This is a question for you electrical network engineers. The problem has arisen in a neuroscience study I am working on, but I hope to be able to glean some insight from other domains that deal with electrical systems and control networks. The brain is an electrical system after all, so I figure it should be governed by similar processes to large-scale electrical closed loops systems (like power grids for example).
I have devised a transfer function, which I am using to investigate human brain networks. We have recorded electrical signals from region A in the brain and mapped them, via this transfer function, to region B.
The transfer function works as follows.
- Take a recorded time series x which describes the time evolution of some brain process.
- Apply Fourier transform to get X
- Apply a constant phase shift to all components of X to give Y, taking care of the symmetry in the frequency domain (e.g. this could be a 90 deg phase shift).
- Apply the inverse Fourier transform to Y to retrieve the time-shifted signal y
The upshot of this is that lower frequencies are shifted in time MORE than higher frequencies. This appears to fit our brain data very well - which is something of a mystery. We don't actually understand why this works so well, so finding analogous systems in engineering would be a great help.
Therefore, my question is whether any of you can identify the type of transfer function we are using here. Does it have a proper name in engineering, is there a theoretical basis for it? The best I have come up with is that it is a minimum phase transfer function, but I don't yet understand how that might apply to a close loop system.
Even if someone could point me to the relevant textbook, that would also be very helpful.