Analysis of time-varying signals using continuous wavelet and synchrosqueezed transforms

Area of Science:

• Signal Processing
• Geophysics
• Astrophysics

Background:

• The continuous wavelet transform (CWT) is vital for time-frequency analysis but suffers from spectral smearing and leakage.
• Interpreting CWT results is challenging due to the imprecise localization of frequency components.

Purpose of the Study:

• To introduce and evaluate the synchrosqueezing transform as a method to overcome CWT limitations.
• To demonstrate the improved time-frequency analysis capabilities of synchrosqueezing using diverse real-world signals.

Main Methods:

• The study compares the continuous wavelet transform (CWT) with the synchrosqueezing transform.
• Frequency reassignment techniques, including synchrosqueezing and ConceFT, are employed to enhance spectral localization.
• Performance is assessed using four distinct time-varying signals: LIGO gravitational waves, a 'FanQuake' vibration, a major earthquake (Chiapas), and volcanic seismic data (Popocatépetl).

Main Results:

• Synchrosqueezing significantly reduces smearing and leakage artifacts present in standard CWT.
• High-localization techniques provide clearer and more accurate time-frequency representations of complex signals.
• The effectiveness of synchrosqueezing is validated across signals from astrophysics, seismology, and volcanology.

Conclusions:

• The synchrosqueezing transform offers a substantial improvement over traditional CWT for analyzing time-varying signals.
• Enhanced time-frequency resolution achieved through synchrosqueezing facilitates more precise interpretation of complex phenomena.
• This technique holds broad applicability in scientific and engineering fields requiring detailed signal analysis.