  We consider the problem of estimating mutual information between dependent
data, an important problem in many science and engineering applications. We
propose a data-driven, non-parametric estimator of mutual information in this
paper. The main novelty of our solution lies in transforming the data to
frequency domain to make the problem tractable. We define a novel
metric--mutual information in frequency--to detect and quantify the dependence
between two random processes across frequency using Cram\'{e}r's spectral
representation. Our solution calculates mutual information as a function of
frequency to estimate the mutual information between the dependent data over
time. We validate its performance on linear and nonlinear models. In addition,
mutual information in frequency estimated as a part of our solution can also be
used to infer cross-frequency coupling in the data.
