We consider specific features of the discrete Fourier transform for signals constructed through multiplicative and additive iterative procedures. It is shown that - in spite of the rather different structure of multiplicative and additive signals - the Fourier transforms of both types of signals exhibit the property of self-affinity. The power spectra of additive signals produced by different generating vectors have similar forms and can be divided into similar branches. The number of branches depends on the generation level and the symmetry of the power spectrum of the generating vector.
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