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Sinusoidal Fitting Decomposition for Instantaneous Characteristic Representation of Multi-Componential Signal.

Donghu Nie1,2,3,4, Xin Su1,2,3, Gang Qiao1,2,3,4

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Summary

This study introduces Sinusoidal Fitting Decomposition (SFD), a novel method for extracting signal components. SFD effectively decomposes non-stationary signals into their Instantaneous Amplitude, Phase, and Frequency, ensuring positive amplitude and smooth phase.

Keywords:
instantaneous frequencyinstantaneous phasemulti-component signal decompositionnon-stationary signal processingtime-frequency analysis

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Area of Science:

  • Signal Processing
  • Non-stationary Signal Analysis
  • Time-Frequency Analysis

Background:

  • Extracting instantaneous characteristics from non-stationary signals is a significant challenge.
  • Existing methods often rely on dictionaries or basis functions, limiting their applicability.
  • Accurate decomposition is crucial for understanding complex signal behaviors.

Purpose of the Study:

  • To propose a new multi-component decomposition method called Sinusoidal Fitting Decomposition (SFD).
  • To extract Instantaneous Amplitude (IA), Instantaneous Phase (IP), and Instantaneous Frequency (IF) from signals.
  • To ensure extracted components possess desirable properties like positive IA and monotonic IP.

Main Methods:

  • Developed Sinusoidal Fitting Decomposition (SFD), a novel iterative synthesis process.
  • SFD decomposes signals into finite mono-component signals.
  • The method avoids reliance on dictionaries, basis function spaces, or sifting operations.

Main Results:

  • SFD ensures extracted IA is positive and IP is monotonically increasing.
  • The synthesized signal from IA and IP is mono-componential and smooth.
  • The method effectively describes instantaneous frequency-amplitude characteristics on the time-frequency plane.

Conclusions:

  • Sinusoidal Fitting Decomposition (SFD) is an effective method for non-stationary signal analysis.
  • The proposed method offers advantages over existing techniques by avoiding complex dependencies.
  • SFD provides accurate and reliable extraction of signal's instantaneous attributes.