Morlet wavelet transform

The complex Morlet wavelet is a complex sinusoid multiplied by a Gaussian envelope; convolving the signal with scaled copies of it yields a continuous time-frequency representation whose window automatically narrows in time at high frequency and widens at low frequency. This constant-Q behaviour (a fixed ratio of centre frequency to bandwidth) matches the roughly logarithmic organization of neural rhythms better than the STFT's fixed window.

Because the wavelet is complex, the transform yields both amplitude and phase at each time and frequency, making it a natural tool for tracking instantaneous power (for ERD/ERS) and for phase-based measures. The single design parameter is the number of cycles in the wavelet, which sets the time-frequency tradeoff: few cycles favour temporal precision (good for transients), while many cycles favour frequency precision (good for narrowband rhythms).