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Related Experiment Videos

Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations.

D V Chudnovsky1, G V Chudnovsky

  • 1Institute for Mathematics and Advanced Supercomputing, Polytechnic University, Brooklyn, NY 11201, USA.

Proceedings of the National Academy of Sciences of the United States of America
|October 27, 1999
PubMed
Summary

This study solves the pulse width modulation (PWM) problem by accurately representing harmonic waveforms using digital pulses. The solution involves advanced mathematical techniques to eliminate high-order harmonics for precise sine-wave reproduction.

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Area of Science:

  • Electrical Engineering
  • Applied Mathematics
  • Signal Processing

Background:

  • Pulse Width Modulation (PWM) aims to represent harmonic waveforms using fixed-height square pulses.
  • Approximation accuracy is crucial, requiring elimination of high-order harmonics in the error term.
  • Reproducing sine-waves accurately with a limited number of pulses is a key challenge.

Purpose of the Study:

  • To provide a complete mathematical solution to the general Pulse Width Modulation problem.
  • To characterize discrete pulses for accurate harmonic waveform approximation.
  • To leverage advanced mathematical concepts for improved PWM signal generation.

Main Methods:

  • Utilizing Pade approximations for function approximation.
  • Employing orthogonal polynomials in the analysis.

Related Experiment Videos

  • Applying soliton theory and solutions to Korteweg-de Vries equations.
  • Characterizing discrete pulse solutions within the framework of rational solutions to KdV equations.

    • Main Results:

    • A comprehensive solution to the PWM problem is presented.
    • Discrete pulse characteristics are defined for accurate analog signal approximation.
    • The solution connects PWM to the theory of rational solutions of Korteweg-de Vries equations.

    Conclusions:

    • The study offers a novel mathematical framework for solving the PWM problem.
    • The findings enable more accurate reproduction of harmonic waveforms using digital pulses.
    • This research bridges advanced mathematical concepts with practical signal processing applications.