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