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A sequency match filtering algorithm based on the generalized Walsh transform for processing rectangular wave

Bin Li1, Sheng-Nan Zhang1, Jie Chen1

  • 1School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, People's Republic of China.

The Review of Scientific Instruments
|February 26, 2024
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Summary
This summary is machine-generated.

This study introduces a generalized Walsh transform for multi-valued rectangular wave signals, improving signal frequency matching and sequency spectrum analysis beyond traditional Walsh functions.

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Area of Science:

  • Signal Processing
  • Applied Mathematics

Background:

  • Conventional Walsh functions are limited to binary values (+1, -1), restricting their ability to analyze complex signals.
  • Walsh functions possess characteristics suitable for capturing the frequency of square wave signals.

Purpose of the Study:

  • To propose a generalized Walsh transform algorithm for processing multi-valued rectangular wave signals.
  • To extend the capabilities of traditional Walsh functions for enhanced signal analysis.

Main Methods:

  • Inferred invariance displacement theory in time and sequency domains to concentrate signal sequency energy.
  • Constructed two types of generalized Walsh functions by combining characteristics of periodic rectangular waves.
  • Deduced orthogonality and completeness properties to validate frequency matching and energy extraction.

Main Results:

  • Generalized Walsh functions demonstrate superior signal frequency matching capabilities.
  • The proposed method effectively extracts sequency spectrum amplitude for valuable signal representation.
  • Demonstrated reliability through comparison with multiple filtering methods.

Conclusions:

  • The generalized Walsh transform algorithm offers a robust method for analyzing multi-valued rectangular wave signals.
  • The developed generalized Walsh functions provide enhanced performance in signal frequency matching and energy extraction.
  • This approach advances signal processing techniques for complex waveform analysis.