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Analytical metrological characterization of the three-parameter sine fit algorithm.

M Martino1, R Losito, A Masi

  • 1Dipartimento di Ingegneria Elettrica, University of Naples Federico II, Via Claudio 21, Naples, 80125, Italy. michele.martino@cern.ch

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|November 4, 2011
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Summary

This study analyzes the three-parameter sine fit algorithm for analog-to-digital converter (ADC) characterization. It identifies optimal parameters for accurate sine wave estimation, improving amplitude and frequency response analysis.

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Area of Science:

  • Metrology
  • Signal Processing
  • Electrical Engineering

Background:

  • The three-parameter sine fit algorithm is crucial for ADC characterization per IEEE standard 1241-2000.
  • Accurate estimation of sine wave parameters from recorded data is essential for reliable ADC performance evaluation.

Purpose of the Study:

  • To perform an analytical metrological characterization of the three-parameter sine fit algorithm.
  • To identify optimal and sub-optimal design parameters, specifically sampling rate and number of samples.
  • To statistically characterize amplitude estimation, especially under additive white Gaussian noise.

Main Methods:

  • Analytical metrological characterization of the sine fit algorithm.
  • Derivation of statistical characterizations for amplitude estimation.
  • Exact probability density function determination for optimal parameters under specific noise conditions.
  • Analysis of frequency behavior and amplitude frequency response.

Main Results:

  • Optimal and sub-optimal parameter sets for the sine fit algorithm were identified.
  • An approximated second-order statistical characterization for amplitude estimation was derived for general noise conditions.
  • The exact probability density function and amplitude frequency response were determined for optimal parameters under additive white Gaussian noise.
  • An easier-to-use approximated expression for amplitude estimation was presented.

Conclusions:

  • The study provides a comprehensive analytical characterization of the three-parameter sine fit algorithm.
  • Optimal parameter selection significantly enhances the accuracy of amplitude and frequency response estimation in ADC characterization.
  • The derived statistical and frequency response analyses offer valuable tools for metrological applications involving sine wave parameter estimation.