Further Generalization and Approximation of Fractional-Order Filters and Their Inverse Functions of the Second-Order Limiting Form

This paper proposes a further generalization of the fractional-order filters whose limiting form is that second-order filter. new filter class can also be regarded as superset recently reported power-law filters. An optimal approach incorporating constraints restricts real part roots numerator and denominator polynomials proposed rational approximant to negative values formulated. Consequently, stable inverse characteristics achieved using suggested method. Accuracy low-pass, high-pass, band-pass, band-stop for various combinations design parameters evaluated absolute relative magnitude/phase error metrics. Current feedback operational amplifier-based circuit simulations validate efficacy four types designed their functions. Experimental results frequency time-domain performances band-pass its counterpart are presented.