Joint frequency spectral lag representation for cross-frequency modulation analysis in the brain

The concepts of modulation frequency along with modulation spectra are originally encountered in acoustics, speech and audio processing. The modulation spectrum, a function of acoustic frequency and modulation frequency, has been proposed and widely used in the speech processing community. However, modulation spectrum, much like time-frequency distribution is a representation of an individual signal and does not quantify the modulation effects between two signals. In this paper, we introduce cross frequency-spectral lag representation based on the Wigner distribution to represent the modulation relationships between two signals. The performance of the proposed distribution is illustrated for simulated signals as well as for electroencephalogram (EEG) signals.