Frequency Content Preservation in Fractional Multi-Frequency Oscillators Despite Reducing the Number of Energy Storage Elements

Recently, a class of fractional multi-frequency oscillators, constructed based on using n integrators and n half-order ones, has been introduced, whose steady-state responses contain sinusoidal components with 0.5 ( 3 n - 1 ) number of selectable frequencies. In this paper, the structure of the introduced multi-frequency oscillator is modified such that, notwithstanding the frequency content preservation, the number of its involved integrators is reduced. With no effect on the frequency content of the generated oscillations, this modification causes that the circuitry implementation of the considered class of multi-frequency oscillators can be done with a less number of energy storage elements.