A better way to define and describe Morlet wavelets for time-frequency analysis

Area of Science:

• Signal Processing
• Neuroscience
• Data Analysis

Background:

• Complex Morlet wavelets are essential for analyzing non-stationary time series, particularly neuroelectrical signals.
• The standard "number of cycles" parameter for Morlet wavelet width lacks clarity, leading to analysis uncertainty.
• This parameter critically influences the temporal-spectral precision trade-off.

Purpose of the Study:

• To present alternative formulations for Morlet wavelets in both time and frequency domains.
• To enable direct parameterization using desired temporal and spectral smoothing (Full-Width at Half-Maximum).
• To enhance clarity, facilitate proper analysis, and improve interpretation of time-frequency results.

Main Methods:

• Reformulating Morlet wavelets in time and frequency domains.
• Parameterizing wavelets using Full-Width at Half-Maximum for temporal and spectral smoothing.
• Providing MATLAB code and sample data for practical application.

Main Results:

• Introduced novel formulations for Morlet wavelets.
• Demonstrated direct control over temporal and spectral smoothing via FWHM.
• Offered a clearer, more interpretable method for wavelet parameter selection.

Conclusions:

• The proposed formulation enhances understanding and application of Morlet wavelets in time-frequency analysis.
• This approach aids researchers in making more informed choices for signal analysis, reporting, and interpretation.
• Facilitates more rigorous and reproducible analysis of complex time series data, including brain signals.