Within the auditory neural pathway there are more neural project downwards from auditory cortex to various regions of the sub-cortex. These downward connections suggest a high level of top-down influence of processing incoming sounds at the sub-cortical level. This may be the reason the frequency following response (FFR), an oscillatory EEG and MEG response that oscillates at the same frequency within the sounds and generated by the inferior colliculus, can be enhanced, or attenuated depending on attentional states. Activity from auditory cortex can be measure via the 40 Hz auditory steady state response (ASSR), which is an oscillatory EEG and MEG component elicited by amplitude modulations to a sound around 40 Hz.  This poses a problem as we need to measure directed connectivity with cross-frequency coupled signals, however many measures of direct connectivity were not developed with this in mind. The goal of this research was then to simulate realistic EEG containing the FFR and 40 Hz ASSR and compare three measures of directed connectivity: symbolic transfer entropy (STE), phase transfer entropy (PTE) and granger causality (GC). We simulated the data such that the phase of the ~40Hz ASSR influenced the amplitude of the FFR as a 100 ms delay, creating uni-directional phase-amplitude coupling. We compared how well these measures could differentiate the source signal (the ~40Hz ASSR) and which was the target (FFR). Additionally, we evaluated how well each measure accurately detected the transmission delay. Overall, no measure could detect the transmission delay, but both STE and PTE distinguished the source from the target signal. GC could not distinguish the source from the target, at least for delay less than 50 ms. Interestingly, STE and PTE are both non-linear measure of directed connectivity and seemed to outperform GC, a linear measure. This suggest that non-linear method may be better at estimating directed connectivity at least when signals are cross-frequency coupled. Further research is needed to determine how these measures behave under different forms of coupling (e.g., amplitude -amplitude coupling or high to low frequency coupling), and compared using