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Numerical stability of spline-based Gabor-like systems.

Darian M Onchis1, Simone Zappalà2, Pedro Real3

  • 1West University of Timisoara, Timisoara, Romania, University of Vienna, Vienna, Austria.

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Summary
This summary is machine-generated.

This study presents a theorem for numerical stability in spline-type systems, essential for signal processing. We analyze Gabor systems and their stability under deformations.

Keywords:
Gabor systemsnumerical stabilityspline-type spaces

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Area of Science:

  • Numerical analysis
  • Signal processing
  • Harmonic analysis

Background:

  • Spline-type systems are constructed from shifted atoms over a time lattice.
  • Gabor systems are a well-established tool in signal processing.
  • Understanding numerical stability is crucial for reliable system performance.

Purpose of the Study:

  • To provide a theorem for characterizing the numerical stability of spline-type systems.
  • To reformulate Gabor systems using modulated spline-type systems.
  • To apply and test the numerical stability of these reformulated systems against deformations.

Main Methods:

  • Development of a theorem for numerical stability characterization.
  • Reformulation of Gabor systems into modulated spline-type systems.
  • Testing numerical stability against various deformations.

Main Results:

  • A theorem is established for the numerical stability of spline-type systems.
  • Gabor systems are successfully reformulated as modulated spline-type systems.
  • The numerical stability of these systems is demonstrated to be consistent under deformations.

Conclusions:

  • The proposed theorem offers a method for analyzing spline-type system stability.
  • The reformulation provides new insights into Gabor system properties.
  • The findings are relevant for applications requiring robust signal processing techniques.