https://scholars.lib.ntu.edu.tw/handle/123456789/155237
標題: | Computation of fractional derivatives using Fourier transform and digital FIR differentiator | 作者: | Tseng, Chien-Cheng SOO-CHANG PEI Hsia, Shih-Chang |
公開日期: | 2000 | 卷: | 80 | 期: | 1 | 起(迄)頁: | 151-159 | 來源出版物: | Signal Processing | 摘要: | In this paper, the computation of a fractional derivative using the Fourier transform and a digital FIR differentiator is investigated. First, the Cauchy integral formula is generalized to define the fractional derivative of functions. Then the fractional differentiation property of the Fourier transform of functions is presented. Using this property, the fractional derivative of a function can be computed in the frequency domain. Next, we develop a least-squares method to design the fractional order digital differentiator. When a signal passes through the designed differentiator, the output will be its fractional derivative. One design example is included to illustrate the effectiveness of this approach. Finally, the designed fractional order differentiator is used to generate a random fractal process which is better than the process obtained by the conventional method. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/142460 | ISSN: | 01651684 | DOI: | 10.1016/S0165-1684(99)00118-8 | SDG/關鍵字: | Differentiating circuits; FIR filters; Fourier transforms; Fractional derivatives; Digital signal processing |
顯示於: | 電機工程學系 |
在 IR 系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。