A Method For Implementing Fractional Order Differentiator and Integrator Based on Digital Oscilloscope

Abstract

With the popularity of high-performance processors and mathematical modeling techniques, it is possible to use digital signal processing method to achieve fractional differential/integral operations. Currently, fractional operations are widely used in many fields such as system control, chaotic systems, and fault detection. In order to simplify the implementation of FPGA-based fractional operations, this paper proposes a method of implementing a digital oscilloscope based on FPGA and using logic resources to implement the fractional arithmetic defined by Grünwald-Letnikov(G-L). In addition, the number of calculation points for fractional operations is fixed and the sampling interval is variable. The simulation and hardware implementation results of fractional order operation of some conventional periodic signals with some selected fractional orders have been presented. The testbech results show that the use of four parallel calculations can increase the calculation speed by about 3.75 times. Sine wave is used to verify the calculation results of some fractional parameters. Experimental results show that high-precision floating-point calculation and large dynamic range measurement technology can improve the accuracy of fractional calculation. The phase accuracy of fractional arithmetic is improved by using waveform synchronization display technology of digital oscilloscope. Additionally, the consistency of simulation and experimental results proves the applicability of fractional order operation in digital oscilloscope.