Sinusoidal time-frequency wavelet family and its application in electrogastrographic signal analysis

This paper introduces a sinusoidal time-frequency wavelet family, with both real sine and complex exponential oscillating patterns, of various window functions. It provides a regular time-frequency analysis rather than a time-scale analysis for wavelet transform time-frequency localization of both stationary and non-stationary signals. It offers a convenient trade-off between time resolution at low frequency and frequency resolution at high frequency for any given time-frequency analysis application. Four different window functions are studied for the sinusoidal time-frequency wavelet family and it has been shown that both the real sine wavelets and the complex exponential wavelets using these four windows satisfy the wavelet admissibility condition. The time-frequency resolution of the corresponding wavelet time-frequency localization analysis has also been investigated. It has been show that the rising-cosine window sinusoidal wavelet provides close to optimal time-frequency resolution. It has also been shown that the modulated Gaussian wavelet becomes a special case of the Gaussian window complex exponential wavelet. We briefly describe our sinusoidal wavelet family and apply it to the time-frequency analysis of electrogastrographic (EGG) signals to simultaneously localize high frequency spike activities and track low frequency slow waves