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Optimal wideband digital fractional-order differentiators using gradient based optimizer.

Mohammed Ali Mohammed Moqbel1,2, Talal Ahmed Ali Ali1,2, Zhu Xiao1,2

  • 1College of Computer Science and Electronic Engineering, Hunan University, Changsha, China.

Peerj. Computer Science
|December 16, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for designing wideband digital fractional order differentiators (DFODs) that significantly improves low-frequency accuracy. The approach optimizes error distribution, achieving better performance for low-frequency applications.

Keywords:
Digital fractional order differentiatorGradient based optimizerInfinite impulse response

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Area of Science:

  • Signal Processing
  • Control Systems Engineering

Background:

  • Fractional order calculus extends traditional calculus concepts to non-integer orders.
  • Digital fractional order differentiators (DFODs) are crucial for systems requiring frequency-dependent differentiation.

Purpose of the Study:

  • To propose a novel optimization approach for designing wideband infinite impulse response (IIR) digital fractional order differentiators (DFODs).
  • To enhance accuracy specifically in low frequency bands for these DFODs.

Main Methods:

  • Formulating the design as an optimization problem with two tuning parameters to control frequency error distribution.
  • Employing a gradient-based optimizer (GBO) on the proposed objective function.

Main Results:

  • Achieved a favorable low frequency performance with approximately 60% relative magnitude error reduction.
  • Maintained comparable accuracy across the Nyquist band compared to existing methods.
  • Demonstrated effectiveness through a wide range of design examples.

Conclusions:

  • The proposed optimization approach effectively designs wideband IIR DFODs with superior low-frequency accuracy.
  • The method offers an attractive solution for applications demanding precise low-frequency signal processing.