Time–frequency analysis with the q-Gaussian W transform

Time–frequency analysis methods are powerful for decoding signals with time-varying statistics and have applications in various scientific areas. By including the dominant frequency information in its convolution kernel, the W transform improves time–frequency resolution compared to the well-established Stockwell transform. However, the W transform is constructed from a Gaussian window function, which can limit its use for time series that are not concentrated in the harmonic domain. We generalize the W transform by introducing a finite-variance q-Gaussian distribution derived from the nonextensive statistical mechanics. The proposed q-Gaussian W transform has a free parameter $q$ to control the window function locality. We verify the time–frequency features of this new transform in two synthetic nonstationary signals and seismic field data as case points. We show that this non-Gaussian kernel with nonzero kurtosis improves the energy concentration of the time–frequency spectra.