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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
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Memorization-Based Training and Testing Paradigm for Robust Vocal Identity Recognition in Expressive Speech Using Event-Related Potentials Analysis
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Set theoretic signal restoration using an error in variables criterion.

G Sharma1, H J Trussell

  • 1Digital Imaging Technol. Center, Xerox Corp., Webster, NY.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 1, 1997
PubMed
Summary

This study introduces new set theoretic estimation methods for signal restoration, enhancing accuracy by incorporating prior information. The novel approach improves upon existing techniques for signals degraded by stochastic impulse responses.

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Area of Science:

  • Signal Processing
  • Estimation Theory
  • Inverse Problems

Background:

  • Signal degradation by stochastic impulse responses presents challenges in accurate restoration.
  • Existing methods like total least squares (TLS) are effective but cannot integrate a priori information.
  • Set theoretic estimation schemes offer flexibility but require specific set formulations.

Purpose of the Study:

  • To develop novel set theoretic estimation techniques for signal restoration problems with uncertainties.
  • To introduce new sets inspired by total least squares (TLS) that allow incorporation of prior information.
  • To establish the mathematical properties (convexity) and projection operators for these new sets.

Main Methods:

  • Formulation of signal restoration as an uncertain problem involving measurements and impulse response.
  • Development of two new convex sets motivated by total least squares principles.
  • Derivation of projection operators onto these newly defined convex sets.

Main Results:

  • The established convexity and projection operators enable practical application of the new sets.
  • Simulations demonstrate the superior performance of the proposed method compared to conventional techniques.
  • The new method effectively incorporates a priori information, leading to improved restoration accuracy.

Conclusions:

  • The introduced set theoretic estimation approach offers significant advantages for signal restoration.
  • This method provides a robust framework for handling uncertainties and prior knowledge in degraded signals.
  • The novel sets and operators enhance the capabilities of set theoretic estimation in signal processing.