Fractional-Order Filter Design

Abstract One of the advantages of fractional order is the extra degree of freedom added by the fractional-order parameters, which enrich the analysis with more details in new dimensions. This chapter introduces factional-order conventional filters of orders α, 2α, and 3α. The general transfer functions of continuous-time filters (low-pass, high-pass, and band-pass filters) to the noninteger-order (fractional-order) domain are investigated. Also, mathematical expressions for the maximum and minimum frequencies, the half power frequencies, and the right-phase frequencies are derived. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced. Numerical spice results are introduced to validate the theoretical findings. Several passive and active filters are studied to validate the concept. This chapter also investigates the effect of an inserted delay parameter on the filter main frequencies. Different filter responses are obtained from the general delayed transfer function. Two delay examples are investigated.