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A delayed-feedback filter with negative group delay.

Henning U Voss1

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Summary
This summary is machine-generated.

This study introduces a novel filter utilizing negative group delay for real-time signal prediction. This universal filter accurately forecasts band-limited signals without needing a specific signal model.

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Area of Science:

  • Physics
  • Signal Processing
  • Control Theory

Background:

  • Real-time signal prediction is crucial for various applications.
  • Existing methods often require specific signal models, limiting their universality.
  • Negative group delay phenomena offer potential for advanced signal manipulation.

Purpose of the Study:

  • To present a novel filter design that achieves negative group delay.
  • To demonstrate the filter's capability for real-time prediction of band-limited signals.
  • To analytically derive and numerically verify the filter's properties and performance.

Main Methods:

  • Designing a filter with multiple time-delayed feedback terms.
  • Inducing negative group delay for baseband frequencies.
  • Analytical derivation of filter properties, including stability.
  • Numerical simulations to validate theoretical findings.

Main Results:

  • The proposed filter exhibits delay-induced negative group delay.
  • The filter enables universal, real-time prediction of band-limited signals.
  • Prediction horizon is dependent on the signal's cutoff frequency.
  • Filter stability is analytically confirmed and numerically demonstrated.
  • Effective prediction is achieved in chaotic systems during predictable phases.

Conclusions:

  • The developed filter offers a universal approach to real-time signal prediction using negative group delay.
  • The filter's performance is robust for band-limited signals, independent of specific signal models.
  • This work provides a theoretical and practical foundation for utilizing negative group delay in predictive signal processing.