Macroscopic 1/f behavior of fractal signals generated by additive substitution
We analyze the structure of the discrete Fourier transform of a particular class of self-similar discrete signals which are iteratively generated by an additive substitution procedure, starting from a finite generator sequence. The amplitude spectra of such signals obtained from different generators have a similar form. The amplitude spectrum contains several affine branches, the number of which depends on the iteration level, on the size of the generator, and on the spectrum's symmetry. It has a macroscopic 1/f-characteristic.
discrete fourier transform deterministic fractal signals 1/f-behavior scaling behavior