Design of fractional-order analog Type-I Chebyshev filter

In this paper, fractional-order Type-I Chebyshev filter is designed in complex w-plane instead of complex s-plane by considering the poles in under-damped, hyper-damped, ultra-damped plane. This is the first attempt to design fractional-order Chebyshev filter in complex w-plane. The stability analysis in w-plane is discussed in this paper. Mathematical formulae for the calculation of order of filter and pole locations are derived. The proposed method is used to design fractional-order Chebyshev filter for a given set of specifications. From the results presented, it is observed that fractional-order Type-I Chebyshev filter gives better performance as compared to its integer-order counterpart for the same set of specifications.