We analyze the structure of the discrete Fourier transform of a particular
class of self-similar discrete signals which are iteratively generated by a
n additive substitution procedure, starting from a finite generator sequenc
e. The amplitude spectra of such signals obtained from different generators
have a similar form. The amplitude spectrum contains several affine branch
es, 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-charact
eristic.