Independent component analysis for one observation of a Signal
You have single channel / observation along x. Splitting it along x would not make it multiple channels. I think you should not split it. You should rather approach it as underdetermined ICA problem, i.e., the number of sources are more than the number of observations. 
For the point, theoretically, all the sources should be transformed via a system. So the observations, generated using different mixing matrices cannot be utilized jointly in a single ICA process.