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首页> 外文会议>Polish Control Conference >Fast Evaluation of Grünwald-Letnikov Variable Fractional-Order Differentiation and Integration Based on the FFT Convolution
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Fast Evaluation of Grünwald-Letnikov Variable Fractional-Order Differentiation and Integration Based on the FFT Convolution

机译：基于FFT卷积的Grünwald-letnikov可变分数和集成快速评估

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The main topic of this research is the development of a new efficient method for solving fractional differential equations in the time domain using the Grünwald-Letnikov (GL) definition of the differintegral operator. The goal is to reduce or, in some cases, eliminate the necessity of introducing the maximum number of samples of the approximation, which is always a trade-off between accuracy, memory consumption, and computational speed. The algorithm involving Fast Fourier Transform and Fast Convolution operations has been proposed. The implementation in two different environments - the MATLAB/Simulink on a PC and on a hardware platform with the STM32H743 microcontroller - is described in this paper and the results of two iterations of experiments are presented. Fast Convolution algorithm is proven to be highly effective for processing block lengths N > 128. In the most complex analyzed case (N = 8192 samples) on the Intel? Core? i5-8250U CPU reduction of the computation time reached 85%, compared to the implementation of the classic definition characterized by the O(N~2) complexity.
机译：该研究的主要课题是使用不同凝集算子的Grünwald-letnikov（GL）定义来开发用于求解时域中的分数微分方程的新技术方法。目标是减少或在某些情况下，消除介绍近似值的最大样本数的必要性，这始终是精度，内存消耗和计算速度之间的权衡。提出了涉及快速傅立叶变换和快速卷积操作的算法。在两个不同的环境中实现 - PC上的MATLAB / Simulink和STM32H743微控制器上的硬件平台 - 在本文中描述，并提出了两次实验迭代的结果。经过证明快速卷积算法对于加工块长度N> 128非常有效。在英特尔上最复杂的分析案例（n = 8192个样本）中？核？ I5-8250U CPU计算时间的计算时间达到85％，而经典定义的实现相比，其特征在于O（n〜2）复杂性。

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