hurst s rescaled range analysis (R/S analysis), which characterizes the time series by the so-called Hurst exponent H = 2 — D. Hurst found that the rescaled range often can be described by the empirical relation... 

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