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Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

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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...
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Michael-David Johnson1, Jacques Cuenca2, Timo Lähivaara3

  • 1Department of Mechanical Engineering, The University of Sheffield, Sheffield, United Kingdom.

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This study introduces a Bayesian framework to quantify uncertainty in reconstructing rough surface geometry from scattered sound. The physics-informed method provides confidence intervals for improved surface property inference.

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Area of Science:

  • Acoustics
  • Materials Science
  • Statistical Physics

Background:

  • Reconstructing rough surface geometry from scattered waves is crucial for applications in medicine, water engineering, and structural health monitoring.
  • Current methods for surface profile reconstruction lack inherent uncertainty prediction.
  • Quantifying reconstruction uncertainty is essential for reliable application of these techniques.

Purpose of the Study:

  • To develop a physics-informed Bayesian framework for inferring rough surface properties and their uncertainties.
  • To incorporate the validity region of the Kirchhoff approximation into the Bayesian formulation.
  • To assess the effectiveness of the proposed method using experimental data.

Main Methods:

  • Utilized a Bayesian framework with an adaptive Metropolis scheme to infer surface properties.
  • Employed the Kirchhoff approximation, constrained by surface smoothness assumptions, as the wave scattering model.
  • Incorporated the validity region of the scattering model into the Bayesian inference process.
  • Validated the approach on experimental data from sinusoidal and random roughness profiles.

Main Results:

  • The Bayesian approach successfully recovered surface properties and provided confidence intervals, quantifying reconstruction uncertainty.
  • The physics-informed method demonstrated improved performance by integrating model validity constraints.
  • Experimental validation confirmed the ability of the method to identify uncertainty in surface reconstruction.

Conclusions:

  • The developed Bayesian framework effectively quantifies uncertainty in rough surface reconstruction from scattered sound.
  • This physics-informed approach offers a reliable method for estimating confidence intervals in surface property inference.
  • The technique has potential applications in various fields requiring accurate surface characterization and uncertainty assessment.