Design and Implementation of Power Law Filters

A new class of non-integer order filters, realized without considering a fractional Laplace operators is presented in this paper. An efficient method of curve fitting allows the transposition of the fractional order transfer function into the integer order domain, yielding the desired behavior of the filter in the frequency domain. Then, using standard integer-order filtering techniques, a rational integer-order transfer function can be obtained for simple implementation. Unlike what this approach suggests, these filters are not subject to the implementation requirements for fractional-order items. A number of simulations, a comparison with prior research, and real-world examples are provided to demonstrate the effectiveness of these designs.