Distributed-Order Fractional Signal Processing

Abstract

AbstractChapter 7 studies the impulse response functions of the distributed-order integrator/differentiator, fractional-order distributed low-pass filter, and the fractional-order distributed parameter low-pass filter from the complex path integral expressed in the definite integral form. Based on these results, we obtained some asymptotic properties, and we can accurately compute the integrals on the whole time domain. Moreover, for practical applications, we presented a technique known as “impulse-response-invariant discretization” to perform the discretization of the above three distributed-order filters. Lastly, it was shown that the distributed-order fractional filters had some unique features compared with the classical integer-order or constant-order fractional filters.KeywordsDefinite Integral FormDiscretization Impulse ResponseDistributed-order Differential EquationFractional-order FilterNumerical Discretization MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.