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Real-Time Simulation of a Family of Fractional-Order Low-Pass Filters

This paper presents a family of low-pass filters, the attenuation of which can be continuously adjusted from 0 decibel per octave (filter is a unit gain) to -6 decibels per octave (standard one-pole filter). This continuum is produced through a filter of fractional-order between 0 (unit gain) and 1 (one-pole filter). Such a filter proves to be a (continuous) infinite combination of one-pole filters. Efficient approximations are proposed from which simulations in the time-domain are built.

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