Using an Optimization Algorithm to Detect Hidden Waveforms of Signals.

Area of Science:

• Signal processing
• Optimization algorithms
• Waveform analysis

Background:

• Source signals contain hidden waveforms crucial for information extraction.
• Discrete Fourier Transform (DFT) and Empirical Mode Decomposition (EMD) are common signal decomposition tools.
• Both DFT and EMD have limitations in frequency resolution and noise susceptibility.

Purpose of the Study:

• To develop a novel signal decomposition technique with enhanced accuracy and resolution.
• To address the limitations of existing methods like DFT and EMD.
• To accurately detect and capture hidden waveforms in complex signals.

Main Methods:

• Utilized the optimization algorithm, Differential Evolution (DE), for signal decomposition, termed Signal Decomposition by DE (SDDE).
• SDDE offers infinite frequency resolution, enabling precise decomposition of source signals.
• Applied SDDE to source signals composed of periodic waves, with and without white noise.

Main Results:

• SDDE accurately or almost accurately determined separate components of periodic waves without noise.
• SDDE successfully identified main components even in the presence of white noise.
• Compared to DFT and EMD, SDDE demonstrated superior performance, avoiding spurious components and decomposition issues.

Conclusions:

• SDDE is a pioneering approach directly applying optimization algorithms to signal decomposition.
• The method exhibits superior accuracy and robustness against noise compared to DFT and EMD.
• SDDE holds significant potential for widespread application in exploring signals for valuable information.