Hilbert Transform Design Based on Fractional Derivatives and Swarm Optimization.

Area of Science:

• Signal Processing
• Filter Design
• Numerical Optimization

Background:

• Implementing the Hilbert transform efficiently is crucial for various signal processing applications.
• Traditional methods can suffer from inaccuracies and computational complexity.
• Optimizing filter design requires advanced techniques to minimize errors.

Purpose of the Study:

• To develop a novel and efficient method for Hilbert transform implementation.
• To leverage fractional derivatives (FDs) and swarm optimization for enhanced filter design.
• To minimize the squared error between desired and designed filter responses.

Main Methods:

• Utilizing fractional derivatives (FDs) to improve accuracy at a reference frequency (ω₀).
• Employing swarm intelligence, specifically constraint-factor particle swarm optimization, to find optimal FD and ω₀ values.
• Minimizing the squared error difference between desired and designed filter responses.

Main Results:

• The proposed FD-based method significantly reduces total phase error by 57%.
• The method achieves higher accuracy at the reference frequency, minimizing overall phase error.
• Evaluated fidelity aspects include maximum phase error, total squared phase error, and group delay errors.

Conclusions:

• Fractional derivatives combined with swarm optimization offer an efficient Hilbert transform implementation.
• The novel approach demonstrably reduces phase error compared to existing methods.
• The technique provides a robust solution for accurate filter design in signal processing.