  We define a metric, mutual information in frequency (MI-in-frequency), to
detect and quantify the statistical dependence between different frequency
components in the data, referred to as cross-frequency coupling and apply it to
electrophysiological recordings from the brain to infer cross-frequency
coupling. The current metrics used to quantify the cross-frequency coupling in
neuroscience cannot detect if two frequency components in non-Gaussian brain
recordings are statistically independent or not. Our MI-in-frequency metric,
based on Shannon's mutual information between the Cramer's representation of
stochastic processes, overcomes this shortcoming and can detect statistical
dependence in frequency between non-Gaussian signals. We then describe two
data-driven estimators of MI-in-frequency: one based on kernel density
estimation and the other based on the nearest neighbor algorithm and validate
their performance on simulated data. We then use MI-in-frequency to estimate
mutual information between two data streams that are dependent across time,
without making any parametric model assumptions. Finally, we use the MI-in-
frequency metric to investigate the cross-frequency coupling in seizure onset
zone from electrocorticographic recordings during seizures. The inferred
cross-frequency coupling characteristics are essential to optimize the spatial
and spectral parameters of electrical stimulation based treatments of epilepsy.
