A Modified Complex Variational Mode Decomposition Method for Analyzing Nonstationary Signals with the Low-Frequency...

Area of Science:

• Signal Processing
• Data Analysis
• Applied Mathematics

Background:

• Complex variational mode decomposition (CVMD) extends variational mode decomposition (VMD) for complex-valued data analysis.
• Conventional CVMD faces challenges with low-frequency trends and requires difficult-to-obtain prior knowledge of decomposition numbers.
• Existing methods struggle to accurately decompose complex signals, especially those with low-frequency components.

Purpose of the Study:

• To propose a modified complex variational mode decomposition (MCVMD) method for enhanced complex-valued signal analysis.
• To address the limitations of conventional CVMD, particularly its difficulties with low-frequency trends and prior parameter requirements.
• To provide a more robust and practical approach for decomposing complex signals.

Main Methods:

• Upsampling complex-valued data in the frequency domain via zero padding.
• Shifting negative frequency components to positive frequencies for analytical signal properties.
• Applying standard VMD to real-valued data derived from analytical signals and frequency shifting back for complex decomposition.

Main Results:

• MCVMD demonstrates superior decomposition of low-frequency signals compared to conventional CVMD.
• The proposed MCVMD method requires less prior knowledge regarding the number of decomposition components.
• Effectiveness verified through analysis of synthetic and real-world complex-valued signals, including time-frequency representation via MCVMD bi-directional Hilbert spectrum.

Conclusions:

• MCVMD offers a significant improvement over conventional CVMD for complex-valued signal decomposition.
• The method effectively handles low-frequency trends and reduces reliance on prior decomposition number knowledge.
• MCVMD provides a more practical and accurate tool for analyzing complex signals in various applications.