Fractional-Order and Power-Law Shelving Filters: Analysis and Design Examples

Low-pass and high-pass non-integer order shelving filter designs, which are suitable for acoustic applications, are presented in this work. A first design is based on a standard fractional-order bilinear transfer function, while a second one is based on the transposition of the integer-order transfer function into its power-law counterpart. Both transfer functions are approximated using the Oustaloup approximation tool, while the implementation in the case of the power-law filters is performed through the employment of the concept of driving-point impedance synthesis. An attractive benefit is the extra degree of freedom, resulting from the variable order of both fractional-order and power-law filters, which allows improved design flexibility compared to the case of integer-order filters. From the implementation point of view, only one building block is required to realize both filter types, thanks to the employment of the Voltage Conveyor.