State Space Representation of Fractional-Order Low-Pass Filters

The attenuation of standard analog low pass filters for low frequencies is an integer multiple of -20 dB/dec. In order to attain intermediate values of roll-off factors, such as -10 dB/dec, it would be required to employ a fractional order filter. Fractional order filters have an infinite dimensional representation and thus finite dimensional approximations are computed through the decomposition of fractional order low pass filters into a weighted sum of standard analog one-pole filters. The optimum weights and the positioning of poles are computed using optimization strategies. The acquired weights and poles are laid out into a state space representation as it is a uniform platform for representing time-varying systems, linear systems as well as nonlinear systems. The magnitude and phase response of the fractional order filters are represented through Bode plots.