FPGA realization of Caputo and Grünwald-Letnikov operators

Mohammed F. Tolba, Amr M. Abdelaty, Lobna A. Said, Ahmed S. Elwakil, Ahmad Taher Azar, Ahmed H. Madian, Adel Ounnas, Ahmed G. Radwan

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    39 Scopus citations

    Abstract

    This paper proposes a hardware platform implementation on FPGA for two fractional-order derivative operators. The Grünwald-Letnikov and Caputo definitions are realized for different fractional orders. The realization is based on non-uniform segmentation algorithm with a variable lookup table. A generic implementation for Grünwald-Letnikov is proposed and a 32 bit Fixed Point Booth multiplier radix-4 is used for Caputo implementation. Carry look-ahead adder, multi-operand adder and booth multiplier are used to improve the performance and other techniques for area and delay minimization have been employed. A comparison between the two presented architectures is introduced. The proposed designs have been simulated using Xilinx ISE and realized on FPGA Xilinx virtex-5 XC5VLX50T. The total area of 2515 look up tables is achieved for Caputo implementation, and maximum frequency of 54.11 MHz and 1498 slices are achieved for Grünwald-Letnikov architecture.

    Original languageBritish English
    Title of host publication2017 6th International Conference on Modern Circuits and Systems Technologies, MOCAST 2017
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    ISBN (Electronic)9781509043866
    DOIs
    StatePublished - 31 May 2017
    Event6th International Conference on Modern Circuits and Systems Technologies, MOCAST 2017 - Thessaloniki, Greece
    Duration: 4 May 20176 May 2017

    Publication series

    Name2017 6th International Conference on Modern Circuits and Systems Technologies, MOCAST 2017

    Conference

    Conference6th International Conference on Modern Circuits and Systems Technologies, MOCAST 2017
    Country/TerritoryGreece
    CityThessaloniki
    Period4/05/176/05/17

    Keywords

    • Caputo
    • FPGA
    • Fractional calculus
    • Grünwald-Letnikov
    • LUT
    • Non-uniform segmentation

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