This paper, with the use of Fourier transform and the filtering theory of linear timeinvariant system, reaches a conclusion that there are high-pass filter characteristicsin derivative and low-pass filter characteristics in integration after analysising fromthe view point of filtering. On the basis above, the author explores the numericalalgorithm of calculus-FFT algorithms and its adaptable condition by combining thesampling theorem of time with frequency domain, which is popularized to the numericalcomputation (NC) of non-integral-order calculus. The analysis and results of NC showthat the algorithm is convenient, fast, and applicable for the NC of low-order calculus,and specially suited to the engineering computation. It will aid in the NC, practicalutilization and error analysis of non-integer-order calculus.
