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Wavelets, adapted waveforms and de-noising

R R Coifman1, M V Wickerhauser

  • 1Department of Mathematics, Yale University, New Haven, CT 06520, USA.

Electroencephalography and Clinical Neurophysiology. Supplement
|January 1, 1996
PubMed
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New waveform libraries, including wavelet packets, offer efficient signal processing. These tools enhance understanding and computation for complex transient signals like speech and hydrophone recordings.

Area of Science:

  • Signal Processing
  • Numerical Analysis
  • Waveform Analysis

Background:

  • Traditional signal analysis methods face challenges with complex transient signals.
  • Efficient computation and structural understanding are crucial for advanced signal processing tasks.

Purpose of the Study:

  • Introduce novel waveform libraries for improved signal analysis.
  • Demonstrate the application of these libraries in feature extraction, data compression, and noise removal.

Main Methods:

  • Utilizing "wavelet packet" and "localized trigonometric" waveform libraries.
  • Developing algorithms for best-adapted time and frequency decompositions.
  • Applying adapted waveform analysis for noise reduction in hydrophone recordings.

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Main Results:

  • Waveform libraries provide efficient computation and structural understanding.
  • Feature extraction and data compression algorithms for speech signals were developed.
  • An algorithm effectively removed fish noises from hydrophone recordings.

Conclusions:

  • Well-localized waveform libraries significantly enhance signal processing efficiency and analytical capabilities.
  • These methods offer a powerful approach for analyzing complex transient signals, with potential applications in electroencephalography (EEG).